text: The left-hand circle in Figure 2 is the orbit showing the velocity vectors at two adjacent times. On the right, these two velocities are moved so their tails coincide. Because speed is constant, the velocity vectors on the right sweep out a circle as time advances.  For a swept angle dθ = ω dt the change in v is a vector at right angles to v and of magnitude v dθ, which in turn means that the magnitude of the acceleration is given by

text: The image at right shows the vector relationships for uniform circular motion. The rotation itself is represented by the angular velocity vector Ω, which is normal to the plane of the orbit (using the right-hand rule) and has magnitude given by:

text: The image at right shows the vector relationships for uniform circular motion. The rotation itself is represented by the angular velocity vector Ω, which is normal to the plane of the orbit (using the

entity_name: Right-hand rule

text: right-hand rule

text: ) and has magnitude given by:

text: The velocity resolution is the minimum radial velocity difference between two objects traveling at the same range before the radar can detect two discrete reflections.

text: For over a century, the conventional rail network has been centralized on the regional capital, Seville, and the national capital, Madrid; in general, there are no direct connections between provincial capitals. High-speed AVE trains run from Madrid via Córdoba to Seville and Málaga. Further AVE routes are under construction. The Madrid-Córdoba-Seville route was the first high-velocity route in Spain (operating since 1992). Other principal routes are the one from Algeciras to Seville and from Almería via Granada to Madrid.

text: For over a century, the conventional rail network has been centralized on the regional capital, Seville, and the national capital, Madrid; in general, there are no direct connections between provincial capitals. High-speed

entity_name: AVE

text: AVE

text: trains run from Madrid via Córdoba to Seville and Málaga. Further AVE routes are under construction. The Madrid-Córdoba-Seville route was the first high-velocity route in Spain (operating since 1992). Other principal routes are the one from Algeciras to Seville and from

entity_name: Almería

text: Almería

text: via Granada to Madrid.

method: ICT-DRMMTKS

text: In physics, uniform circular motion describes the motion of a body traversing a circular path at constant speed. Since the body describes circular motion, its distance from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant: velocity, a vector quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, produced by a centripetal force which is also constant in magnitude and directed towards the axis of rotation.

text: In

entity_name: Physics

text: physics

text: , uniform circular motion describes the motion of a body traversing a

entity_name: Circle

text: circular

text: path at constant

entity_name: Speed

text: speed

text: . Since the body describes circular motion, its

entity_name: Distance

text: distance

text: from the axis of rotation remains constant at all times. Though the body's speed is constant, its

entity_name: Velocity

text: velocity

text: is not constant: velocity, a

entity_name: Euclidean vector

text: vector

text: quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this

entity_name: Acceleration

entity_section: Tangential and centripetal acceleration

text: centripetal acceleration

text: is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, produced by a

entity_name: Centripetal force

text: centripetal force

text: which is also constant in magnitude and directed towards the axis of rotation.

text: and their velocity vectors

text: and their velocity vectors

text: The plane-wave equation works for arbitrary combinations of ω and k, but any real physical medium will only allow such waves to propagate for those combinations of ω and k that satisfy the dispersion relation of the medium.  The dispersion relation is often expressed as a function, ω(k).  The ratio ω/|k| gives the magnitude of the phase velocity and dω/dk gives the group velocity.  For electromagnetism in an isotropic medium with index of refraction n, the phase velocity is c/n, which equals the group velocity if the index is not frequency-dependent.

text: The plane-wave equation works for arbitrary combinations of ω and k, but any real physical medium will only allow such waves to propagate for those combinations of ω and k that satisfy the

entity_name: Dispersion relation

text: dispersion relation

text: of the medium.  The dispersion relation is often expressed as a function, ω(k).  The ratio ω/|k| gives the magnitude of the

entity_name: Phase velocity

text: phase velocity

text: and dω/dk gives the

entity_name: Group velocity

text: group velocity

text: .  For electromagnetism in an isotropic medium with index of refraction n, the phase velocity is c/n, which equals the group velocity if the index is not frequency-dependent.

method: UNH-ecn

text: In 1929, Edwin Hubble provided a comprehensive observational foundation for Lemaître's theory. Hubble's experimental observations discovered that, relative to the Earth and all other observed bodies, galaxies are receding in every direction at velocities (calculated from their observed red-shifts) directly proportional to their distance from the Earth and each other. In 1929, Hubble and Milton Humason formulated the empirical Redshift Distance Law of galaxies, nowadays known as Hubble's law, which, once the redshift is interpreted as a measure of recession speed, is consistent with the solutions of Einstein's General Relativity Equations for a homogeneous, isotropic expanding space.  The isotropic nature of the expansion was direct proof that it was the space (the fabric of existence) itself that was expanding, not the bodies in space that were simply moving further outward and apart into an infinitely larger preexisting empty void. It was this interpretation that led to the concept of the expanding universe. The law states that the greater the distance between any two galaxies, the greater their relative speed of separation. This discovery later resulted in the formulation of the Big Bang model.

text: In 1929,

entity_name: Edwin Hubble

text: Edwin Hubble

text: provided a comprehensive observational foundation for Lemaître's theory. Hubble's experimental observations discovered that, relative to the Earth and all other observed bodies, galaxies are receding in every direction at velocities (calculated from their observed red-shifts) directly proportional to their distance from the Earth and each other. In 1929, Hubble and

entity_name: Milton L. Humason

text: Milton Humason

text: formulated the empirical Redshift Distance Law of galaxies, nowadays known as

entity_name: Hubble's law

text: Hubble's law

text: , which, once the redshift is interpreted as a measure of recession speed, is consistent with the solutions of Einstein's General Relativity Equations for a homogeneous, isotropic expanding space.  The isotropic nature of the expansion was direct proof that it was the space (the fabric of existence) itself that was expanding, not the bodies in space that were simply moving further outward and apart into an infinitely larger preexisting empty void. It was this interpretation that led to the concept of the expanding universe. The law states that the greater the distance between any two galaxies, the greater their relative speed of separation. This discovery later resulted in the formulation of the Big Bang model.

text: Gyroscopic drift is an interaction of the bullet's mass and aerodynamics with the atmosphere that it is flying in.Even in completely calm air, with no sideways air movement at all, a spin-stabilized projectile will experience a spin-induced sideways component. For a right hand (clockwise) direction of rotation this component will always be to the right. For a left hand (counterclockwise) direction of rotation this component will always be to the left.This is because the projectile's longitudinal axis (its axis of rotation) and the direction of the velocity vector of the center of gravity (CG) deviate by a small angle, which is said to be the equilibrium yaw or the yaw of repose. The magnitude of the yaw of repose angle is typically less than 0.5 degree. Since rotating objects react with an angular velocity vector 90 degrees from the applied torque vector the bullet's axis of symmetry moves with a component in the vertical plane and a component in the horizontal plane; for right-handed (clockwise) spinning bullets, the bullet's axis of symmetry deflects to the right and a little bit upward with respect to the direction of the velocity vector as the projectile moves along its ballistic arc. As the result of this small inclination, there is a continuous air stream, which tends to deflect the bullet to the right. Thus the occurrence of the yaw of repose is the reason for the bullet drifting to the right (for right-handed spin) or to the left (for left-handed spin). This means that the bullet is "skidding" sideways at any given moment, and thus experiencing a sideways component.

text: Gyroscopic drift is an interaction of the bullet's mass and aerodynamics with the atmosphere that it is flying in.Even in completely calm air, with no sideways air movement at all, a spin-stabilized projectile will experience a spin-induced sideways component. For a right hand (clockwise) direction of rotation this component will always be to the right. For a left hand (counterclockwise) direction of rotation this component will always be to the left.This is because the projectile's longitudinal axis (its axis of rotation) and the direction of the velocity vector of the center of gravity (CG) deviate by a small angle, which is said to be the equilibrium

entity_name: Flight dynamics

text: yaw

text: or the yaw of repose. The magnitude of the yaw of repose angle is typically less than 0.5 degree. Since rotating objects react with an angular velocity vector 90 degrees from the applied torque vector the bullet's axis of symmetry moves with a component in the vertical plane and a component in the horizontal plane; for right-handed (clockwise) spinning bullets, the bullet's axis of symmetry deflects to the right and a little bit upward with respect to the direction of the velocity vector as the projectile moves along its ballistic arc. As the result of this small inclination, there is a continuous air stream, which tends to deflect the bullet to the right. Thus the occurrence of the yaw of repose is the reason for the bullet drifting to the right (for right-handed spin) or to the left (for left-handed spin). This means that the bullet is "skidding" sideways at any given moment, and thus experiencing a sideways component.

text: Most motorcycle helmet standards use impacts at speeds between 4–7 m/s (9–16 mph). While motorcyclists frequently ride at speeds higher than 20 m/s (45 mph), the perpendicular impact speed of the helmet is usually not the same as the road speed of the motorcycle, and the severity of the impact is determined not only by the speed of the head but also by the surface it hits and the angle of impact. Since the surface of the road is almost parallel to the direction a motorcyclist moves while driving, only a small component of their velocity is directed perpendicularly (though other surfaces may be perpendicular to the motorcyclist's velocity, such as trees, walls, and the sides of other vehicles). The severity of an impact is also influenced by the nature of the surface struck. The sheet metal wall of a car door may bend inwards to a depth of  during a helmeted-head impact, allowing more stopping distance for the rider's head than the helmet itself. A perpendicular impact against a flat steel anvil at 5 m/s (11 mph) may be of approximate severity to an oblique impact against a concrete surface at 30 m/s (67 mph) or a perpendicular impact against a sheet metal car door or windscreen at 30 m/s. Since there is a wide range of severity in the impacts that could happen in a motorcycle accident, some will be more severe than the impacts used in the standard tests and some will be less.

text: Most motorcycle helmet standards use impacts at speeds between 4–7 m/s (9–16 mph). While motorcyclists frequently ride at

text: speed

text: s higher than 20 m/s (45 mph), the perpendicular impact speed of the helmet is usually not the same as the road speed of the motorcycle, and the severity of the impact is determined not only by the speed of the head but also by the surface it hits and the angle of impact. Since the surface of the road is almost parallel to the direction a motorcyclist moves while driving, only a small component of their velocity is directed perpendicularly (though other surfaces may be perpendicular to the motorcyclist's velocity, such as trees, walls, and the sides of other vehicles). The severity of an impact is also influenced by the nature of the surface struck. The sheet metal wall of a car door may bend inwards to a depth of  during a helmeted-head impact, allowing more stopping distance for the rider's head than the helmet itself. A perpendicular impact against a flat steel

entity_name: Anvil

text: anvil

text: at 5 m/s (11 mph) may be of approximate severity to an oblique impact against a concrete surface at 30 m/s (67 mph) or a perpendicular impact against a sheet metal car door or windscreen at 30 m/s. Since there is a wide range of severity in the impacts that could happen in a motorcycle accident, some will be more severe than the impacts used in the standard tests and some will be less.

text: Consider the flow of a fluid through a region of space.  At any given time, any point of the fluid has a particular velocity associated with it; thus there is a vector field associated to any flow.  The converse is also true: it is possible to associate a flow to a vector field having that vector field as its velocity.

method: dangnt-nlp

text: Another apparent contradiction lies in the fact that the group velocity in anomalously dispersive media is higher than the speed of light. This was investigated by Arnold Sommerfeld (1907, 1914) and Léon Brillouin (1914). They came to the conclusion that in such cases the signal velocity is not equal to the group velocity, but to the front velocity which is never faster than the speed of light. Similarly, it is also argued that the apparent superluminal effects discovered by Günter Nimtz can be explained by a thorough consideration of the velocities involved.

text: Another apparent contradiction lies in the fact that the

text: group velocity

text: in

entity_name: Dispersion (optics)

text: anomalously dispersive media

text: is higher than the speed of light. This was investigated by

entity_name: Arnold Sommerfeld

text: Arnold Sommerfeld

text: (1907, 1914) and

entity_name: Léon Brillouin

text: Léon Brillouin

text: (1914). They came to the conclusion that in such cases the

entity_name: Signal velocity

text: signal velocity

text: is not equal to the group velocity, but to the

entity_name: Front velocity

text: front velocity

text: which is never faster than the speed of light. Similarly, it is also argued that the apparent superluminal effects discovered by

entity_name: Günter Nimtz

text: Günter Nimtz

text: can be explained by a thorough consideration of the velocities involved.

text: René Descartes believed that the total "quantity of motion" in the universe is conserved, where the quantity of motion is understood as the product of size and speed. This should not be read as a statement of the modern law of momentum, since he had no concept of mass as distinct from weight and size, and more importantly he believed that it is speed rather than velocity that is conserved. So for Descartes if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion.  Galileo, later, in his Two New Sciences, used the Italian word impeto.

entity_name: René Descartes

text: René Descartes

text: believed that the total "quantity of motion" in the universe is conserved, where the quantity of motion is understood as the product of size and speed. This should not be read as a statement of the modern law of momentum, since he had no concept of mass as distinct from weight and size, and more importantly he believed that it is speed rather than velocity that is conserved. So for Descartes if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion.

entity_name: Galileo Galilei

text: Galileo

text: , later, in his

entity_name: Two New Sciences

text: Two New Sciences

text: , used the

entity_name: Italian language

text: Italian

text: word impeto.

method: Bert-ConvKNRM

text: This simplistic explanation, however, breaks down in cases where the light is propagating through a medium which has a refractive index that is not one. In that case, relativistic addition of velocities can be used to calculate the lab frame phase velocity of the light moving in the same direction as the rotation as well as for the light moving in the opposite direction from the rotation. The difference in lab frame phase velocities determines the difference in travel times, and this difference in travel times can be multiplied by the optical frequency to determine a phase difference.

text: This simplistic explanation, however, breaks down in cases where the light is propagating through a medium which has a refractive index that is not one. In that case, relativistic addition of velocities can be used to calculate the

entity_name: Laboratory frame of reference

text: lab frame

text: phase velocity of the light moving in the same direction as the rotation as well as for the light moving in the opposite direction from the rotation. The difference in lab frame phase velocities determines the difference in travel times, and this difference in travel times can be multiplied by the optical frequency to determine a phase difference.

text: Nomenclature of a Velocity Triangle:

text: Nomenclature of a Velocity Triangle:

text: The calculation of the velocity and the velocity potential at a given point is encapsulated inside the class definition of the vortex rings. The method that is actually implemented differ from the topology of the inducing ring (triangular or quadrilateral). Each lattice exposes then a method that allows the same calculation at lattice level by running over all contained rings.

text: The group velocity itself is usually a function of the wave's frequency. This results in group velocity dispersion (GVD), which causes a short pulse of light to spread in time as a result of different frequency components of the pulse travelling at different velocities. GVD is often quantified as the group delay dispersion parameter (again, this formula is for a uniform medium only):

text: The group velocity itself is usually a function of the wave's frequency. This results in

entity_name: Group velocity dispersion

text: group velocity dispersion

text: (GVD), which causes a short pulse of light to spread in time as a result of different frequency components of the pulse travelling at different velocities. GVD is often quantified as the

entity_name: Group delay and phase delay

text: group delay

text: dispersion parameter (again, this formula is for a uniform medium only):

text: A steam turbine consists of one or more rotors (rotating discs) mounted on a drive shaft, alternating with a series of stators (static discs) fixed to the turbine casing. The rotors have a propeller-like arrangement of blades at the outer edge. Steam acts upon these blades, producing rotary motion. The stator consists of a similar, but fixed, series of blades that serve to redirect the steam flow onto the next rotor stage. A steam turbine often exhausts into a surface condenser that provides a vacuum. The stages of a steam turbine are typically arranged to extract the maximum potential work from a specific velocity and pressure of steam, giving rise to a series of variably sized high- and low-pressure stages. Turbines are only efficient if they rotate at relatively high speed, therefore they are usually connected to reduction gearing to drive lower speed applications, such as a ship's propeller. In the vast majority of large electric generating stations, turbines are directly connected to generators with no reduction gearing. Typical speeds are 3600 revolutions per minute (RPM) in the USA with 60 Hertz power, and 3000 RPM in Europe and other countries with 50 Hertz electric power systems. In nuclear power applications the turbines typically run at half these speeds, 1800 RPM and 1500 RPM. A turbine rotor is also only capable of providing power when rotating in one direction. Therefore, a reversing stage or gearbox is usually required where power is required in the opposite direction.

text: A steam turbine consists of one or more

entity_name: Steam turbine

entity_section: Reaction turbines

text: rotors

text: (rotating discs) mounted on a drive shaft, alternating with a series of

text: stators

text: (static discs) fixed to the turbine casing. The rotors have a propeller-like arrangement of blades at the outer edge. Steam acts upon these blades, producing rotary motion. The stator consists of a similar, but fixed, series of blades that serve to redirect the steam flow onto the next rotor stage. A steam turbine often exhausts into a

entity_name: Surface condenser

text: surface condenser

text: that provides a vacuum. The stages of a steam turbine are typically arranged to extract the maximum potential work from a specific velocity and pressure of steam, giving rise to a series of variably sized high- and low-pressure stages. Turbines are only efficient if they rotate at relatively high speed, therefore they are usually connected to reduction gearing to drive lower speed applications, such as a ship's propeller. In the vast majority of large electric generating stations, turbines are directly connected to generators with no reduction gearing. Typical speeds are 3600 revolutions per minute (RPM) in the USA with 60 Hertz power, and 3000 RPM in Europe and other countries with 50 Hertz electric power systems. In nuclear power applications the turbines typically run at half these speeds, 1800 RPM and 1500 RPM. A turbine rotor is also only capable of providing power when rotating in one direction. Therefore, a reversing stage or gearbox is usually required where power is required in the opposite direction.

text: Many of the concepts of special relativity are illustrated through the biquaternion structures laid out. The subspace M corresponds to Minkowski space, with the four coordinates giving the time and space locations of events in a resting frame of reference. Any hyperbolic versor exp(ahr) corresponds to a velocity in direction r of speed c tanh a  where c is the velocity of light. The inertial frame of reference of this velocity can be made the resting frame by applying the Lorentz boost T given by g = exp(0.5ahr) since then

text: Many of the concepts of

entity_name: Special relativity

text: special relativity

text: are illustrated through the biquaternion structures laid out. The subspace M corresponds to

entity_name: Minkowski space

text: Minkowski space

text: , with the four coordinates giving the time and space locations of events in a resting

entity_name: Frame of reference

text: frame of reference

text: . Any hyperbolic versor exp(ahr) corresponds to a

text: velocity

text: in direction r of speed c tanh a  where c is the

entity_name: Speed of light

text: velocity of light

text: . The inertial frame of reference of this velocity can be made the resting frame by applying the

entity_name: Lorentz transformation

entity_section: boost

text: Lorentz boost

text: T given by g = exp(0.5ahr) since then

text: Until recently, ultrasound images have been 2D views and have relied on highly trained specialists to properly orient the probe and select the position within the body to image with only few and complex visual cues.  The complete measurement of 3D velocity vectors makes many post processing techniques possible. Not only the volumetric flow across any plane is measurable, but also other physical information such as stress and pressure can be calculated based on the 3D velocity field. However, it is quite challenging to measure the complex blood flow to give velocity vectors, due to the fast acquisition rate and the massive computations needed for it. Plane wave technique is thus promising as it can generate very high frame rate.

text: One might note that the long-term results of Velocity Verlet, and similarly of Leapfrog are one order better than the semi-implicit Euler method. The algorithms are almost identical up to a shifted by half of a timestep in the velocity.  This is easily proven by rotating the above loop to start at Step 3 and then noticing that the acceleration term in Step 1 could be eliminated by combining Steps 2 and 4.  The only difference is that the midpoint velocity in velocity Verlet is considered the final velocity in semi-implicit Euler method.

text: One might note that the long-term results of Velocity Verlet, and similarly of Leapfrog are one order better than the

entity_name: Semi-implicit Euler method

text: semi-implicit Euler method

text: . The algorithms are almost identical up to a shifted by half of a timestep in the velocity.  This is easily proven by rotating the above loop to start at Step 3 and then noticing that the acceleration term in Step 1 could be eliminated by combining Steps 2 and 4.  The only difference is that the midpoint velocity in velocity Verlet is considered the final velocity in semi-implicit Euler method.

text: Rough calculations for the basic ablation effect are relatively simple: the energy from the primary is distributed evenly onto all of the surfaces within the outer radiation case, with the components coming to a thermal equilibrium, and the effects of that thermal energy are then analyzed. The energy is mostly deposited within about one X-ray optical thickness of the tamper/pusher outer surface, and the temperature of that layer can then be calculated. The velocity at which the surface then expands outwards is calculated and, from a basic Newtonian momentum balance, the velocity at which the rest of the tamper implodes inwards.

text: Rough calculations for the basic ablation effect are relatively simple: the energy from the primary is distributed evenly onto all of the surfaces within the outer radiation case, with the components coming to a

entity_name: Thermal equilibrium

text: thermal equilibrium

text: , and the effects of that thermal energy are then analyzed. The energy is mostly deposited within about one X-ray

entity_name: Optical depth

text: optical thickness

text: of the tamper/pusher outer surface, and the temperature of that layer can then be calculated. The velocity at which the surface then expands outwards is calculated and, from a basic Newtonian

entity_name: Momentum

text: momentum

text: balance, the velocity at which the rest of the tamper implodes inwards.

text: It has also been suggested that Rømer was measuring a Doppler effect. The original effect discovered by Christian Doppler 166 years later refers to propagating electromagnetic waves. The generalization referred to here is the change in observed frequency of an oscillator (in this case, Io orbiting around Jupiter) when the observer (in this case, on Earth's surface) is moving: the frequency is higher when the observer is moving towards the oscillator and lower when the observer is moving away from the oscillator. This apparently anachronistic analysis implies that Rømer was measuring the ratio , where c is the speed of light and v is the Earth's orbital velocity (strictly, the component of the Earth's orbital velocity parallel to the Earth–Jupiter vector), and indicates that the major inaccuracy of Rømer's calculations was his poor knowledge of the orbit of Jupiter.

text: It has also been suggested that Rømer was measuring a

entity_name: Doppler effect

text: Doppler effect

text: . The original effect discovered by

entity_name: Christian Doppler

text: Christian Doppler

text: 166 years later refers to propagating electromagnetic waves. The generalization referred to here is the change in observed frequency of an oscillator (in this case, Io orbiting around Jupiter) when the observer (in this case, on Earth's surface) is moving: the frequency is higher when the observer is moving towards the oscillator and lower when the observer is moving away from the oscillator. This apparently anachronistic analysis implies that Rømer was measuring the ratio , where c is the speed of light and v is the Earth's orbital velocity (strictly, the

entity_name: Vector projection

text: component

text: of the Earth's orbital velocity parallel to the Earth–Jupiter

text: vector

text: ), and indicates that the major inaccuracy of Rømer's calculations was his poor knowledge of the orbit of Jupiter.

text: Usually each particle has a velocity vector and a position vector, containing information about the particle’s current velocity and position respectively. The particles next position is calculated by adding its velocity vector to its position vector. A very simple operation (again why particle systems are so desirable). Its velocity vector changes over time, in response to the forces acting on the particle. For example a collision with another particle will cause it to change direction.

text: Here, the prime symbol denotes the derivative with respect to . Thus, the tangential angle specifies the direction of the velocity vector , while the speed specifies its magnitude. The vector

text: Here, the

entity_name: Prime (symbol)

text: prime symbol

text: denotes the

entity_name: Derivative

text: derivative

text: with respect to . Thus, the tangential angle specifies the direction of the

text: velocity

text: vector , while the

text: speed

text: specifies its magnitude. The vector

text: In considering motions of objects over time the instantaneous velocity of the object is the rate of change of the displacement as a function of time. The velocity then is distinct from the instantaneous speed which is the time rate of change of the distance traveled along a specific path. The velocity may be equivalently defined as the time rate of change of the position vector. If one considers a moving initial position, or equivalently a moving origin (e.g. an initial position or origin which is fixed to a train wagon, which in turn moves with respect to its rail track), the velocity of P (e.g. a point representing the position of a passenger walking on the train) may be referred to as a relative velocity, as opposed to an absolute velocity, which is computed with respect to a point which is considered to be 'fixed in space' (such as, for instance, a point fixed on the floor of the train station).

text: In considering motions of objects over time the instantaneous

text: velocity

text: of the object is the rate of change of the displacement as a function of time. The velocity then is distinct from the instantaneous

text: speed

text: which is the

text: time rate

text: of change of the distance traveled along a specific path. The velocity may be equivalently defined as the time rate of change of the position vector. If one considers a moving initial position, or equivalently a moving origin (e.g. an initial position or origin which is fixed to a train wagon, which in turn moves with respect to its rail track), the velocity of P (e.g. a point representing the position of a passenger walking on the train) may be referred to as a relative velocity, as opposed to an absolute velocity, which is computed with respect to a point which is considered to be 'fixed in space' (such as, for instance, a point fixed on the floor of the train station).

text: Velocities (speeds) do not simply add. If the observer in S measures an object moving along the x axis at velocity u, then the observer in the S′ system, a frame of reference moving at velocity v in the x direction with respect to S, will measure the object moving with velocity u′ where (from the Lorentz transformations above):

text: Wind speed and direction are very important for a successful throw. A right-handed boomerang is thrown with the wind on one's left cheek. The angle to the wind depends on the boomerang, but starting with a 45-degree angle is recommended. Depending on where the boomerang lands, this angle can be modified so that a closer return is achieved. For example, if the boomerang lands too far on the left, turn to throw more to the right of the wind the next time. If the return goes over one's head, then throw softer. If it falls short, then throw harder. As for the wind speed, a light wind of three to five miles an hour is ideal. If the wind is strong enough to fly a kite, then that is usually too strong for boomerangs.

text: Velocity triangles can be used to calculate the basic performance of a turbine stage. Gas exits the stationary turbine nozzle guide vanes at absolute velocity V. The rotor rotates at velocity U. Relative to the rotor, the velocity of the gas as it impinges on the rotor entrance is V. The gas is turned by the rotor and exits, relative to the rotor, at velocity V. However, in absolute terms the rotor exit velocity is V. The velocity triangles are constructed using these various velocity vectors. Velocity triangles can be constructed at any section through the blading (for example: hub, tip, midsection and so on) but are usually shown at the mean stage radius. Mean performance for the stage can be calculated from the velocity triangles, at this radius, using the Euler equation:

entity_name: Velocity triangle

text: Velocity triangle

text: s can be used to calculate the basic performance of a turbine stage. Gas exits the stationary turbine nozzle guide vanes at absolute velocity V. The rotor rotates at velocity U. Relative to the rotor, the velocity of the gas as it impinges on the rotor entrance is V. The gas is turned by the rotor and exits, relative to the rotor, at velocity V. However, in absolute terms the rotor exit velocity is V. The velocity triangles are constructed using these various velocity vectors. Velocity triangles can be constructed at any section through the blading (for example: hub, tip, midsection and so on) but are usually shown at the mean stage radius. Mean performance for the stage can be calculated from the velocity triangles, at this radius, using the Euler equation:

text: In a typical implementation, the radar or sodar can sample along each of five beams: one is aimed vertically to measure vertical velocity, and four are tilted off vertical and oriented orthogonal to one another to measure the horizontal components of the air's motion. A profiler's ability to measure winds is based on the assumption that the turbulent eddies that induce scattering are carried along by the mean wind. The energy scattered by these eddies and received by the profiler is orders of magnitude smaller than the energy transmitted. However, if sufficient samples can be obtained, then the amplitude of the energy scattered by these eddies can be clearly identified above the background noise level, then the mean wind speed and direction within the volume being sampled can be determined. The radial components measured by the tilted beams are the vector sum of the horizontal motion of the air toward or away from the radar and any vertical motion present in the beam. Using appropriate trigonometry, the three-dimensional meteorological velocity components (u,v,w) and wind speed and wind direction are calculated from the radial velocities with corrections for vertical motions.

text: In a typical implementation, the radar or sodar can sample along each of five beams: one is aimed vertically to measure vertical velocity, and four are tilted off vertical and oriented orthogonal to one another to measure the horizontal components of the air's motion. A profiler's ability to measure winds is based on the assumption that the turbulent eddies that induce scattering are carried along by the mean wind. The energy scattered by these eddies and received by the profiler is

entity_name: Order of magnitude

text: orders of magnitude

text: smaller than the energy transmitted. However, if sufficient samples can be obtained, then the amplitude of the energy scattered by these eddies can be clearly identified above the background noise level, then the mean wind speed and direction within the volume being sampled can be determined. The radial components measured by the tilted beams are the vector sum of the horizontal motion of the air toward or away from the radar and any vertical motion present in the beam. Using appropriate trigonometry, the three-dimensional meteorological velocity components (u,v,w) and wind speed and wind direction are calculated from the radial velocities with corrections for vertical motions.

text: where ω is the angular velocity in degrees per day, φ is the solar latitude and A, B, and C are constants. The values of A, B, and C differ depending on the techniques used to make the measurement, as well as the time period studied. A current set of accepted average values is:

text: Another example relates to motion, where in some cases only the normal velocity relative to some edge can be extracted.  If two such features have been extracted and they can be assumed to refer to same true velocity, this velocity is not given as the average of the normal velocity vectors.  Hence, normal velocity vectors are not averageable.  Instead, there are other representations of motions, using matrices or tensors, that give the true velocity in terms of an average operation of the normal velocity descriptors.

text: Although the GUI is essentially the same as in Phun, many significant changes have occurred in the scope of Algodoo's simulations.  Two notable changes include a new optics modeling engine and a snap-to grid feature allowing for higher precision scene creation.  The inclusion of optics has granted much more freedom in terms of using Algodoo's scripting language "Thyme", as one may now initiate events by hitting a geometry with a stream of laser light.  Other notable changes include the inclusion of a velocities menu, allowing one to set a geometry's velocity to a set value, incompressible water, which allows for much more realistic fluid simulation, a plotting menu which allows one to compare and contrast different properties of a geometry, i.e. velocity at a certain time, position on the X and Y axis, velocity along the X and Y axis, etc., a new tab in the 'options' menu that allows the user to visualize in real time many different forces that are affecting the objects in a scene,and many other new features, bug fixes, optimizations and improvements.

text: Although the GUI is essentially the same as in

text: Phun

text: , many significant changes have occurred in the scope of Algodoo's simulations.  Two notable changes include a new optics modeling engine and a snap-to grid feature allowing for higher precision scene creation.  The inclusion of optics has granted much more freedom in terms of using Algodoo's scripting language "Thyme", as one may now initiate events by hitting a geometry with a stream of laser light.  Other notable changes include the inclusion of a velocities menu, allowing one to set a geometry's velocity to a set value, incompressible water, which allows for much more realistic fluid simulation, a plotting menu which allows one to compare and contrast different properties of a geometry, i.e. velocity at a certain time, position on the X and Y axis, velocity along the X and Y axis, etc., a new tab in the 'options' menu that allows the user to visualize in real time many different forces that are affecting the objects in a scene,and many other new features, bug fixes, optimizations and improvements.

text: Some techniques using two alternating pulse repetition frequencies (PRF) allow a greater Doppler range. The velocities noted with the first pulse rate could be equal or different with the second. For instance, if the maximum velocity with a certain rate is 10 metre/second and the one with the other rate is 15 m/s. The data coming from both will be the same up to 10 m/s, and will differ thereafter. It is then possible to find a mathematical relation between the two returns and calculate the real velocity beyond the limitation of the two PRFs.

text: To calculate velocity, a team first has to determine how many units of work each task is worth and the length of each interval. During development, the team has to keep track of completed tasks and, at the end of the interval, count the number of units of work completed during the interval. The team then writes down the calculated velocity in a chart or on a graph.

text: The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if proper distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally. (See comoving distance for a discussion of different notions of 'velocity' in cosmology.) Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10 seconds after the Big Bang to around 10 seconds), when the universe may have rapidly expanded by a factor of around 10 to 10.

text: The expansion of the

text: universe

text: causes distant galaxies to recede from us faster than the speed of light, if

text: proper distance

text: and

text: cosmological time

text: are used to calculate the speeds of these galaxies. However, in

text: general relativity

text: , velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally. (See

text: comoving distance

text: for a discussion of different notions of 'velocity' in cosmology.) Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the

text: inflationary epoch

text: thought to have occurred in a tiny fraction of the second after the

text: Big Bang

text: (models suggest the period would have been from around 10 seconds after the Big Bang to around 10 seconds), when the universe may have rapidly expanded by a factor of around 10 to 10.

text: Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector  ud}} and the velocity of the second object by the vector  ve}}, where u is the speed of the first object, v is the speed of the second object, and d and e are unit vectors in the directions of motion of each particle respectively, then the velocity of the first object as seen by the second object is

text: Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector  ud}} and the velocity of the second object by the vector  ve}}, where u is the speed of the first object, v is the speed of the second object, and d and e are

text: unit vector

text: s in the directions of motion of each particle respectively, then the velocity of the first object as seen by the second object is

text: Explosive velocity, also known as detonation velocity or velocity of detonation (VoD), is the velocity at which the shock wave front travels through a detonated explosive. The data listed for a specific substance is usually a rough prediction based upon gas behavior theory (see Chapman-Jouguet condition), as in practice it is difficult to measure.  Explosive velocities are always faster than the local speed of sound in the material.

text: Explosive velocity, also known as detonation velocity or velocity of detonation (VoD), is the

text: velocity

text: at which the

text: shock wave

text: front travels through a

text: detonated

text: explosive

text: . The data listed for a specific substance is usually a rough prediction based upon

text: gas behavior theory

text: (see

text: Chapman-Jouguet condition

text: ), as in practice it is difficult to measure.  Explosive velocities are always faster than the local

text: speed of sound

text: in the material.

text: The velocity vector can change in magnitude and in direction or both at once. Hence, the acceleration is the rate of change of the magnitude of the velocity vector plus the rate of change of direction of that vector. The same reasoning used with respect to the position of a particle to define velocity, can be applied to the velocity to define acceleration. The acceleration of a particle is the vector defined by the rate of change of the velocity vector.  The average acceleration of a particle over a time interval is defined as the ratio.

text: The velocity vector can change in magnitude and in direction or both at once. Hence, the acceleration is the rate of change of the magnitude of the velocity vector plus the rate of change of direction of that vector. The same reasoning used with respect to the position of a particle to define velocity, can be applied to the velocity to define acceleration. The

text: acceleration

text: of a particle is the vector defined by the rate of change of the velocity vector.  The average acceleration of a particle over a time interval is defined as the ratio.

text: In three dimensions, the angular velocity becomes a bit more complicated. The angular velocity in this case is generally thought of as a vector, or more precisely, a pseudovector. It now has not only a magnitude, but a direction as well. The magnitude is the angular speed, and the direction describes the axis of rotation that Euler's rotation theorem guarantees must exist. The right-hand rule indicates the positive direction of the angular velocity pseudovector.

text: In three dimensions, the angular velocity becomes a bit more complicated. The angular velocity in this case is generally thought of as a vector, or more precisely, a

text: pseudovector

text: . It now has not only a magnitude, but a direction as well. The magnitude is the angular speed, and the direction describes the

text: axis of rotation

text: that

text: Euler's rotation theorem

text: guarantees must exist. The

text: right-hand rule

text: indicates the positive direction of the angular velocity pseudovector.

text: Wave velocity  is a general concept, of various kinds of wave velocities, for a wave's phase and speed concerning energy (and information) propagation. The phase velocity is given as:

text: Wave velocity  is a general concept, of various kinds of wave velocities, for a wave's

text: phase

text: and

text: speed

text: concerning energy (and information) propagation. The

text: phase velocity

text: is given as:

text: The HLLE (Harten, Lax, van Leer and  Einfeldt) solver is an approximate solution to the Riemann problem,  which is only based on the integral form of the conservation laws and the largest and smallest signal velocities at the interface.  The stability and robustness of the HLLE solver is closely related to the signal velocities and a single central average state, as proposed by Einfeldt in the original paper. The description of the HLLE scheme in the book mentioned below is incomplete and partially wrong. The reader is referred to the original paper. Actually, the HLLE scheme is based on a new stability theory for discontinuities in fluids, which was never published.

text: The HLLE (

text: Harten

text: Lax

text: van Leer

text: and  Einfeldt) solver is an approximate solution to the Riemann problem,  which is only based on the integral form of the conservation laws and the largest and smallest signal velocities at the interface.  The stability and robustness of the HLLE solver is closely related to the signal velocities and a single central average state, as proposed by Einfeldt in the original paper. The description of the HLLE scheme in the book mentioned below is incomplete and partially wrong. The reader is referred to the original paper. Actually, the HLLE scheme is based on a new stability theory for discontinuities in fluids, which was never published.

text: Small sonar systems attached to floating buoys, called sonobuoys have been used by geologists to shoot seismic transects across the Adare Basin in order to establish 2D velocity models of the subsurface stratigraphy beneath the seafloor down to a depth of 5.5 km. The deeper deposited sediment has been compacted under heavier pressures for longer time periods, causing the sediment to become denser and the velocity of the seismic waves to increase with depth. Velocities from beneath the Adare Trough tend to be slightly higher than the average, indicating that the lithosphere is slightly thicker underneath the trough than the surrounding basin. Within the depth capable of measurement 6 distinct stratigraphic units have been established with characteristic velocities. The first unit begins at the seafloor with a velocity of 2000 m/s. The second unit lies 0.6 km beneath the seafloor and waves propagate with a velocity of 3000 m/s. The third layer begins at 1.8 km beneath the seafloor and has a velocity of 4200 m/s. The next layer begins at 2.3 km and has a velocity of 4900 m/s, followed by a layer at 3.1 km with 5700 m/s wave velocity. The final layer lies 3.3 km beneath the surface and displays velocities of 6000 m/s.

text: Small sonar systems attached to floating buoys, called

text: sonobuoy

text: s have been used by

text: geologists

text: to shoot seismic transects across the Adare Basin in order to establish 2D velocity models of the

text: subsurface

text: stratigraphy beneath the

text: seafloor

text: down to a depth of 5.5 km. The deeper deposited

text: sediment

text: has been compacted under heavier pressures for longer time periods, causing the sediment to become denser and the velocity of the

text: seismic waves

text: to increase with depth. Velocities from beneath the

text: Adare Trough

text: tend to be slightly higher than the average, indicating that the lithosphere is slightly thicker underneath the trough than the surrounding basin. Within the depth capable of measurement 6 distinct stratigraphic units have been established with characteristic velocities. The first unit begins at the seafloor with a velocity of 2000 m/s. The second unit lies 0.6 km beneath the seafloor and waves propagate with a velocity of 3000 m/s. The third layer begins at 1.8 km beneath the seafloor and has a velocity of 4200 m/s. The next layer begins at 2.3 km and has a velocity of 4900 m/s, followed by a layer at 3.1 km with 5700 m/s wave velocity. The final layer lies 3.3 km beneath the surface and displays velocities of 6000 m/s.

text: where R represents the ideal gas constant, 8.314 J/(mol·K), T is the temperature of the gas in kelvins, and M is the molar mass of the gas in kilograms. The generally accepted terminology for speed as compared to velocity is that the former is the scalar magnitude of the latter. Therefore, although the average speed is between zero and the RMS speed, the average velocity for a stationary gas is zero.

text: where R represents the

text: ideal gas constant

text: , 8.314 J/(mol·K), T is the temperature of the gas in

text: kelvin

text: s, and M is the

text: molar mass

text: of the gas in kilograms. The generally accepted terminology for speed as compared to velocity is that the former is the scalar magnitude of the latter. Therefore, although the average speed is between zero and the RMS speed, the average velocity for a stationary gas is zero.

text: The high frequency Rayleigh wave inversion performed by Xia et al. (1999) analyzed the earth using Knopoff’s method.  By varying different properties used in creating the dispersion curve, it was discovered that different earth properties had significantly different effects on phase velocities.  Changing the S-wave velocity input has a dramatic impact on Rayleigh wave phase velocities at high frequencies (greater than 5 Hz).  A change in S-wave velocity of 25% changes the Rayleigh wave velocity by 39%.  Conversely, P-wave velocity and density have a relatively small impact on Rayleigh wave phase velocity.  A change in density of 25% will cause a less than 10% change in surface wave velocity.  A change in P-wave velocity will have even less effect (3%).

text: The usefulness of surface waves in determining subsurface elastic properties arises from the way in which they disperse.  Dispersion (geology) is the way in which surface waves spread out as they travel across the surface of the earth.  Basically, if ten waves travel along the surface of the earth at the same speed, there is no dispersion.  If several of the waves start to travel faster than the others, dispersion is occurring.  Surface waves of varying wavelengths penetrate to different depths (Figure 2) and travel at the velocity of the mediums they are travelling through.  Figure 2 was generated by plotting the amplitude of surface waves against depth.  This was done for two different wavelengths.  Both waves have the same total energy, but the longer wavelength has its energy spread out over a larger interval.  If earth materials’ elastic parameters yield higher velocities with depth, longer wavelength surface waves will travel faster than those with shorter wavelengths.  The variation of velocities with wavelength makes it possible to infer critical information about the subsurface.  Dobrin (1951) uses a water disturbance example to illustrate the phenomenon that longer wavelengths tend to travel faster.  This increase in speed with wavelength is seen for both group velocities and phase velocities.  A wave group consists of waves at varying wavelengths and frequencies.  Individual waves of a wave group are usually generated at the same time, but tend to spread out within the group because each wavelet travels at a different speed.  A group velocity is basically the speed at which a wave group travels.  A phase velocity is the speed at which an individual wave travels, having its own characteristic wavelength and frequency.  Fourier theory tells us that a sharp impulse is made up of infinite frequency content in phase at one point.  If each frequency travels at the same speed, that peak will remain intact.  If each frequency travels at a different speed, that peak will spread out (Figure 3).  This spreading out is dispersion.  Phase and group velocity are both dependent on wavelength and are related by the equation

text: The usefulness of surface waves in determining subsurface elastic properties arises from the way in which they disperse.  Dispersion (geology) is the way in which surface waves spread out as they travel across the surface of the earth.  Basically, if ten waves travel along the surface of the earth at the same speed, there is no dispersion.  If several of the waves start to travel faster than the others, dispersion is occurring.  Surface waves of varying

text: wavelengths

text: penetrate to different depths (Figure 2) and travel at the velocity of the mediums they are travelling through.  Figure 2 was generated by plotting the amplitude of surface waves against depth.  This was done for two different wavelengths.  Both waves have the same total energy, but the longer wavelength has its energy spread out over a larger interval.  If earth materials’ elastic parameters yield higher velocities with depth, longer wavelength surface waves will travel faster than those with shorter wavelengths.  The variation of velocities with wavelength makes it possible to infer critical information about the subsurface.  Dobrin (1951) uses a water disturbance example to illustrate the phenomenon that longer wavelengths tend to travel faster.  This increase in speed with wavelength is seen for both

text: group velocities

text: and

text: phase velocities

text: .  A wave group consists of waves at varying wavelengths and

text: frequencies

text: .  Individual waves of a wave group are usually generated at the same time, but tend to spread out within the group because each wavelet travels at a different speed.  A group velocity is basically the speed at which a wave group travels.  A phase velocity is the speed at which an individual wave travels, having its own characteristic wavelength and frequency.

text: Fourier theory

text: tells us that a sharp impulse is made up of infinite frequency content in phase at one point.  If each frequency travels at the same speed, that peak will remain intact.  If each frequency travels at a different speed, that peak will spread out (Figure 3).  This spreading out is dispersion.  Phase and group velocity are both dependent on wavelength and are related by the equation

text: Above and to the right is a plot of the average velocity as a function of the density of cars, obtained from a simulation of the original Nagel–Schreckenberg model. In the deterministic limit, p = 0, the velocity is constant at the maximum velocity (here 5) up to a density ρ = 1/(maximum velocity + 1) = 1 / 6 = 0.167, at which point there is a discontinuity in the slope due to the sudden appearance of traffic jams. Then as the density increases further, the average velocity decreases until it reaches zero when the road is 100% occupied. When p = 0.3, and so there are random decreases in velocity, then at low densities the average velocity is of course slower. However, note p > 0 also shifts the density at which jams appear to lower densities – traffic jams appear at the knee in the curve which for p = 0.3 is close to 0.15, and the random decelerations round off the discontinuity in the slope found for p = 0 at the onset of traffic jams.

text: In order to calculate and record the velocity components, the vector averaging circuitry is turned on by a rotor count, which is signaled by a proper sequence of changes in the levels of the magnetodiodes. The instrument heading (

text: While a planetary system may enjoy a location favorable to complex life, it must also maintain that location for a span of time sufficiently long for complex life to evolve. Hence a central star with a galactic orbit that steers clear of galactic regions where radiation levels are high, such as the Galactic Center and the spiral arms, would appear most favourable. If the central star's galactic orbit is eccentric (elliptic or hyperbolic), it will pass through some spiral arms, but if the orbit is a near perfect circle and the orbital velocity equals the "rotational" velocity of the spiral arms, the star will drift into a spiral arm region only gradually—if at all. Therefore, Rare Earth proponents conclude that a life-bearing star must have a galactic orbit that is nearly circular about the center of its galaxy. The required synchronization of the orbital velocity of a central star with the wave velocity of the spiral arms can occur only within a fairly narrow range of distances from the Galactic Center. This region is termed the "galactic habitable zone". Lineweaver et al. calculate that the galactic habitable zone is a ring 7 to 9 kiloparsecs in diameter, that includes no more than 10% of the stars in the Milky Way. Based on conservative estimates of the total number of stars in the galaxy, this could represent something like 20 to 40 billion stars. Gonzalez, et al. would halve these numbers; he estimates that at most 5% of stars in the Milky Way fall in the galactic habitable zone.

text: While a planetary system may enjoy a location favorable to complex life, it must also maintain that location for a span of time sufficiently long for complex life to evolve. Hence a central star with a galactic orbit that steers clear of galactic regions where radiation levels are high, such as the Galactic Center and the spiral arms, would appear most favourable. If the central star's galactic orbit is

text: eccentric

text: (elliptic or hyperbolic), it will pass through some spiral arms, but if the orbit is a near perfect circle and the orbital velocity equals the "rotational" velocity of the spiral arms, the star will drift into a spiral arm region only gradually—if at all. Therefore, Rare Earth proponents conclude that a life-bearing star must have a galactic orbit that is nearly circular about the center of its galaxy. The required synchronization of the orbital velocity of a central star with the wave velocity of the spiral arms can occur only within a fairly narrow range of distances from the Galactic Center. This region is termed the "galactic habitable zone". Lineweaver et al. calculate that the galactic habitable zone is a ring 7 to 9

text: kiloparsecs

text: in diameter, that includes no more than 10% of the stars in the

text: Milky Way

text: . Based on conservative estimates of the total number of stars in the galaxy, this could represent something like 20 to 40 billion stars. Gonzalez, et al. would halve these numbers; he estimates that at most 5% of stars in the Milky Way fall in the galactic habitable zone.

text: When light propagates in a medium, its speed is reduced, in the rest frame of the medium, to  }}, where  is the index of refraction of the medium . The speed of light in a medium uniformly moving with speed  in the positive -direction as measured in the lab frame is given directly by the velocity addition formulas. For the forward direction (standard configuration, drop index  on ) one gets,

text: When light propagates in a medium, its speed is reduced, in the rest frame of the medium, to  }}, where  is the

text: index of refraction

text: of the medium . The speed of light in a medium uniformly moving with speed  in the positive -direction as measured in the lab frame is given directly by the velocity addition formulas. For the forward direction (standard configuration, drop index  on ) one gets,

text: Speed describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified.

text: Speed

text: describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified.

text: Max is a human granted superhuman speed by ancient Native American rituals. His speed is enough that he can accelerate well beyond the standard Mach 1 super-speed limit, or the speed of sound; though he cannot reach escape velocity. Over time, he tried to find the fuel for his powers (and those of other speedsters): the Speed Force. Though he never quite entered it nor obtained its energies to power his speed, his attempts allowed him to travel forward through time.

text: Max is a human granted superhuman speed by ancient

text: Native American

text: rituals. His speed is enough that he can accelerate well beyond the standard Mach 1 super-speed limit, or the speed of sound; though he cannot reach

text: escape velocity

text: . Over time, he tried to find the fuel for his powers (and those of other

text: speedster

text: s): the

text: Speed Force

text: . Though he never quite entered it nor obtained its energies to power his speed, his attempts allowed him to

text: travel forward through time

text: that is, the difference in flow velocity between points separated by a vector  (since the turbulence is assumed isotropic, the flow velocity increment depends only on the modulus of ). Flow velocity increments are useful because they emphasize the effects of scales of the order of the separation  when statistics are computed.  The statistical scale-invariance implies that the scaling of flow velocity increments should occur with a unique scaling exponent , so that when  is scaled by a factor ,

text: In addition to the Poynting vector criterion, Laue and Møller suggested a criterion of four-vector covariance imposed on the propagation velocity of EM energy in a moving medium, just like the velocity of a massive particle. The Laue–Møller criterion supports Minkowski EM tensor, because the Minkowski tensor is a real four-tensor while Abraham's is not, as re-discovered by Veselago and Shchavlev recently. But some scientists disagree, criticizing that "it is widely recognized now that Abraham's tensor is also capable of describing optical experiments," and such a criterion of this type is only "a test of a tensor's convenience rather than its correctness ". Some scientists also criticized the justifications of the energy–velocity definition and the imposed four-vector covariance in Laue–Møller criterion. Regarding the energy–velocity definition which is given by Poynting vector divided by EM energy density in Laue–Møller criterion, they say "the Poynting vector does not necessarily denote the direction of real power flowing" in a moving medium. Regarding the imposed four-velocity covariance, which was probably prompted by the relativistic velocity addition rule applied to illustrating Fizeau running water experiment, they say "one essential difference between massive particles and photons is that any massive particle has its four-velocity, while the photon (the carrier of EM energy) does not."

text: In addition to the Poynting vector criterion, Laue and Møller suggested a criterion of

text: four-vector

text: covariance imposed on the propagation velocity of EM energy in a moving medium, just like the velocity of a massive particle. The Laue–Møller criterion supports Minkowski EM tensor, because the Minkowski tensor is a real

text: four-tensor

text: while Abraham's is not, as re-discovered by Veselago and Shchavlev recently. But some scientists disagree, criticizing that "it is widely recognized now that Abraham's tensor is also capable of describing optical experiments," and such a criterion of this type is only "a test of a tensor's convenience rather than its correctness ". Some scientists also criticized the justifications of the energy–velocity definition and the imposed four-vector covariance in Laue–Møller criterion. Regarding the energy–velocity definition which is given by Poynting vector divided by EM energy density in Laue–Møller criterion, they say "the Poynting vector does not necessarily denote the direction of real power flowing" in a moving medium. Regarding the imposed

text: four-velocity

text: covariance, which was probably prompted by the relativistic velocity addition rule applied to illustrating

text: Fizeau

text: running water experiment, they say "one essential difference between massive particles and photons is that any massive particle has its four-velocity, while the photon (the carrier of EM energy) does not."

text: is the group velocity. For a uniform medium, the group velocity is

text: is the

text: group velocity

text: . For a uniform medium, the group velocity is

text: Unlike the Flash's natural connection to the Speed Force, Johnny Quick from the Crime Syndicate of Amerika receives his powers by injecting himself with an enhancer drug called "Speed Juice". Whether or not Speed Juice has any relationship to Velocity 9 is unknown at this time.

text: Unlike the Flash's natural connection to the

text: Speed Force

text: Johnny Quick

text: from the

text: Crime Syndicate of Amerika

text: receives his powers by injecting himself with an enhancer drug called "Speed Juice". Whether or not Speed Juice has any relationship to Velocity 9 is unknown at this time.

text: Before 1887 it was generally believed that light travelled as a wave at a constant speed relative to the hypothesised medium of the aether. For an observer in motion with respect to the aether, this would result in slightly different two-way speeds of light in different directions. In 1887, the Michelson–Morley experiment showed that the two-way speed of light was constant regardless of direction or motion through the aether. At the time, the obvious explanation for this effect was that objects in motion through the aether experience the combined effects of time dilation and length contraction in the direction of motion.

text: Before 1887 it was generally believed that light travelled as a wave at a constant speed relative to the hypothesised medium of the aether. For an observer in motion with respect to the aether, this would result in slightly different two-way speeds of light in different directions. In 1887, the

text: Michelson–Morley experiment

text: showed that the two-way speed of light was constant regardless of direction or motion through the aether. At the time, the obvious explanation for this effect was that objects in motion through the aether experience the combined effects of time dilation and length contraction in the direction of motion.

text: SFC varies with throttle setting, altitude and climate. For jet engines, flight speed also has a significant effect upon SFC; SFC is roughly proportional to air speed (actually exhaust velocity), but speed along the ground is also proportional to air speed. Since work done is force times distance, mechanical power is force times speed. Thus, although the nominal SFC is a useful measure of fuel efficiency, it should be divided by speed to get a way to compare engines that fly at different speeds.

text: The algorithm integrated for crowd simulation in this approach is the RVO2 library which is a simple but effective model. Aside from the basic information such as the radius and maximum speed of each agent, it only requires the current position and preferred velocity of the agent to simulate one step. This approach adopts a strategy called ORCA (Optimal Reciprocal Collision Avoidance) based on the computation of the velocity obstacles. At each time step, for each agent in the environment, velocity obstacles from other agents are computed. Then, the global optimal solution is then solved by linear programming. However, there is a small problem, the simulation needs information about the preferred velocity of each agent. This is typically done by using a vector with the direction towards the goal position and magnitude equal to the preferred speed. Here, it is not possible to learn about the goal position of each agent until the agent reaches there. Therefore, the velocity is estimated according the historical information. Then using the velocity we have a good chance of predicting the goal position of the agent. This estimation procedure is based on the sampling accelerations from each agent (Using the derivative of velocity). This leads to the problem solution.From conducted simulations, this method of tracking leads to an increase of tracking by 2% to 5% in the MOTP and MOTA metrics, on the UCSD crowd dataset.

text: The algorithm integrated for

text: crowd simulation

text: A diagram called a velocity triangle helps us in determining the flow geometry at the entry and exit of a blade. A minimum number of data are required to draw a velocity triangle at a point on blade. Some component of velocity varies at different point on the blade due to changes in the direction of flow. Hence an infinite number of velocity triangles are possible for a given blade. In order to describe the flow using only two velocity triangles we define mean values of velocity and their direction. Velocity triangle of any turbo machine has three components as shown:

text: Defined a little more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity and end at infinity with a residual speed of zero, without any additional acceleration. All speeds and velocities measured with respect to the field. Additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point. In common usage, the initial point is on the surface of a planet or moon. On the surface of the Earth, the escape velocity is about 11.2 km/s, which is approximately 33 times the speed of sound (Mach 33) and several times the muzzle velocity of a rifle bullet (up to 1.7 km/s). However, at 9,000 km altitude in "space", it is slightly less than 7.1 km/s.

text: Defined a little more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity and end at infinity with a residual speed of zero, without any additional acceleration. All speeds and velocities measured with respect to the field. Additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point. In common usage, the initial point is on the surface of a

text: planet

text: or

text: moon

text: . On the surface of the Earth, the escape velocity is about 11.2 km/s, which is approximately 33 times the

text: speed of sound

text: (Mach 33) and several times the

text: muzzle velocity

text: of a rifle bullet (up to 1.7 km/s). However, at 9,000 km altitude in "space", it is slightly less than 7.1 km/s.

text: Displacement of these peaks away from their known frequencies is called the “echo Doppler shift” and allows one to assess the radial velocity of a surface current. That is; the scatter velocity along the line between the hit surface and the radar. In fact, the magnitude of this component of the velocity is proportional to the degree of signal-shift.Therefore, CODAR measures the Doppler-induced frequency-shift (along with the distance from the radar to the sector and directional angle) to provide an estimate of the radial-component of wave-speed in the sector of sea surface of interest.

text: Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative accelerations.

text: The distance to Tau Ceti, along with its proper motion and radial velocity, allow the motion of the star through space to be calculated. The space velocity relative to the Sun is about .<ref group="nb">The space velocity components are: U = +18; V = +29, and W = +13. This yields a net space velocity of:

text: The distance to Tau Ceti, along with its proper motion and radial velocity, allow the motion of the star through space to be calculated. The

text: space velocity

text: relative to the Sun is about .<ref group="nb">The space velocity components are: U = +18; V = +29, and W = +13. This yields a net space velocity of:

text: is the 4-velocity (4-vector); and

text: is the

text: (4-vector); and

text: Real motion has both direction and velocity and must be represented by a vector. In a coordinate system with  axes, velocity has components  in the  direction,  in the  direction,  in the  direction. The vector is represented by a boldface symbol:

text: Real motion has both direction and velocity and must be represented by a

text: vector

text: . In a coordinate system with  axes, velocity has components  in the  direction,  in the  direction,  in the  direction. The vector is represented by a boldface symbol:

text: The value of the magnitude of an object's four-velocity, i.e. the quantity obtained by applying the metric tensor  to the four-velocity , that is , is always equal to , where  is the speed of light. Whether the plus or minus sign applies depends on the choice of metric signature. For an object at rest its four-velocity is parallel to the direction of the time coordinate with  c}}. A four-velocity is thus the normalized future-directed timelike tangent vector to a world line, and is a contravariant vector. Though it is a vector, addition of two four-velocities does not yield a four-velocity: the space of four-velocities is not itself a vector space.

text: The value of the

text: magnitude

text: of an object's four-velocity, i.e. the quantity obtained by applying the

text: metric tensor

text: to the four-velocity , that is , is always equal to , where  is the

text: speed of light

text: . Whether the plus or minus sign applies depends on the choice of

text: metric signature

text: . For an object at rest its four-velocity is parallel to the direction of the time coordinate with  c}}. A four-velocity is thus the normalized future-directed timelike tangent vector to a world line, and is a

entity_name: Covariance and contravariance of vectors

text: contravariant vector

text: . Though it is a vector, addition of two four-velocities does not yield a four-velocity: the space of four-velocities is not itself a

text: vector space

text: with c the group velocity (m/s).Due to the dispersion relation for water waves under the action of gravity, the group velocity depends on the wavelength λ, or equivalently, on the wave period T. Further, the dispersion relation is a function of the water depth h. As a result, the group velocity behaves differently in the limits of deep and shallow water, and at intermediate depths:

text: with c the group velocity (m/s).Due to the

text: dispersion relation

text: for water waves under the action of gravity, the group velocity depends on the wavelength λ, or equivalently, on the wave

text: period

text: T. Further, the dispersion relation is a function of the water depth h. As a result, the group velocity behaves differently in the limits of deep and shallow water, and at intermediate depths:

text: The big difference can be noticed when we consider movement around a circle. When something moves in a circle and returns to its starting point, its average velocity is zero but its average speed is found by dividing the circumference of the circle by the time taken to move around the circle. This is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled.

text: The big difference can be noticed when we consider movement around a circle. When something moves in a circle and returns to its starting point, its average velocity is zero but its average

text: speed

text: is found by dividing the

text: circumference

text: of the

text: circle

text: by the time taken to move around the

text: circle

text: . This is because the average velocity is calculated by only considering the

text: displacement

text: between the starting and the end points while the average speed considers only the total

text: distance

text: traveled.

text: Bojonegoro has 42-100% of humidity. Maximum humidity is 100% and average humidity is 81%. Bojonegoro has 0-35 km/hr of wind velocity. Maximum wind velocity is at 35 km/h (18.9 knot). Average wind velocity is 30 km/hr (16.2 knot). It has average temperature of 27.1C - 28.2C.

text: The use of vectors allows positions and velocities to be expressed in arbitrary directions compactly. A single boost in any direction depends on the full relative velocity vector  with a magnitude  that cannot equal or exceed , so that .

text: The use of vectors allows positions and velocities to be expressed in arbitrary directions compactly. A single boost in any direction depends on the full relative

text: velocity vector

text: with a magnitude  that cannot equal or exceed , so that .

text: If the velocity of the boat and the velocity and the angle of the apparent wind are known, for instance from a measurement, the true wind velocity and direction can be calculated with:

text: If the velocity of the boat and the velocity and the angle of the apparent wind are known, for instance from a

text: measurement

text: , the true wind velocity and direction can be calculated with:

text: To have a constant velocity, an object must have a constant speed in a constant direction.  Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed.

text: The unit vector e is the radial basis vector of a polar coordinate system in the plane. The velocity vector of the particle is

text: The

text: unit vector

text: e is the radial basis vector of a

text: polar coordinate system

text: in the plane. The

text: velocity

text: vector of the particle is

text: Velocity

text: Velocity

text: Numerous variants of even a basic PSO algorithm are possible. For example, there are different ways to initialize the particles and velocities (e.g. start with zero velocities instead), how to dampen the velocity, only update p and g after the entire swarm has been updated, etc. Some of these choices and their possible performance impact have been discussed in the literature.

text: such that the proper velocity is calculated as the Lorentz transformation of the proper velocity at rest

text: There are three different modes of camera control. Free mode allows movement without inertia, and the user can set a constant velocity to travel when a navigation key is held down. Spacecraft and aircraft modes enable inertia, and the user sets an acceleration rather than a velocity. Users can travel at any velocity they wish, and are not bound by physical limits. The only difference between spacecraft and aircraft mode is that in aircraft mode the direction of motion follows the orientation of the camera.

text: The velocity of the wings is zero both at the beginning and at the end of the wing stroke, meaning the maximum linear velocity is higher than the average velocity. If we assume that the velocity varies sinusoidally along the wing path, the maximum velocity is twice as high as the average velocity. Therefore, the maximum angular velocity is:

text: Uniform circular motion, that is constant speed along a circular path, is an example of a body experiencing acceleration resulting in velocity of a constant magnitude but change of direction. In this case, because the direction of the object's motion is constantly changing, being tangential to the circle, the object's linear velocity vector also changes, but its speed does not. This acceleration is a radial acceleration since it is always directed toward the centre of the circle and takes the magnitude:

text: Uniform

text: circular motion

text: , that is constant speed along a circular path, is an example of a body experiencing acceleration resulting in velocity of a constant magnitude but change of direction. In this case, because the direction of the object's motion is constantly changing, being tangential to the circle, the object's linear

text: velocity

text: vector also changes, but its speed does not. This acceleration is a radial acceleration since it is always directed toward the centre of the circle and takes the magnitude:

text: is called a trajectory. Given the initial positions (e.g., from theoretical knowledge) and velocities (e.g., randomized Gaussian), we can calculate all future (or past) positions and velocities.

text: The undulations form a standing wave pattern, relative to the undular bore front. So, the phase velocity (propagation velocity relative to still water) of the undulations is just high enough to keep the undulations stationary relative to the bore front.  Now, in water waves, the group velocity (which is also the energy-transport velocity) is less than the phase velocity. Therefore, on average, wave energy of the undulations is transported away from the front, and contributing to the energy loss in the region of the front.

text: The undulations form a

text: standing wave

text: pattern, relative to the undular bore front. So, the

text: phase velocity

text: (propagation velocity relative to still water) of the undulations is just high enough to keep the undulations stationary relative to the bore front.  Now, in

text: water wave

text: s, the

text: group velocity

text: (which is also the energy-transport velocity) is less than the

text: phase velocity

text: . Therefore, on average, wave energy of the undulations is transported away from the front, and contributing to the energy loss in the region of the front.

text: Strain rate is the rate of deformation. In ultrasound it is usually measured from the velocity gradient SR = (v - v)L where vand v are the myocardial velocities at two different points, and L is the instantaneous distance between them. This is thus equivalent to the velocity difference per length unit (the spatial derivative of velocity) and has the unit s. Strain is then integrated from strain rate. This method, however, yields the Eulerian strain rate and strain. By tradition it has become traditional to use the Velocity gradient, but in integrating strain rate it is converted to Lagrangian strain by the formula ε = e - 1.

text: Strain rate is the rate of deformation. In ultrasound it is usually measured from the velocity gradient SR = (v - v)L where vand v are the myocardial velocities at two different points, and L is the instantaneous distance between them. This is thus equivalent to the velocity difference per length unit (the spatial derivative of velocity) and has the unit s. Strain is then integrated from strain rate. This method, however, yields the Eulerian strain rate and strain. By tradition it has become traditional to use the

text: Velocity gradient

text: , but in integrating strain rate it is converted to Lagrangian strain by the formula ε = e - 1.

text: It is possible to measure the average kinetic energy of constituent microscopic particles if they are allowed to escape from the bulk of the system. The spectrum of velocities has to be measured, and the average calculated from that. It is not necessarily the case that the particles that escape and are measured have the same velocity distribution as the particles that remain in the bulk of the system, but sometimes a good sample is possible.

text: Cyclorotors can produce lift and thrust at high advance ratios, which, in theory, would enable a cyclogyro aircraft to fly at subsonic speeds well exceeding those of single rotor helicopters. Single rotor helicopters are limited in forward speed by a combination of retreating blade stall and sonic blade tip constraints. As helicopters accelerate, the tip of the advancing blade experiences a wind velocity that is the sum of the helicopter forward speed and rotor rotational speed. This value cannot exceed the speed of sound if the rotor is to be efficient and quiet. Slowing the rotor rotational speed avoids this problem, but presents another disadvantage. If the problem is assumed according to the traditional method of the composition of velocity it easy to understand that the velocity experienced by the retreating blade assumes a value that is produced by the vector composition of two velocities: the velocity of blade rotation and the freestream velocity. In this conditions, it is evident that in presence of a sufficiently high advance ratio the velcity of air on the retreating blade is low. The flapping movement of the blade changes the angle of attach. It is then possible for the blade to reach the stall condition. In this case it is necessary that the stalling blade increases the pitch angle to keep some lift capability. This negative element oblige to focus a particular attention on the accurate design of the system in order to avoid this risk. It is then necessary an accurate choice of the wing profile, a careful dimensioning process of the radius of the rotor for the specific speed range. Slow speed Cyclorotos bypass this problem via a horizontal axis of rotation and operating at comparatively low blade tip speed. For higher speeds which could be necessary for future industrial applications it seems necessary to adopt more sophisticated strategies and solutions. A solution is the independent actuation of the blades which have been recently patented and successfully tested for naval use  by use on hydraulic actuation system. In the aeronautic domain similar solutions appear difficult, because of the necessity of maintaining a low ratio between weight and thrust. One solution has been proposed by the Austrian inventor Meinhard Schwaiger with his turbomachine patent. The horizontal axis of rotation always provides an advancement of the upper blades, that produce always a positive lift by the full rotor. These characteristics could help overcome two issues met on helicopters: the low energy efficiency and the advance ratio limitation.

text: Cyclorotors can produce lift and thrust at high advance ratios, which, in theory, would enable a cyclogyro aircraft to fly at subsonic speeds well exceeding those of single rotor helicopters. Single rotor helicopters are limited in forward speed by a combination of

text: retreating blade stall

text: and sonic blade tip constraints. As helicopters accelerate, the tip of the advancing blade experiences a wind velocity that is the sum of the helicopter forward speed and rotor rotational speed. This value cannot exceed the speed of sound if the rotor is to be efficient and quiet. Slowing the rotor rotational speed avoids this problem, but presents another disadvantage. If the problem is assumed according to the traditional method of the composition of velocity it easy to understand that the velocity experienced by the retreating blade assumes a value that is produced by the vector composition of two velocities: the velocity of blade rotation and the freestream velocity. In this conditions, it is evident that in presence of a sufficiently high

text: advance ratio

text: The four-velocity is the tangent four-vector of a timelike world line.The four-velocity

text: The four-velocity is the tangent four-vector of a

text: timelike

text: world line

text: .The four-velocity

text: is the velocity vector (which should not be confused with four-velocity)

text: is the velocity vector (which should not be confused with

text: four-velocity

text: As most other models made by DHI, MIKE 21C applies an add-on concept in which the overall time-loop can contain processes to be simulated, selected by the user. In its basic form the model is a 2-dimensional hydrodynamic model that can simulate dynamic as well as quasi-steady or steady-state hydrodynamic solutions. The hydrodynamic model solves the Saint-Venant equations in two dimensions with the water depth defined in cell centers and a staggered velocity field (internally the code solves the flux field, i.e. the water depth multiplied by the velocity vector) defined with direction as the local grid base vector.

text: As most other models made by DHI, MIKE 21C applies an add-on concept in which the overall time-loop can contain processes to be simulated, selected by the user. In its basic form the model is a 2-dimensional hydrodynamic model that can simulate dynamic as well as quasi-steady or steady-state hydrodynamic solutions. The

text: hydrodynamic

text: model solves the Saint-Venant equations in two dimensions with the water depth defined in cell centers and a staggered velocity field (internally the code solves the flux field, i.e. the water depth multiplied by the velocity vector) defined with direction as the local grid base vector.

text: -dimensional radius-vector. Similarly, three-dimensional velocity vectors

text: is used. That is, there is no fundamental difference between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-called Fizeau-Doppler formula

text: is used. That is, there is no fundamental difference between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-called

text: Fizeau-Doppler formula

text: One finds . While they are equal in magnitude, there is an angle between them. For a single boost between two inertial frames, there is only one unambiguous relative velocity (or its negative). For two boosts, the peculiar result of two inequivalent relative velocities instead of one seems to contradict the symmetry of relative motion between any two frames. Which is the correct velocity of  relative to ? Since this inequality may be somewhat unexpected and potentially breaking EPVR, this question is warranted.

text: Fluids or gases with controlled velocity pass through a laminar flow reactor in a fashion of laminar flow. That is, streams of fluids or gases slide over each other like cards. When analyzing fluids with the same viscosity ("thickness" or "stickiness") but different velocity, fluids are typically characterized into two types of flows: laminar flow and turbulent flow.  Compared to turbulent flow, laminar flow tends to have a lower velocity and is generally at a lower Reynolds number. Turbulent flow, on the other hand, is irregular and travels at a higher speed. Therefore the flow velocity of a turbulent flow on one cross section is often assumed to be constant, or "flat". The "non-flat" flow velocity of laminar flow helps explain the mechanism of an LFR. For the fluid/gas moving in an LFR, the velocity near the center of the pipe is higher than the fluids near the wall of the pipe.  Thus, the velocity distribution of the reactants tends to decrease from the center to the wall.

text: Fluids or gases with controlled velocity pass through a laminar flow reactor in a fashion of

text: laminar flow

text: . That is, streams of fluids or gases slide over each other like cards. When analyzing fluids with the same

text: viscosity

text: ("thickness" or "stickiness") but different velocity, fluids are typically characterized into two types of flows:

text: laminar flow

text: and

text: turbulent flow

text: .  Compared to turbulent flow, laminar flow tends to have a lower velocity and is generally at a lower

text: Reynolds number

text: . Turbulent flow, on the other hand, is irregular and travels at a higher speed. Therefore the

text: flow velocity

text: of a turbulent flow on one cross section is often assumed to be constant, or "flat". The "non-flat" flow velocity of laminar flow helps explain the mechanism of an LFR. For the fluid/gas moving in an LFR, the velocity near the center of the pipe is higher than the fluids near the wall of the pipe.  Thus, the velocity distribution of the reactants tends to decrease from the center to the wall.

text: In addition to providing increased adhesion, car aerodynamics are frequently designed to compensate for the inherent increase in oversteer as cornering speed increases. When a car corners, it must rotate about its vertical axis as well as translate its center of mass in an arc. However, in a tight-radius (lower speed) corner the angular velocity of the car is high, while in a longer-radius (higher speed) corner the angular velocity is much lower. Therefore, the front tires have a more difficult time overcoming the car's moment of inertia during corner entry at low speed, and much less difficulty as the cornering speed increases. So the natural tendency of any car is to understeer on entry to low-speed corners and oversteer on entry to high-speed corners. To compensate for this unavoidable effect, car designers often bias the car's handling toward less corner-entry understeer (such as by lowering the front roll center), and add rearward bias to the aerodynamic downforce to compensate in higher-speed corners. The rearward aerodynamic bias may be achieved by an airfoil or "spoiler" mounted near the rear of the car, but a useful effect can also be achieved by careful shaping of the body as a whole, particularly the aft areas.

text: In addition to providing increased adhesion, car aerodynamics are frequently designed to compensate for the inherent increase in oversteer as cornering speed increases. When a car corners, it must rotate about its vertical axis as well as translate its

text: center of mass

text: in an arc. However, in a tight-radius (lower speed) corner the

text: angular velocity

text: of the car is high, while in a longer-radius (higher speed) corner the

text: angular velocity

text: is much lower. Therefore, the front tires have a more difficult time overcoming the car's

text: moment of inertia

text: during corner entry at low speed, and much less difficulty as the cornering speed increases. So the natural tendency of any car is to understeer on entry to low-speed corners and oversteer on entry to high-speed corners. To compensate for this unavoidable effect, car designers often bias the car's handling toward less corner-entry understeer (such as by lowering the front

text: roll center

text: ), and add rearward bias to the aerodynamic downforce to compensate in higher-speed corners. The rearward aerodynamic bias may be achieved by an airfoil or "spoiler" mounted near the rear of the car, but a useful effect can also be achieved by careful shaping of the body as a whole, particularly the aft areas.

text: is a scalar of the electron thermal velocity vector

text: To understand the aberration effect, again imagine two people playing catch on two parallel conveyor belts (moving sidewalks) moving in opposite direction. The pitcher must aim differently depending on the speed and the spacing of the belts, and where the catcher is.   The catcher will see the balls coming at a different angle than the pitcher chose to throw them.  These angle changes depend on: 1) the instantaneous angle between the pitcher-catcher line and the relative velocity vector, and 2) the pitcher-catcher velocity relative to the speed of the ball. By analogy, the aberration of light depends on: 1) the instantaneous angle between the emitter-observer line and the relative velocity vector, and 2) the emitter-observer velocity relative to the speed of light.

text: . The velocity vector is:

text: . The velocity vector is:

text: Medieval navigation relied on two parameters, direction and distance.  On board ship, direction was determined by the mariner's compass (which emerged around 1300).  Distance was measured by dead reckoning, (i.e., distance = speed × time), where time was measured by a half-hour-glass, and speed readings were taken with by some form of a chip log (the archaic method, used in the 14th and 15th centuries, involved heaving a piece of wood or flotsam overboard; the crew engaged in a rhythmic chant to mark the time it took for the chip to float past the length of the ship).

text: Medieval navigation relied on two parameters, direction and distance.  On board ship, direction was determined by the

text: mariner's compass

text: (which emerged around 1300).  Distance was measured by

text: dead reckoning

text: , (i.e., distance = speed × time), where time was measured by a half-

text: hour-glass

text: , and speed readings were taken with by some form of a

text: chip log

text: (the archaic method, used in the 14th and 15th centuries, involved heaving a piece of wood or flotsam overboard; the crew engaged in a rhythmic chant to mark the time it took for the chip to float past the length of the ship).

text: In those instances where a velocity measurement is additionally used as a surrogate, an index velocity determination is conducted.  This analysis uses a velocity sensor, often either magnetic or acoustic, to measure the velocity of the flow at a particular location in the stream cross section.  Once again, discrete measurements of streamflow discharge are made by the technician or hydrologist at a variety of stages.  For each discrete determination of streamflow discharge, the mean velocity of the cross section is determined by dividing streamflow discharge by the cross-sectional area.  A rating curve, similar to that used for stage-discharge determinations, is constructed using the mean velocity and the index velocity from the permanently mounted meter.  An additional rating curve is constructed that relates stage of the stream to cross-sectional area.  Using these two ratings, the automatically collected stage produces an estimate of the cross-sectional area, and the automatically collected index velocity produces an estimate of the mean velocity of the cross section.  The streamflow discharge is computed as the estimate of the cross section area and the estimate of the mean velocity of the streamflow.

text: In those instances where a velocity measurement is additionally used as a surrogate, an index velocity determination is conducted.  This analysis uses a velocity sensor, often either magnetic or acoustic, to measure the velocity of the flow at a particular location in the stream cross section.  Once again, discrete measurements of streamflow discharge are made by the technician or hydrologist at a variety of stages.  For each discrete determination of streamflow discharge, the mean velocity of the cross section is determined by dividing streamflow discharge by the cross-sectional area.  A rating curve, similar to that used for stage-discharge determinations, is constructed using the mean velocity and the index velocity from the permanently mounted meter.  An additional rating curve is constructed that relates stage of the stream to cross-sectional area.  Using these two ratings, the automatically collected stage produces an estimate of the cross-sectional area, and the automatically collected index velocity produces an estimate of the mean velocity of the

text: cross section

text: .  The streamflow discharge is computed as the estimate of the cross section area and the estimate of the mean velocity of the streamflow.

text: In terms of a displacement-time (x vs. t) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the slope of the tangent line to the curve at any point, and the average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity.

text: In terms of a displacement-time (x vs. t) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the

text: slope of the tangent line to the curve at any point

text: , and the average velocity as the slope of the

text: secant line

text: between two points with t coordinates equal to the boundaries of the time period for the average velocity.

text: This gives us the velocity of the aircraft right after it takes off. Because we know all forces acting on it from this point on, we can calculate net acceleration using Newton's second law. Given the velocity that the aircraft takes off with and the acceleration at any point, the velocity can also be calculated at any given point.

text: This gives us the velocity of the aircraft right after it takes off. Because we know all forces acting on it from this point on, we can calculate net acceleration using

text: Newton's second law

text: . Given the velocity that the aircraft takes off with and the acceleration at any point, the velocity can also be calculated at any given point.

text: Equation 2 can be solved for the velocity of water in terms of the difference in pressure between the two legs of the manometer. Equation 3 shows that velocity is a function of the square root of the pressure difference.

text: Better, more costly electronic keyboards, called touch sensitive or velocity sensitive keyboards, have two switches for each key, which close at different times in the key's travel. Determining the timing between the activation of the two switches gives the velocity of a key press, which the keyboard's electronics can use to produce softer sounds for soft touches and louder sounds for hard touches. In this way, an electronic keyboard can imitate the touch sensitive dynamics of a real acoustic instrument.

text: Wind direction is usually expressed in terms of the direction from which it originates. For example, a northerly wind blows from the north to the south. Weather vanes pivot to indicate the direction of the wind. At airports, windsocks indicate wind direction, and can also be used to estimate wind speed by the angle of hang. Wind speed is measured by anemometers, most commonly using rotating cups or propellers. When a high measurement frequency is needed (such as in research applications), wind can be measured by the propagation speed of ultrasound signals or by the effect of ventilation on the resistance of a heated wire. Another type of anemometer uses pitot tubes that take advantage of the pressure differential between an inner tube and an outer tube that is exposed to the wind to determine the dynamic pressure, which is then used to compute the wind speed.

text: Wind direction

text: is usually expressed in terms of the direction from which it originates. For example, a northerly wind blows from the north to the south.

text: Weather vane

text: s pivot to indicate the direction of the wind. At airports,

text: windsock

text: s indicate wind direction, and can also be used to estimate wind speed by the angle of hang. Wind speed is measured by

text: anemometer

text: s, most commonly using rotating cups or propellers. When a high measurement frequency is needed (such as in research applications), wind can be measured by the propagation speed of

text: ultrasound

text: signals or by the effect of ventilation on the resistance of a heated wire. Another type of anemometer uses

text: pitot tube

text: s that take advantage of the pressure differential between an inner tube and an outer tube that is exposed to the wind to determine the dynamic pressure, which is then used to compute the wind speed.

text: The ball's direction and speed can be controlled by the paddle's velocity and point of contact. Changing direction the moment the ball comes into contact with the paddle, called a snap technique, will bounce the ball upward with increased speed. Moving the paddle quickly in the opposite direction than the ball is headed will result in the ball bouncing in the same horizontal direction as the paddle at a 15° angle. If the player contacts the ball with the body of the paddle before it falls into the pit below, it will bounce back into the playing field. However, if instead either corner of the paddle collides with the ball at that moment, it will be knocked directly into the pit.

text: The book reconstructs theoretical frameworks originally used in building up the concept of a field.  It shows that the field of Faraday's electricity and the field of Einstein's relativity are distinct; although both make different assumptions about physical reality, Berkson suggests that the assumptions of either conception of the field still remain as plausible today as when first conceived. These separate field theories share at least one significant and testable difference in comparison with Newtonian physics: whereas Newton's action-at-a-distance occurs instantaneously, the field theories predict a propagation delay. Berkson explains that Faraday's prediction of a physically measurable propagation delay (finite velocity) from his own conception of a physical field permeating space is one important difference separating this idea from that of Newton's (infinite velocity).

text: The book reconstructs theoretical frameworks originally used in building up the concept of a field.  It shows that the field of

text: Faraday

text: 's electricity and the field of

text: Einstein

text: 's relativity are distinct; although both make different assumptions about physical reality, Berkson suggests that the assumptions of either conception of the field still remain as plausible today as when first conceived. These separate field theories share at least one significant and testable difference in comparison with Newtonian physics: whereas Newton's

text: action-at-a-distance occurs instantaneously

text: , the field theories predict a propagation delay. Berkson explains that Faraday's prediction of a physically measurable propagation delay (finite velocity) from his own conception of a physical field permeating space is one important difference separating this idea from that of

text: Newton

text: 's (infinite velocity).

text: The layering of Earth has been inferred indirectly using the time of travel of refracted and reflected seismic waves created by earthquakes.  The core does not allow shear waves to pass through it, while the speed of travel (seismic velocity) is different in other layers.  The changes in seismic velocity between different layers causes refraction owing to Snell's law, like light bending as it passes through a prism.  Likewise, reflections are caused by a large increase in seismic velocity and are similar to light reflecting from a mirror.

text: The layering of Earth has been inferred indirectly using the time of travel of refracted and reflected seismic waves created by earthquakes.  The core does not allow shear waves to pass through it, while the speed of travel (

text: seismic velocity

text: ) is different in other layers.  The changes in seismic velocity between different layers causes refraction owing to

text: Snell's law

text: , like light bending as it passes through a prism.  Likewise, reflections are caused by a large increase in seismic velocity and are similar to light reflecting from a mirror.

text: The velocity vector

text: The velocity vector

text: The piano, being velocity-sensitive, responds to the speed of the key-press in how fast the hammers strike the strings, which in turn changes the tone and volume of the sound. Several piano predecessors, such as the harpsichord, were not velocity-sensitive like the piano. Some confuse pressure-sensitive with velocity-sensitive. To avoid this confusion, pressure sensitivity is often, perhaps usually, called aftertouch. The MIDI standard supports both velocity and aftertouch.

text: The

text: piano

text: , being velocity-sensitive, responds to the speed of the key-press in how fast the hammers strike the strings, which in turn changes the tone and volume of the sound. Several piano predecessors, such as the

text: harpsichord

text: , were not velocity-sensitive like the piano. Some confuse pressure-sensitive with velocity-sensitive. To avoid this confusion, pressure sensitivity is often, perhaps usually, called aftertouch. The

text: MIDI

text: standard supports both velocity and aftertouch.

text: The phase velocity of an electromagnetic wave, when traveling through a medium, can routinely exceed c, the vacuum velocity of light. For example, this occurs in most glasses at X-ray frequencies. However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely monochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information.Thus a phase velocity above c does not imply the propagation of signals with a velocity above c.

text: The

text: phase velocity

text: of an

text: electromagnetic wave

text: , when traveling through a medium, can routinely exceed c, the vacuum velocity of light. For example, this occurs in most glasses at

text: X-ray

text: frequencies. However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely

text: monochromatic

text: ) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information.Thus a phase velocity above c does not imply the propagation of

text: signals

text: with a velocity above c.

text: Around 1900, Paul Drude developed the foundation for classical conduction. He reasoned that since metals conduct electricity so well, they must contain free electrons that move through a lattice of positive ions. This motion of electrons led to the formation of Ohm's laws, as well as related the motion in a conductor to two types of conduction: heat and electrical.  The free-moving electrons act just as a gas would; moving in every direction throughout the lattice. These electrons collide with the lattice ions as they move about, which is key in understanding thermal equilibrium. The average velocity due to the thermal energy is zero since the electrons are going in every direction, leading to velocity vectors that are randomly oriented. What is not zero, and is in fact a high value, is the speed of these electrons, which can be calculated using the equation

text: Around 1900,

text: Paul Drude

text: developed the foundation for classical conduction. He reasoned that since metals conduct

text: electricity

text: so well, they must contain free electrons that move through a lattice of positive ions. This motion of electrons led to the formation of

text: Ohm's law

text: s, as well as related the motion in a

text: conductor

text: to two types of conduction:

text: heat

text: and

text: electrical

text: .  The free-moving electrons act just as a gas would; moving in every direction throughout the lattice. These electrons collide with the lattice ions as they move about, which is key in understanding

text: thermal equilibrium

text: . The average velocity due to the thermal energy is zero since the electrons are going in every direction, leading to velocity vectors that are randomly oriented. What is not zero, and is in fact a high value, is the speed of these electrons, which can be calculated using the equation

text: More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel, and the average Eulerian flow velocity of the fluid at a fixed position. This nonlinear phenomenon is named after George Gabriel Stokes, who derived expressions for this drift in his 1847 study of water waves.

text: More generally, the Stokes drift velocity is the difference between the

text: average

entity_name: Lagrangian and Eulerian specification of the flow field

text: Lagrangian

text: flow velocity

text: of a fluid parcel, and the average

text: Eulerian

text: flow velocity

text: of the

text: fluid

text: at a fixed position. This

text: nonlinear

text: phenomenon is named after

text: George Gabriel Stokes

text: , who derived expressions for this drift in

text: his 1847 study

text: of

text: water waves

text: and is calculating the divergence of the velocity.

text: and is calculating the

text: divergence

text: of the velocity.

text: is known as the group velocity and corresponds to the speed at which the peak of the pulse  propagates, a value different from the phase velocity.

text: is known as the

text: group velocity

text: and corresponds to the speed at which the peak of the pulse  propagates, a value different from the

text: phase velocity

text: The spindle motor speed can use one of two types of disk rotation methods: 1) constant linear velocity (CLV), used mainly in optical storage, varies the rotational speed of the optical disc depending upon the position of the head, and 2) constant angular velocity (CAV), used in HDDs, standard FDDs, a few optical disc systems, and vinyl audio records, spins the media at one constant speed regardless of where the head is positioned.

text: The spindle motor speed can use one of two types of disk rotation methods: 1)

text: constant linear velocity

text: (CLV), used mainly in optical storage, varies the rotational speed of the optical disc depending upon the position of the head, and 2)

text: constant angular velocity

text: (CAV), used in HDDs, standard FDDs, a few optical disc systems, and

text: vinyl audio records

text: , spins the media at one constant speed regardless of where the head is positioned.

text: A barycentric velocity is a velocity of one body relative to the center of mass of a system of bodies. A relative velocity is the velocity of one body with respect to another. Relative escape velocity is defined only in systems with two bodies. For systems of two bodies the term "escape velocity" is ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. In gravitational fields "escape velocity" refers to the escape velocity of zero mass test particles relative to the barycenter of the masses generating the field.

text: A

text: barycentric

text: velocity is a velocity of one body relative to the center of mass of a system of bodies. A

text: relative velocity

text: is the velocity of one body with respect to another. Relative escape velocity is defined only in systems with two bodies. For systems of two bodies the term "escape velocity" is ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. In gravitational fields "escape velocity" refers to the escape velocity of zero mass

text: test particles

text: relative to the barycenter of the masses generating the field.

text: Though it just a particular case of a moving particle, this is a very important one for its relationship with the rigid body study, and special tools have been developed for this case. There are two possible ways to describe the angular velocity of a rotating frame: the angular velocity vector and the angular velocity tensor. Both entities are related and they can be calculated from each other.

text: Though it just a particular case of a moving particle, this is a very important one for its relationship with the

text: rigid body

text: study, and special tools have been developed for this case. There are two possible ways to describe the angular velocity of a rotating frame: the angular velocity vector and the angular velocity tensor. Both entities are related and they can be calculated from each other.

text: As in sonic booms and bow shocks, the angle of the shock cone is directly related to the velocity of the disruption. The Cherenkov angle is zero at the threshold velocity for the emission of Cherenkov radiation. The angle takes on a maximum as the particle speed approaches the speed of light. Hence, observed angles of incidence can be used to compute the direction and speed of a Cherenkov radiation-producing charge.

text: As in sonic booms and bow shocks, the angle of the shock

text: cone

text: is directly related to the velocity of the disruption. The Cherenkov angle is zero at the threshold velocity for the emission of Cherenkov radiation. The angle takes on a maximum as the particle speed approaches the speed of light. Hence, observed angles of incidence can be used to compute the direction and speed of a Cherenkov radiation-producing charge.

text: The phase velocity and group velocity found from the dispersion relation predict the unusual property that they are perpendicular and that the vertical components of the phase and group velocities have opposite sign: if a wavepacket moves upward to the right, the crests move downward to the right.

text: The

text: phase velocity

text: and

text: group velocity

text: found from the dispersion relation predict the unusual property that they are perpendicular and that the vertical components of the phase and group velocities have opposite sign: if a wavepacket moves upward to the right, the crests move downward to the right.

text: Mickeys per second is a unit of measurement for the speed and movement direction of a computer mouse, where direction is often expressed as "horizontal" versus "vertical" mickey count.  However, speed can also refer to the ratio between how many pixels the cursor moves on the screen and how far the mouse moves on the mouse pad, which may be expressed as pixels per mickey, pixels per inch, or pixels per centimeter.

text: Mickeys per second is a unit of measurement for the speed and movement direction of a computer mouse, where direction is often expressed as "horizontal" versus "vertical" mickey count.  However, speed can also refer to the ratio between how many pixels the cursor moves on the screen and how far the mouse moves on the mouse pad, which may be expressed as

text: pixels

text: per mickey,

text: pixels

text: per

text: inch

text: , or pixels per

text: centimeter

text: It was shown above that even if a displacement field is objective, the velocity field is not. An objective vector

text: Velocity of the football is dependent on both the velocity of the foot upon contact as well as the quality of contact between the foot and the ball. The most effective way to transfer speed to the ball is to hit the ball at its center point with the upper portion of the foot, keeping the ankle firm.

text: Velocity

text: of the

text: football

text: is dependent on both the velocity of the foot upon contact as well as the quality of contact between the foot and the ball. The most effective way to transfer speed to the ball is to hit the ball at its center point with the upper portion of the foot, keeping the ankle firm.

text: The average velocity is the same as the velocity averaged over time – that is to say, its time-weighted average, which may be calculated as the time integral of the velocity:

text: The velocity of the siphon is thus driven solely by the height difference between the surface of the upper reservoir and the drain point. The height of the intermediate high point, h, does not affect the velocity of the siphon. However, as the siphon is a single system, v = v and the intermediate high point does limit the maximum velocity. The drain point cannot be lowered indefinitely to increase the velocity. Equation 3 will limit the velocity to a positive pressure at the intermediate high point to prevent cavitation. The maximum velocity may be calculated by combining equations 1 and 3:

text: The velocity of the siphon is thus driven solely by the height difference between the surface of the upper reservoir and the drain point. The height of the intermediate high point, h, does not affect the velocity of the siphon. However, as the siphon is a single system, v = v and the intermediate high point does limit the maximum velocity. The drain point cannot be lowered indefinitely to increase the velocity. Equation 3 will limit the velocity to a positive pressure at the intermediate high point to prevent

text: cavitation

text: . The maximum velocity may be calculated by combining equations 1 and 3:

text: The term  is the decrement of the real part of the refractive index, and the imaginary part  describes the absorption index or extinction coefficient.Note that in contrast to optical light, the real part of the refractive index is less than but close to unity, this is "due to the fact that the X-ray spectrum generally lies to the high-frequency side of various resonances associated with the binding of electrons". The phase velocity inside of the object is larger than the velocity of light c. This leads to a different behavior of X-rays in a medium compared to visible light (e.g. refractive angles have negative values) but does not contradict the law of relativity, "which requires that only signals carrying information do not travel faster than c. Such signals move with the group velocity, not with the phase velocity, and it can be shown that the group velocity is in fact less than c."

text: The term  is the decrement of the real part of the refractive index, and the imaginary part  describes the absorption index or extinction coefficient.Note that in contrast to optical light, the real part of the refractive index is less than but close to unity, this is "due to the fact that the X-ray spectrum generally lies to the high-frequency side of various resonances associated with the binding of electrons". The

text: phase velocity

text: inside of the object is larger than the

text: velocity of light

text: c. This leads to a different behavior of X-rays in a medium compared to visible light (e.g. refractive angles have negative values) but does not contradict the

text: law of relativity

text: , "which requires that only signals carrying information do not travel faster than c. Such signals move with the

text: group velocity

text: , not with the phase velocity, and it can be shown that the group velocity is in fact less than c."

text: The space velocity components of this star are U = +77.2, V = -99.5 and W = -35.6 km/s. It is orbiting through the Milky Way galaxy with an orbital eccentricity of 0.45, and a distance from the galactic core that varies from 3,510 to 9,150 parsecs. By comparison, the Sun is currently 8,500 parsecs from the core. Stars with high peculiar velocities are termed runaway stars. This star has a high peculiar velocity of 111.3 km/s, and the velocity vector for this star may link it with the Tucana-Horologium and/or the AB Doradus stellar associations.

text: The

text: space velocity

text: components of this star are U = +77.2, V = -99.5 and W = -35.6 km/s. It is orbiting through the

text: Milky Way

text: galaxy with an

text: orbital eccentricity

text: of 0.45, and a distance from the galactic core that varies from 3,510 to 9,150 parsecs. By comparison, the Sun is currently 8,500 parsecs from the core. Stars with high

text: peculiar velocities

text: are termed

text: runaway star

text: s. This star has a high peculiar velocity of 111.3 km/s, and the velocity vector for this star may link it with the Tucana-Horologium and/or the

text: AB Doradus

text: stellar association

text: s.

text: The manufacturer recommends the use of hirudin as anticoagulant for samples to be tested, but studies have shown that heparin is a good alternative. 300 µL of blood is needed for each analysis, and is diluted with the same amount of saline. After pipetting blood and saline into the cuvette, the test is incubated for three minutes before the chosen agonist is added. The test is then started, and platelet aggregation is recorded at approximately 0.5 second intervals for six minutes. Three parameters are calculated: aggregation, velocity and area under the curve (AUC). Aggregation (in AU) is the maximum height of the aggregation curve, and velocity (in AU/min) is the maximum slope of the curve. AUC is the most important parameter. It is recorded in Units (U), and is affected by both the height and the slope of the aggregation curve, and is the best overall measure of platelet activity.

text: The manufacturer recommends the use of

text: hirudin

text: as

text: anticoagulant

text: for samples to be tested, but studies have shown that

text: heparin

text: is a good alternative. 300 µL of blood is needed for each analysis, and is

text: diluted

text: with the same amount of

text: saline

text: . After

text: pipetting

text: blood and saline into the cuvette, the test is

text: incubated

text: for three minutes before the chosen agonist is added. The test is then started, and platelet aggregation is recorded at approximately 0.5 second intervals for six minutes. Three parameters are calculated:

text: aggregation

text: velocity

text: and

text: area under the curve

text: (AUC). Aggregation (in AU) is the

text: maximum

text: height

text: of the aggregation

text: curve

text: , and velocity (in AU/min) is the maximum

text: slope

text: of the curve. AUC is the most important

text: parameter

text: . It is recorded in Units (U), and is affected by both the height and the slope of the aggregation curve, and is the best overall measure of platelet activity.

text: They supersede the Galilean transformation of Newtonian physics, which assumes an absolute space and time (see Galilean relativity). The Galilean transformation is a good approximation only at relative speeds much smaller than the speed of light. Lorentz transformations have a number of unintuitive features that do not appear in Galilean transformations. For example, they reflect the fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events, but always such that the speed of light is the same in all inertial reference frames. The invariance of light speed is one of the postulates of special relativity.

text: They supersede the

text: Galilean transformation

text: of

text: Newtonian physics

text: , which assumes an absolute space and time (see

text: Galilean relativity

text: ). The Galilean transformation is a good approximation only at relative speeds much smaller than the speed of light. Lorentz transformations have a number of unintuitive features that do not appear in Galilean transformations. For example, they reflect the fact that observers moving at different

text: velocities

text: may measure different

text: distances

text: elapsed times

text: , and even different

text: orderings of events

text: , but always such that the

text: speed of light

text: is the same in all inertial reference frames. The invariance of light speed is one of the

text: postulates of special relativity

text: The simplest but still a relatively new method is to measure the acoustic particle velocity using a particle velocity probe. The particle velocity is a vector and thus also contains directional information.

text: The simplest but still a relatively new method is to measure the acoustic particle velocity using a

text: particle velocity probe

text: . The particle velocity is a

text: vector

text: and thus also contains directional information.

text: The velocity of particular locations within the thin shell of the Homunculus lobes can be measured using the doppler shift of the spectral lines at that point, assuming the lobes are symmetrical.  There are two different doppler shifts visible in the spectrum: one for direct emission lines; and one for reflected lines from Eta Carinae A.  The direct line doppler shift gives the expansion velocity of the shell project onto the line of sight.  Assuming an origin in Eta Carinae's Great Eruption and a constant expansion velocity, this gives the linear distance of the shell from the central star projected along the line of sight.  The difference between the reflected line doppler shift velocity and the direct line velocity gives the actual (i.e. not projected) distance of the shell from the central star, again assuming expansion at constant velocity since the Great Eruption.

text: The velocity of particular locations within the thin shell of the Homunculus lobes can be measured using the

text: doppler shift

text: of the spectral lines at that point, assuming the lobes are symmetrical.  There are two different doppler shifts visible in the spectrum: one for direct emission lines; and one for reflected lines from Eta Carinae A.  The direct line doppler shift gives the expansion velocity of the shell project onto the line of sight.  Assuming an origin in Eta Carinae's Great Eruption and a constant expansion velocity, this gives the linear distance of the shell from the central star projected along the line of sight.  The difference between the reflected line doppler shift velocity and the direct line velocity gives the actual (i.e. not projected) distance of the shell from the central star, again assuming expansion at constant velocity since the Great Eruption.

text: The relative velocity is constant:

text: The relative velocity is constant:

text: and the weighted average velocity,

text: and the weighted average velocity,

text: Unlike the more familiar coordinate velocity v, proper velocity is synchrony-free (does not require synchronized clocks) and is useful for describing both super-relativistic and sub-relativistic motion.  Like coordinate velocity and unlike four-vector velocity, it resides in the three-dimensional slice of spacetime defined by the map frame.  As shown below and in the example figure at right, proper-velocities even add as three vectors with rescaling of the out-of-frame component. This makes them more useful for map-based (e.g. engineering) applications, and less useful for gaining coordinate-free insight.  Proper speed divided by lightspeed c is the hyperbolic sine of rapidity η, just as the Lorentz factor γ is rapidity's hyperbolic cosine, and coordinate speed v over lightspeed is rapidity's hyperbolic tangent.

text: Unlike the more familiar coordinate velocity v, proper velocity is synchrony-free (does not require synchronized clocks) and is useful for describing both super-relativistic and sub-relativistic motion.  Like coordinate velocity and unlike four-vector velocity, it resides in the three-dimensional slice of spacetime defined by the map frame.  As shown below and in the example figure at right, proper-velocities even add as three vectors with rescaling of the out-of-frame component. This makes them more useful for map-based (e.g. engineering) applications, and less useful for gaining coordinate-free insight.  Proper speed divided by lightspeed c is the

text: hyperbolic sine

text: of rapidity η, just as the Lorentz factor γ is rapidity's hyperbolic cosine, and coordinate speed v over lightspeed is rapidity's hyperbolic tangent.

text: }}, then the group velocity and phase velocity are different. The envelope of a wave packet (see figure on right) will travel at the group velocity, while the individual peaks and troughs within the envelope will move at the phase velocity.

text: }}, then the group velocity and phase velocity are different. The envelope of a

text: wave packet

text: (see figure on right) will travel at the group velocity, while the individual peaks and troughs within the envelope will move at the phase velocity.

text: Velocity (also called linear velocity) and angular velocity are measured with respect to a frame of reference.

text: Velocity

text: (also called linear velocity) and

text: angular velocity

text: are measured with respect to a

text: frame of reference

text: is the difference inthe group velocity and

text: The acoustoelastic effect describes how the sound velocities (both longitudinal and shear wave velocities) of an elastic material change if subjected to an initial static stress field. This is a non-linear effect of the constitutive relation between mechanical stress and finite strain in a material of continuous mass. In classical linear elasticity theory small deformations of most elastic materials can be described by a linear relation between the applied stress and the resulting strain. This relationship is commonly known as the generalised Hooke's law. The linear elastic theory involves second order elastic constants (e.g.  and  ) and yields constant longitudinal and shear sound velocities in an elastic material, not affected by an applied stress. The acoustoelastic effect on the other hand include higher order expansion of the constitutive relation (non-linear elasticity theory) between the applied stress and resulting strain, which yields longitudinal and shear sound velocities dependent of the stress state of the material. In the limit of an unstressed material the sound velocities of the linear elastic theory are reproduced.

text: The acoustoelastic effect describes how the

text: sound velocities

text: (both

text: longitudinal

text: and

text: shear

text: wave velocities) of an

text: elastic material

text: change if subjected to an initial static

text: stress

text: field. This is a non-linear effect of the

text: constitutive relation

text: between

text: mechanical stress

text: and

text: finite strain

text: in a

text: material of continuous mass

text: . In classical

text: linear elasticity

text: theory small deformations of most elastic materials can be described by a linear relation between the applied stress and the resulting strain. This relationship is commonly known as the generalised

text: Hooke's law

text: . The linear elastic theory involves second order

text: elastic constants

text: (e.g.

text: and

text: ) and yields constant longitudinal and shear sound velocities in an elastic material, not affected by an applied stress. The acoustoelastic effect on the other hand include higher order expansion of the constitutive relation (non-linear elasticity theory) between the applied stress and resulting strain, which yields longitudinal and shear sound velocities dependent of the stress state of the material. In the limit of an unstressed material the sound velocities of the linear elastic theory are reproduced.

text: If an object A is moving with velocity vector v and an object B with velocity vector w, then the velocity of object A relative to object B is defined as the difference of the two velocity vectors:

text: If an object A is moving with velocity

text: vector

text: v and an object B with velocity vector w, then the velocity of object A relative to object B is defined as the difference of the two velocity vectors:

text: where dP is the differential change in pressure, M is the Mach number, ρ is the density of the gas, V is the velocity of the flow, A is the area of the duct, and dA is the change in area of the duct. This equation states that, for subsonic flow, a converging duct (dA<0) increases the velocity of the flow and a diverging duct (dA>0) decreases velocity of the flow. For supersonic flow, the opposite occurs due to the change of sign of (1-M). A converging duct (dA<0) now decreases the velocity of the flow and a diverging duct (dA>0) increases the velocity of the flow. At Mach = 1, a special case occurs in which the duct area must be either a maximum or minimum. For practical purposes, only a minimum area can accelerate flows to Mach 1 and beyond. See table of sub-supersonic diffusers and nozzles.

text: Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.

text: Vectors play an important role in

text: physics

text: : the

text: velocity

text: and

text: acceleration

text: of a moving object and the

text: force

text: s acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example,

text: position

text: or

text: displacement

text: ), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the

text: coordinate system

text: used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include

text: pseudovector

text: s and

text: tensor

text: s.

text: The zonal (x-direction) phase speed and group velocity of the Rossby wave are then given by

text: The zonal (x-direction)

text: phase speed

text: and

text: group velocity

text: of the Rossby wave are then given by

text: The Milky Way is moving with respect to the cosmic microwave background radiation (CMB) in the direction of the constellation Hydra with a speed of 550 km/s, and the Sun's resultant velocity with respect to the CMB is about 370 km/s in the direction of Crater or Leo.

text: The Milky Way is moving with respect to the

text: cosmic microwave background radiation

text: (CMB) in the direction of the constellation

text: Hydra

text: with a speed of 550 km/s, and the Sun's resultant velocity with respect to the CMB is about 370 km/s in the direction of

text: Crater

text: or

text: Leo

text: The CNGS measurements also became important when the OPERA group announced in September and November 2011, that they have measured superluminal neutrinos (see faster-than-light neutrino anomaly). Shortly afterwards, the ICARUS collaboration published a paper in which they argued, that the energy distribution of the neutrinos is not compatible with superluminal particles. This conclusion was based on a theory of Cohen and Sheldon Lee Glashow.In March 2012, they published a direct neutrino velocity measurement based on seven neutrinos events. The result was in agreement with the speed of light and thus special relativity, and contradicts the OPERA result. In August 2012, another neutrino velocity measurement based on 25 neutrino events was published with increased accuracy and statistics, again in agreement with the speed of light, see measurements of neutrino speed.

text: The CNGS measurements also became important when the OPERA group announced in September and November 2011, that they have measured

text: superluminal

text: neutrinos (see

text: faster-than-light neutrino anomaly

text: ). Shortly afterwards, the ICARUS collaboration published a paper in which they argued, that the energy distribution of the neutrinos is not compatible with superluminal particles. This conclusion was based on a theory of Cohen and

text: Sheldon Lee Glashow

text: .In March 2012, they published a direct neutrino velocity measurement based on seven neutrinos events. The result was in agreement with the speed of light and thus special relativity, and contradicts the OPERA result. In August 2012, another neutrino velocity measurement based on 25 neutrino events was published with increased accuracy and statistics, again in agreement with the speed of light, see

text: measurements of neutrino speed

text: will be incorrectly calculated as moving in the opposite direction.  However, there is a direct trade-off between the maximum velocity that can be encoded and the signal-to-noise ratio of the velocity measurements. This can be described by:

text: will be incorrectly calculated as moving in the opposite direction.  However, there is a direct trade-off between the maximum velocity that can be encoded and the

text: signal-to-noise ratio

text: of the velocity measurements. This can be described by:

text: As an example of the velocity changes involved, a spacecraft travelling from low Earth orbit to Mars using a simple trajectory must first undergo a change in speed (also known as a delta-v), in this case an increase, of about 3.8 km/s. Then, after intercepting Mars, it must change its speed by another 2.3 km/s in order to match Mars' orbital speed around the Sun and enter an orbit around it. For comparison, launching a spacecraft into low Earth orbit requires a change in speed of about 9.5 km/s.

text: As an example of the velocity changes involved, a spacecraft travelling from low Earth orbit to Mars using a simple trajectory must first undergo a change in speed (also known as a

text: delta-v

text: ), in this case an increase, of about 3.8 km/s. Then, after intercepting Mars, it must change its speed by another 2.3 km/s in order to match Mars' orbital speed around the Sun and enter an orbit around it. For comparison, launching a spacecraft into low Earth orbit requires a change in speed of about 9.5 km/s.

text: As Cartesian moments are non-orthogonal, so are Cartesian velocity moments, so different moments can be closely correlated. These velocity moments do however provide translation and scale invariance (unless the scale changes within the sequence of images).

text: Velocity 10 is a derivative of Velocity 9. The drug also granted its users super speed but with a different consequence; It caused different parts of the body to metabolize at different rates.

text: In 1818, Augustin-Jean Fresnel examined Arago's results using a wave theory of light. He realised that even if light were transmitted as waves the refractive index of the glass-air interface should have varied as the glass moved through the aether to strike the incoming waves at different velocities when the earth rotated and the seasons changed. Fresnel proposed that the glass prism would carry some of the aether along with it so that "..the aether is in excess inside the prism".He realised that the velocity of propagation of waves depends on the density of the medium so proposed that the velocity of light in the prism would need to be adjusted by an amount of 'drag'. The velocity of light

text: In 1818,

text: Augustin-Jean Fresnel

text: examined Arago's results using a wave theory of light. He realised that even if light were transmitted as waves the refractive index of the glass-air interface should have varied as the glass moved through the aether to strike the incoming waves at different velocities when the earth rotated and the seasons changed. Fresnel proposed that the glass prism would carry some of the aether along with it so that "..the aether is in excess inside the prism".He realised that the velocity of propagation of waves depends on the density of the medium so proposed that the velocity of light in the prism would need to be adjusted by an amount of 'drag'. The velocity of light

text: Ultrasonic transit time flow meters measure the difference of the transit time of ultrasonic pulses propagating in and against the direction of flow. This time difference is a measure for the average velocity of the fluid along the path of the ultrasonic beam. By using the absolute transit times both the averaged fluid velocity and the speed of sound can be calculated. Using the two transit times

text: A simple explanation for the fluid slip can be given as :Consider an impeller with z number of blades rotating at angular velocity ω. A difference in pressure and velocity during the course of clockwise flow through the impeller passage can be observed between the trailing and leading faces of the impeller blades. High pressure and low velocity is observed at the leading face of impellers blade as compared to lower pressure with high velocity at the trailing face of the blade. This results in a circulation in the direction of ω around the impeller blade which prevents the air from acquiring the whirl velocity equivalent to impeller speed with non-uniform velocity distribution at any radius.

text: Fluid undergoes shear when one area of fluid travels with a different velocity relative to an adjacent area. A high-shear mixer uses a rotating impeller or high-speed rotor, or a series of such impellers or inline rotors, usually powered by an electric motor, to "work" the fluid, creating flow and shear. The tip velocity, or speed of the fluid at the outside diameter of the rotor, will be higher than the velocity at the center of the rotor, and it is this velocity difference that creates shear.

text: In July 2013, Lupi et al. proposed that the Lusi mud eruption was the result of a natural event, triggered by a distant earthquake at Yogyakarta two days before. As a result, seimic waves were geometrically focused at the Lusi site leading to mud and CO2 generation and a reactivation of the local Watukosek Fault. According to their hypothesis the fault is linked to a deep hydrothermal system that feeds the eruption.  However, this hypothesis has been heavily criticised due to the original models containing a major error. The original study proposed that a “high velocity layer” focussed earthquake waves, amplifying the effect of the earthquake. However, the “high velocity layer” has since been demonstrated to be a non-existent artefact caused by velocity measurements of the steel casing in the Banjar Panji-1 well, which resulted in the original models assuming that a ‘layer of steel’ existed underground. Lupi et al. have acknowledged this error, but argue in a corrigendum that it makes no difference to their results, as they have proposed in a new velocity model, arguing for the existence of a different high velocity layer at the same depth. There still remains significant doubt about this revised model, as another study indicates that there is no geological or geophysical evidence for any significant domed high velocity layer at the mudflow location that would reflect and amplify seismic waves. A study by Rudolph et al. in 2015 replicated the seismic wave propagation modelling at the Sidoarjo mudflow location using the two competing velocity models, and proposed that the modelling conducted by Lupi et al. exaggerates the effect of the Yogyakarta earthquake at the mudflow location.

text: In July 2013, Lupi et al. proposed that the Lusi mud eruption was the result of a natural event, triggered by a distant earthquake at

text: Yogyakarta

text: In physics, a field is a physical quantity, typically a number or tensor, that has a value for each point in space and time. For example, on a weather map, the surface wind velocity is described by assigning a vector to each point on a map. Each vector represents the speed and direction of the movement of air at that point. As another example, an electric field can be thought of as a "condition in space" emanating from an electric charge and extending throughout the whole of space. When a test electric charge is placed in this electric field, the particle accelerates due to a force. Physicists have found the notion of a field to be of such practical utility for the analysis of forces that they have come to think of a force as due to a field.

text: In physics, a field is a

text: physical quantity

text: , typically a number or

text: tensor

text: , that has a value for each

text: point

text: in space and time. For example, on a weather map, the surface wind

text: velocity

text: is described by assigning a vector to each point on a map. Each vector represents the speed and direction of the movement of air at that point. As another example, an

text: electric field

text: can be thought of as a "condition in space" emanating from an

text: electric charge

text: and extending throughout the whole of space. When a

text: test electric charge

text: is placed in this electric field, the particle accelerates due to a force. Physicists have found the notion of a field to be of such practical utility for the analysis of forces that they have come to think of a force as due to a field.

text: If there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an acceleration.

text: If there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an

text: acceleration

text: A historical analysis of money velocity and monetary base shows an inverse correlation: for a given percentage decrease in the monetary base the result is nearly equal percentage increase in money velocity. This is to be expected because monetary base (M), velocity of base money (V), price level (P) and real output (Y) are related by definition: MV = PY. However, it is important to note that the monetary base is a much narrower definition of money than M money supply. Additionally, the velocity of the monetary base is interest rate sensitive, the highest velocity being at the highest interest rates.

text: A historical analysis of money velocity and

text: monetary base

text: shows an inverse correlation: for a given percentage decrease in the

text: monetary base

text: the result is nearly equal percentage increase in money velocity. This is to be expected because monetary base (M),

text: velocity

text: of base money (V), price level (P) and real output (Y) are related by definition: MV = PY. However, it is important to note that the monetary base is a much narrower definition of money than

entity_section: Empirical measures in the United States Federal Reserve System

text: M money supply

text: . Additionally, the velocity of the monetary base is interest rate sensitive, the highest velocity being at the highest interest rates.

text: Velocity is a capacity planning tool sometimes used in agile software development. Velocity tracking is the act of measuring said velocity. The velocity is calculated by counting the number of units of work completed in a certain interval, the length of which is determined at the start of the project.

text: Velocity is a capacity planning tool sometimes used in

text: agile software development

text: . Velocity tracking is the act of measuring said velocity. The velocity is calculated by counting the number of units of work completed in a certain interval, the length of which is determined at the start of the project.

text: The collimation of the machine means that, while rotating, the X-rays project only a limited portion of the anatomy onto the film at any given instant but, as the rotation progresses around the skull, a composite picture of the maxillo-facial block is created. While the arm rotates, the film moves in a such way that the projected partial skull image (limited by the beam section) scrolls over it and exposes it entirely. Not all of the overlapping individual images projected on the film have the same magnification because the beam is divergent and the images have differing focus points. Also not all the element images move with the same velocity on the target film as some of them are more distant from and others closer to the instant rotation center. The velocity of the film is controlled in such fashion to fit exactly the velocity of projection of the anatomical elements of the dental arch side which is closest to the film. Therefore, they are recorded sharply while the elements in different places are recorded blurred as they scroll at different velocity.

text: The

text: collimation

text: of the machine means that, while rotating, the X-rays project only a limited portion of the

text: anatomy

text: onto the film at any given instant but, as the rotation progresses around the skull, a composite picture of the maxillo-facial block is created. While the arm rotates, the film moves in a such way that the projected partial skull image (limited by the beam section) scrolls over it and exposes it entirely. Not all of the overlapping individual images projected on the film have the same magnification because the beam is

text: divergent

text: and the images have differing focus points. Also not all the element images move with the same

text: velocity

text: on the target film as some of them are more distant from and others closer to the instant rotation center. The velocity of the film is controlled in such fashion to fit exactly the velocity of projection of the anatomical elements of the dental arch side which is closest to the film. Therefore, they are recorded sharply while the elements in different places are recorded blurred as they scroll at different velocity.

text: Impact cratering involves high velocity collisions between solid objects, typically much greater than the velocity of sound in those objects.  Such hyper-velocity impacts produce physical effects such as melting and vaporization that do not occur in familiar sub-sonic collisions.  On Earth, ignoring the slowing effects of travel through the atmosphere, the lowest impact velocity with an object from space is equal to the gravitational escape velocity of about 11 km/s. The fastest impacts occur at about 72 km/s in the "worst case" scenario which an object in a retrograde near-parabolic orbit hits Earth. (Because kinetic energy scales as velocity squared, Earth's gravity only contributes 1 km/s to this figure, not 11 km/s). The median impact velocity on Earth is about 20 km/s.

text: Impact cratering involves high velocity collisions between solid objects, typically much greater than the

text: velocity of sound

text: in those objects.  Such hyper-velocity impacts produce physical effects such as

text: melting

text: and

text: vaporization

text: that do not occur in familiar sub-sonic collisions.  On Earth, ignoring the slowing effects of travel through the atmosphere, the lowest impact velocity with an object from space is equal to the gravitational

text: escape velocity

text: of about 11 km/s. The fastest impacts occur at about 72 km/s in the "worst case" scenario which an object in a retrograde near-parabolic orbit hits Earth. (Because kinetic energy scales as velocity squared, Earth's gravity only contributes 1 km/s to this figure, not 11 km/s). The

text: median

text: impact velocity on Earth is about 20 km/s.

text: Wind speed is affected by a number of factors and situations, operating on varying scales (from micro to macro scales). These include the pressure gradient, Rossby waves and jet streams, and local weather conditions. There are also links to be found between wind speed and wind direction, notably with the pressure gradient and terrain conditions.

text: Wind speed is affected by a number of factors and situations, operating on varying scales (from micro to macro scales). These include the pressure gradient, Rossby waves and

text: jet stream

text: s, and local weather conditions. There are also links to be found between wind speed and

text: wind direction

text: , notably with the pressure gradient and terrain conditions.

text: A related assumption is the no-slip condition where the flow velocity at a solid surface is presumed equal to the velocity of the surface itself, which is a direct consequence of assuming continuum flow. The no-slip condition implies that the flow is viscous, and as a result a boundary layer forms on bodies traveling through the air at high speeds, much as it does in low-speed flow.

text: A related assumption is the

text: no-slip condition

text: where the flow velocity at a solid surface is presumed equal to the velocity of the surface itself, which is a direct consequence of assuming continuum flow. The no-slip condition implies that the flow is viscous, and as a result a

text: boundary layer

text: forms on bodies traveling through the air at high speeds, much as it does in low-speed flow.

text: During a central eclipse, the Moon's umbra (or antumbra, in the case of an annular eclipse) moves rapidly from west to east across the Earth. The Earth is also rotating from west to east, at about 28 km/min at the Equator, but as the Moon is moving in the same direction as the Earth's spin at about 61 km/min, the umbra almost always appears to move in a roughly west-east direction across a map of the Earth at the speed of the Moon's orbital velocity minus the Earth's rotational velocity.

text: Initially, Velocity was different from most other frequent flyer programs, as points were earned relative to the cost of a flight, rather than distance. Velocity members originally earned 6 points per dollar spent on Virgin Australia flights. This was later altered due to the introduction of status levels; Red members now earned 5 points per dollar, Silver members remained at 6 points, and Gold members earned 7. Points accrual on V Australia, as well as the majority of Velocity's airline partners, have always based on distance.

text: For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity. (Note that the average velocity, as a vector, differs from the average speed that is the ratio of the path length — a scalar — and the time interval.)

text: For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity. (Note that the average

text: velocity

text: , as a vector, differs from the

text: average speed

text: that is the ratio of the path length — a scalar — and the time interval.)

text: These two equations used to determine the velocity of a vehicle in the next timestep represent free-flow and congested conditions, respectively. If the vehicle is in free-flow, the free-flow branch of the equation indicates that the speed of the vehicle will increase as a function of its current speed, the speed at which the driver intends to travel, and the acceleration of the vehicle. Analyzing the variables in these two equations, it becomes apparent that as the gap between two vehicles decreases (i.e. a following vehicle approaches a leading vehicle) the velocity given by the congested branch of the equation will decrease and is more likely to prevail.

text: Because keeping a constant transfer rate for the whole disc is not so important in most contemporary CD uses, a pure CLV approach had to be abandoned to keep the rotational speed of the disc safely low while maximizing data rate. Some drives work in a partial CLV (PCLV) scheme, by switching from CLV to CAV only when a rotational limit is reached. But switching to CAV requires considerable changes in hardware design, so instead most drives use the zoned constant linear velocity (Z-CLV) scheme. This divides the disc into several zones, each having its own constant linear velocity. A Z-CLV recorder rated at "52×", for example, would write at 20× on the innermost zone and then progressively increase the speed in several discrete steps up to 52× at the outer rim. Without higher rotational speeds, increased read performance may be attainable by simultaneously reading more than one point of a data groove, but drives with such mechanisms are more expensive, less compatible, and very uncommon.

text: Because keeping a constant transfer rate for the whole disc is not so important in most contemporary CD uses, a pure CLV approach had to be abandoned to keep the rotational speed of the disc safely low while maximizing data rate. Some drives work in a partial CLV (PCLV) scheme, by switching from CLV to CAV only when a rotational limit is reached. But switching to CAV requires considerable changes in hardware design, so instead most drives use the

text: zoned constant linear velocity

text: (Z-CLV) scheme. This divides the disc into several zones, each having its own constant linear velocity. A Z-CLV recorder rated at "52×", for example, would write at 20× on the innermost zone and then progressively increase the speed in several discrete steps up to 52× at the outer rim. Without higher rotational speeds, increased read performance may be attainable by simultaneously reading more than one point of a data groove, but drives with such mechanisms are more expensive, less compatible, and very uncommon.

text: Wind speed and direction are determined by a roll of the dice; sail ships can only make slow progress against the wind by tacking.  A protractor is used to measure the angle between the wind direction and the ship direction, and this determines ship speed.

text: Wind speed and direction are determined by a roll of the dice; sail ships can only make slow progress against the wind by

text: tacking

text: .  A

text: protractor

text: is used to measure the angle between the wind direction and the ship direction, and this determines ship speed.

text: Inertia is primarily a speedster, remaining disconnected from the Speed Force after Infinite Crisis and injecting himself with Velocity 9. Although Velocity 9 has been unstable, Deathstroke's new variety seems to have no negative side effects. Inertia briefly shares his powers before his death with Zoom, who lends him his speed to pressure him into becoming a new Kid Flash. As a maddened Kid Zoom, he masters human time streams and reverts Zoom to the powerless Hunter Zolomon before he is killed by the Rogues.

text: Inertia is primarily a

text: speedster

text: , remaining disconnected from the Speed Force after Infinite Crisis and injecting himself with

text: Velocity 9

text: . Although Velocity 9 has been unstable, Deathstroke's new variety seems to have no negative

text: side effects

text: . Inertia briefly shares his powers before his death with Zoom, who lends him his speed to pressure him into becoming a new Kid Flash. As a maddened Kid Zoom, he masters human time streams and reverts Zoom to the powerless Hunter Zolomon before he is killed by the Rogues.

text: provided the bend is small enough that the horizontal velocity is unaffected. Averaged over all stars at

text: The atmosphere and ocean are continuously stratified: potential density generally increases steadily downward. Internal waves in a continuously stratified medium may propagate vertically as well as horizontally. The dispersion relation for such waves is curious: For a freely-propagating internal wave packet, the direction of propagation of energy (group velocity) is perpendicular to the direction of propagation of wave crests and troughs (phase velocity). An internal wave may also become confined to a finite region of altitude or depth, as a result of varying stratification or wind. Here, the wave is said to be ducted or trapped, and a vertically standing wave may form, where the vertical component of group velocity approaches zero. A ducted internal wave mode may propagate horizontally, with parallel group and phase velocity vectors, analogous to propagation within a waveguide.

text: The atmosphere and ocean are continuously stratified:

text: potential density

text: generally increases steadily downward. Internal waves in a continuously stratified medium may propagate vertically as well as horizontally. The

text: dispersion relation

text: for such waves is curious: For a freely-propagating internal wave

text: packet

text: , the direction of propagation of energy (

text: group velocity

text: ) is perpendicular to the direction of propagation of wave crests and troughs (

text: phase velocity

text: ). An internal wave may also become confined to a finite region of

text: altitude

text: or depth, as a result of varying stratification or

text: wind

text: . Here, the wave is said to be ducted or trapped, and a vertically

text: standing wave

text: may form, where the vertical component of

text: group velocity

text: approaches zero. A ducted internal wave mode may

text: propagate

text: horizontally, with parallel

text: group

text: and

text: phase velocity

text: vectors

text: , analogous to

text: propagation

text: within a

text: waveguide

text: The acceleration, or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time):

text: The

text: acceleration

text: , or rate of change of velocity, is the

text: derivative

text: of the velocity with respect to time (the

text: second derivative

text: of the position with respect to time):

text: Since the resulting velocity vectors are based on cross-correlating the intensity distributions over small areas of the flow, the resulting velocity field is a spatially averaged representation of the actual velocity field. This obviously has consequences for the accuracy of spatial derivatives of the velocity field, vorticity, and spatial correlation functions that are often derived from PIV velocity fields.

text: Since the resulting velocity vectors are based on cross-correlating the intensity distributions over small areas of the flow, the resulting velocity field is a spatially averaged representation of the actual velocity field. This obviously has consequences for the accuracy of spatial derivatives of the velocity field, vorticity, and spatial

text: correlation function

text: s that are often derived from PIV velocity fields.

text: In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field which is used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar.

text: In

text: continuum mechanics

text: the macroscopic velocity, also flow velocity in

text: fluid dynamics

text: or drift velocity in

text: electromagnetism

text: , is a

text: vector field

text: which is used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar.

text: At low speeds (subsonic speeds) increases in static pressure are however limited to a few percent. Given that the air velocity is reduced to zero without losses the pressure increase can be calculated accordingly. The lack of losses also means without heating the air. Thus a ram-air intake also is a cold air intake. In some cars the intake is placed behind the radiator, where not only the air is hot, but the pressure is below ambient pressure. The ram-air intake effect may be small, but so are other mild tuning techniques to increase cylinder filling like using larger, fresh air filters, high flow mass flow sensors, velocity stacks, tuned air box and large tubes from the filter to the engine.

text: At low speeds (subsonic speeds) increases in static pressure are however limited to a few percent. Given that the air velocity is reduced to zero without losses the pressure increase can be calculated accordingly. The lack of losses also means without heating the air. Thus a ram-air intake also is a

text: cold air intake

text: . In some cars the intake is placed behind the radiator, where not only the air is hot, but the pressure is below ambient pressure. The ram-air intake effect may be small, but so are other mild tuning techniques to increase cylinder filling like using larger, fresh

text: air filter

text: s, high flow

text: mass flow sensor

text: s, velocity stacks, tuned air box and large tubes from the filter to the engine.

text: The Low Level sight used this angular velocity principle to time the drop. The aircraft's altitude and the type of bomb being used produced the time that the bomb would take to reach the ground, and when that was multiplied by the airspeed, the range was produced. The ballistics did not have to be more complex than that, there simply wasn't enough time for drag to be significant. The derivative of this calculation reveals the angular velocity of an object at that range as seen from the bomber's altitude and speed. To simplify operation, all of this was carried out in a simple mechanical computer.

text: In 1992, Velocity introduced the "173", also known as the long wing. This model had a longer wing giving it a lower landing speed. The name was a play on the name of a popular model of Cessna, the Cessna 172, the idea being it is one better. Some flying Velocity planes experienced "deep stall" incidents, where the main wing stalled before the canard causing an unrecoverable stall. After a lengthy investigation, Velocity found and solved the cause of these stalls. The 173 included airfoil modifications that prevented the deep stall. The original kit was also modified to prevent a deep stall, and was now known as the Standard model.

text: In 1992, Velocity introduced the "173", also known as the long wing. This model had a longer wing giving it a lower landing speed. The name was a play on the name of a popular model of Cessna, the

text: Cessna 172

text: , the idea being it is one better. Some flying Velocity planes experienced "deep stall" incidents, where the main wing stalled before the canard causing an unrecoverable stall. After a lengthy investigation, Velocity found and solved the cause of these stalls. The 173 included airfoil modifications that prevented the deep stall. The original kit was also modified to prevent a deep stall, and was now known as the Standard model.

text: With the important exception of the E-cross-B drift, the drift velocities of different species will be different. The differential velocity of charged particles results in a current, while the mass dependence of the drift velocity can result in chemical separation.

text: This star has the third highest proper motion of any star visible to the unaided eye, after Groombridge 1830 and 61 Cygni, and the ninth highest overall. This motion will move the star into the constellation Tucana around 2640 AD. Epsilon Indi A has a space velocity relative to the Sun of 86 km/s, which is unusually high for what is considered a young star. It is thought to be a member of the ε Indi moving group of at least sixteen population I stars. This is an association of stars that have similar space velocity vectors, and therefore most likely formed at the same time and location.

text: This star has the third highest

text: proper motion

text: of any star visible to the unaided eye, after

text: Groombridge 1830

text: and

text: 61 Cygni

text: , and the ninth highest overall. This motion will move the star into the constellation

text: Tucana

text: around 2640 AD. Epsilon Indi A has a

text: space velocity

text: relative to the Sun of 86

text: km/s

text: , which is unusually high for what is considered a young star. It is thought to be a member of the ε Indi

text: moving group

text: of at least sixteen

text: population I

text: stars. This is an association of stars that have similar

text: space velocity

text: vectors, and therefore most likely formed at the same time and location.

text: In early January, it was announced that the band do a split with Such Gold for release the following month on No Sleep, however, it failed to materialise. On February 10, 2011, they announced signing with Rise/Velocity. The band had previously met a Velocity representative, Dave, who suggested the idea of signing the band with a Rise representative, Craig. The band went on tour with Streetlight Manifesto through the U.S. in February and March. The band went on a tour of the UK with This Time Next Year, supporting Set Your Goals in May. Recording for their Rise/Velocity debut was done in May and June with producer Andrew Wade. As Dangora mentions, the choice of Wade came down to the albums that he worked on previously as they were "really good sonically [...] and we think he can get the best out of us." The album was going to sound similar to their previous album "but improve on it [...] [with] big sounding, loud guitars and catchy vocals." Arsenault, on the other hand, said that Wade was recommended by Dave Shapiro from Velocity. The band went on the 2011 Summer Partery Tour with In Fear and Faith, Vanna, Close to Home, Chunk! No, Captain Chunk!, Ten After Two and Adestria throughout July and August. The band supported Cruel Hand, with The Greenery and Maker, for the Back to School Jam tour in September and October.

text: In early January, it was announced that the band do a split with Such Gold for release the following month on

text: No Sleep

text: , however, it failed to materialise. On February 10, 2011, they announced signing with Rise/Velocity. The band had previously met a Velocity representative, Dave, who suggested the idea of signing the band with a Rise representative, Craig. The band went on tour with

text: Streetlight Manifesto

text: through the U.S. in February and March. The band went on a tour of the UK with This Time Next Year, supporting

text: Set Your Goals

text: in May. Recording for their Rise/Velocity debut was done in May and June with producer

text: Andrew Wade

text: . As Dangora mentions, the choice of Wade came down to the albums that he worked on previously as they were "really good sonically [...] and we think he can get the best out of us." The album was going to sound similar to their previous album "but improve on it [...] [with] big sounding, loud guitars and catchy vocals." Arsenault, on the other hand, said that Wade was recommended by Dave Shapiro from Velocity. The band went on the 2011 Summer Partery Tour with

text: In Fear and Faith

text: , Vanna,

text: Close to Home

text: Chunk! No, Captain Chunk!

text: , Ten After Two and Adestria throughout July and August. The band supported

text: Cruel Hand

text: , with The Greenery and Maker, for the Back to School Jam tour in September and October.

text: In turbomachinery, a velocity triangle or a velocity diagram is a triangle representing the various components of velocities of the working fluid in a turbomachine. Velocity triangles may be drawn for both the inlet and outlet sections of any turbomachine. The vector nature of velocity is utilized in the triangles, and the most basic form of a velocity triangle consists of the tangential velocity, the absolute velocity and the relative velocity of the fluid making up three sides of the triangle.

text: In

text: turbomachinery

text: , a velocity triangle or a velocity diagram is a triangle representing the various components of velocities of the

text: working fluid

text: in a

text: turbomachine

text: . Velocity triangles may be drawn for both the inlet and outlet sections of any turbomachine. The

text: vector

text: nature of

text: velocity

text: is utilized in the triangles, and the most basic form of a velocity triangle consists of the tangential velocity, the absolute velocity and the relative velocity of the fluid making up three sides of the triangle.

text: The flow on a transportation route (in tons/hour, trains/day, etc.) is simply equal to the product of velocity and linear density (gross tons/meter or trains/km etc.).  For a railway line as a whole (in one direction), one would use the average linear density along the whole line, where most points on the line have no trains on them and thus have zero density there.  One would also need to use the average velocity which turns out to be the weighted harmonic mean where the weights are the lengths of the various segments of the train run (with the speed approximately constant on each segment).  Another way to find the average velocity is to simply find the weighted arithmetic mean where the weights is this case are the times on each segment.  For a segment of a train run where the speed is very slow, the train thus spends a long time traversing this segment and thus the weight for this segment is quite high (since it is weighted by time).  Thus even thought the slow speed segments are only a small part of the trip, they may drastically reduce the average speed (and thus the flow).

text: The flow on a transportation route (in tons/hour, trains/day, etc.) is simply equal to the product of velocity and linear density (gross tons/meter or trains/km etc.).  For a railway line as a whole (in one direction), one would use the average linear density along the whole line, where most points on the line have no trains on them and thus have zero density there.  One would also need to use the average velocity which turns out to be the

text: weighted harmonic mean

text: where the weights are the lengths of the various segments of the train run (with the speed approximately constant on each segment).  Another way to find the average velocity is to simply find the

text: weighted arithmetic mean

text: where the weights is this case are the times on each segment.  For a segment of a train run where the speed is very slow, the train thus spends a long time traversing this segment and thus the weight for this segment is quite high (since it is weighted by time).  Thus even thought the slow speed segments are only a small part of the trip, they may drastically reduce the average speed (and thus the flow).

text: This equation is derived from the fact that the interaction between the two bodies is easily calculated along the contact angle, meaning the velocities of the objects can be calculated in one dimension by rotating the x and y axis to be parallel with the contact angle of the objects, and then rotated back to the original orientation to get the true x and y components of the velocities

text: In the case where two objects are traveling in parallel directions, the relativistic formula for relative velocity is similar in form to the formula for addition of relativistic velocities.

text: Since this instant centre of rotation P is the centre for all points on the body BAC for any random point, say point C, the speed and direction of movement may be determined: connect P to C. The direction of movement of point C is perpendicular to this connection. The speed is proportional to the distance to point P.

text: According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. This change is not noticeable at low velocities but as the velocity increases towards the speed of light it becomes important. The addition law is also called a composition law for velocities. For collinear motions, the speed of the object (e.g. a cannonball fired horizontally away from, or towards Galilei) on the ship relative to the shore is given by

text: According to the theory of

text: special relativity

text: , the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. This change is not noticeable at low velocities but as the velocity increases towards the speed of light it becomes important. The addition law is also called a composition law for velocities. For collinear motions, the speed of the object (e.g. a cannonball fired horizontally away from, or towards Galilei) on the ship relative to the shore is given by

text: Maxwell Model concerns Maxwell fluids or Maxwell material. The material in Maxwell Model is a fluid which means it respects continuity properties for conservative equations :  Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. Maxwell model is made to estimate local conservative values of viscoselasticity by a global measure in the integral volume of the model to be transposed to different flow situations. Blood is a complex material where different cells like red blood cells are discontinuous in plasma. Their size and shape are irregular too because they are not perfect spheres. Complicating moreover blood volume shape, red cells are not identically distributed in a blood sample volume because they migrate with velocity gradients in direction to the highest speed areas calling the famous representation of the Fåhræus–Lindqvist effect, aggregate or separate in sheath or plug flows described by Thurston. Typically, the Maxwell Model described below is uniformly considering the material (uniform blue color) as a perfect distributed particles fluid everywhere in the volume (in blue) but Thurston reveals that packs of red cells, plugs, are more present in the high speed region, if y is the height direction in the Maxwell model figure, (y~H) and there is a free cells layer in the lower speed area (y~0) what means the plasma fluid phase that deforms under Maxwell Model is strained following inner linings that completely escape from the analytical model by Maxwell.

text: Maxwell Model concerns Maxwell fluids or

text: Maxwell material

text: . The material in Maxwell Model is a

text: fluid

text: which means it respects continuity properties for conservative equations :  Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. Maxwell model is made to estimate local conservative values of viscoselasticity by a global measure in the integral volume of the model to be transposed to different flow situations. Blood is a complex material where different cells like red blood cells are discontinuous in plasma. Their size and shape are irregular too because they are not perfect spheres. Complicating moreover blood volume shape, red cells are not identically distributed in a blood sample volume because they migrate with velocity gradients in direction to the highest speed areas calling the famous representation of the

text: Fåhræus–Lindqvist effect

text: , aggregate or separate in sheath or plug flows described by Thurston. Typically, the Maxwell Model described below is uniformly considering the material (uniform blue color) as a perfect distributed particles fluid everywhere in the volume (in blue) but Thurston reveals that packs of red cells, plugs, are more present in the high speed region, if y is the height direction in the Maxwell model figure, (y~H) and there is a free cells layer in the lower speed area (y~0) what means the plasma fluid phase that deforms under Maxwell Model is strained following inner linings that completely escape from the analytical model by Maxwell.

text: For example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Hence, the car is considered to be undergoing an acceleration.

text: from the cyclone's central axis, the particle is therefore subjected to drag, centrifugal, and buoyant forces.  Given that the fluid velocity is moving in a spiral the gas velocity can be broken into two component velocities: a tangential component,

text: from the cyclone's central axis, the particle is therefore subjected to

text: drag

text: centrifugal

text: , and

text: buoyant

text: forces.  Given that the fluid velocity is moving in a spiral the gas velocity can be broken into two component velocities: a tangential component,

text: For angular velocity tensor maps velocities to positions, it is a vector field. In particular, this vector field is a Killing vector field belonging to an element of the Lie algebra so(3) of the 3-dimensional rotation group SO(3). This element of so(3) can also be regarded as the angular velocity vector.

text: For angular velocity tensor maps velocities to positions, it is a

text: vector field

text: . In particular, this vector field is a

text: Killing vector field

text: belonging to an element of the

text: Lie algebra

text: so(3) of the 3-dimensional

text: rotation group SO(3)

text: . This element of so(3) can also be regarded as the angular velocity vector.

text: is the velocity vector,

text: is the velocity vector,

text: Because ΔL=c(T-T), the following travel length differences are given (ΔL being the initial travel length difference and v the initial velocity of the apparatus, and ΔL and v after rotation or velocity change due to Earth's own rotation or its rotation around the Sun):

text: Nozzles direct forceful, high-speed streams of water against a rotary series of spoon-shaped buckets, also known as impulse blades, which are mounted around the circumferential rim of a drive wheelalso called a runner (see photo, 'Old Pelton wheel..'). As the water jet impinges upon the contoured bucket-blades, the direction of water velocity is changed to follow the contours of the bucket. Water impulse energy exerts torque on the bucket-and-wheel system, spinning the wheel; the water stream itself does a "u-turn" and exits at the outer sides of the bucket, decelerated to a low velocity. In the process, the water jet's momentum is transferred to the wheel and hence to a turbine. Thus, "impulse" energy does work on the turbine. For maximum power and efficiency, the wheel and turbine system is designed such that the water jet velocity is twice the velocity of the rotating buckets. A very small percentage of the water jet's original kinetic energy will remain in the water, which causes the bucket to be emptied at the same rate it is filled, (see conservation of mass) and thereby allows the high-pressure input flow to continue uninterrupted and without waste of energy. Typically two buckets are mounted side-by-side on the wheel, which permits splitting the water jet into two equal streams (see photo).  This balances the side-load forces on the wheel and helps to ensure smooth, efficient transfer of momentum of the fluid jet of water to the turbine wheel.

text: Nozzles direct forceful, high-speed streams of water against a rotary series of spoon-shaped buckets, also known as impulse blades, which are mounted around the circumferential rim of a drive wheelalso called a runner (see photo, 'Old Pelton wheel..'). As the water jet impinges upon the contoured bucket-blades, the direction of water velocity is changed to follow the contours of the bucket. Water impulse energy exerts torque on the bucket-and-wheel system, spinning the wheel; the water stream itself does a "u-turn" and exits at the outer sides of the bucket, decelerated to a low velocity. In the process, the water jet's momentum is transferred to the wheel and hence to a turbine. Thus, "

text: impulse

text: " energy does

text: work

text: on the turbine. For maximum power and efficiency, the wheel and turbine system is designed such that the water jet velocity is twice the velocity of the rotating buckets. A very small percentage of the water jet's original

text: kinetic energy

text: will remain in the water, which causes the bucket to be emptied at the same rate it is filled, (see

text: conservation of mass

text: ) and thereby allows the high-pressure input flow to continue uninterrupted and without waste of energy. Typically two buckets are mounted side-by-side on the wheel, which permits splitting the water jet into two equal streams (see photo).  This balances the side-load forces on the wheel and helps to ensure smooth, efficient transfer of momentum of the fluid jet of water to the turbine wheel.

text: A change of reference frame can often simplify the analysis of a collision. For example, suppose there are two bodies of equal mass , one stationary and one approaching the other at a speed  (as in the figure). The center of mass is moving at speed  and both bodies are moving towards it at speed . Because of the symmetry, after the collision both must be moving away from the center of mass at the same speed. Adding the speed of the center of mass to both, we find that the body that was moving is now stopped and the other is moving away at speed . The bodies have exchanged their velocities. Regardless of the velocities of the bodies, a switch to the center of mass frame leads us to the same conclusion. Therefore, the final velocities are given by

text: For air-breathing jet engines, particularly turbofans, the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This is because a good deal of additional momentum is obtained by using air as reaction mass. This allows a better match between the airspeed and the exhaust speed, which saves energy/propellant and enormously increases the effective exhaust velocity while reducing the actual exhaust velocity.

text: For air-breathing jet engines, particularly

text: turbofan

text: s, the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This is because a good deal of additional momentum is obtained by using air as reaction mass. This allows a better match between the airspeed and the exhaust speed, which saves energy/propellant and enormously increases the effective exhaust velocity while reducing the actual exhaust velocity.

text: Unlike most other 4-vectors, the 4-Velocity has only 3 independent components

text: Introducing a unit vector  v/v  β/β}} in the direction of relative motion, the relative velocity is  vn}} with magnitude  and direction , and vector projection and rejection give respectively

text: Introducing a

text: unit vector

text: v/v  β/β}} in the direction of relative motion, the relative velocity is  vn}} with magnitude  and direction , and

text: vector projection

text: and rejection give respectively

text: Then, the velocities can be calculated:

text: Then, the velocities can be calculated:

text: The principle requires physical laws to be the same for any body moving at constant velocity as they are for a body at rest. A consequence is that an observer in an inertial reference frame cannot determine an absolute speed or direction of travel in space,  and may only speak of speed or direction relative to some other object.

text: u=r.ω  the inlet circumferential velocity vector

text: As the pennate muscle is activated, the fibers rotate as they shorten and pull at an angle. In pennate muscles, fibers are oriented at an angle to the muscle's line of action and rotate as they shorten, becoming more oblique such that the fraction of force directed along the muscle's line of action decreases throughout a contraction. Force output is dependent upon the angle of fiber rotation, so changes in muscle thickness and the vector of change in thickness vary; based upon the force being produced. Due to the rotational motion; pennate muscles operate at low velocities (low shortening distance). The shortening velocity of the pennate muscle as a whole is greater than that of the individual fibers. This gives rise to the property of AGR. Fiber rotation decreases a muscle's output force but increases output velocity by allowing the muscle to function at a higher gear ratio (muscle velocity/fiber velocity). Azizi and Brainerd demonstrated that the gear ratio of pennate muscle can vary; dependent on external load.

text: As the pennate muscle is activated, the fibers rotate as they shorten and pull at an angle. In pennate muscles, fibers are oriented at an angle to the muscle's

text: line of action

text: and rotate as they shorten, becoming more

text: oblique

text: such that the fraction of force directed along the muscle's line of action decreases throughout a contraction. Force output is dependent upon the angle of fiber rotation, so changes in muscle thickness and the vector of change in thickness vary; based upon the force being produced. Due to the rotational motion; pennate muscles operate at low velocities (low shortening distance). The shortening velocity of the pennate muscle as a whole is greater than that of the individual fibers. This gives rise to the property of AGR. Fiber rotation decreases a muscle's output force but increases output velocity by allowing the muscle to function at a higher gear ratio (muscle velocity/fiber velocity). Azizi and Brainerd demonstrated that the gear ratio of pennate muscle can vary; dependent on external load.

text: Although velocity addition is nonlinear, non-associative, and non-commutative, the result of the operation correctly obtains a velocity with a magnitude less than . If ordinary vector addition was used, it would be possible to obtain a velocity with a magnitude larger than . The Lorentz factor  of both composite velocities are equal,

text: Although velocity addition is

text: nonlinear

text: , non-

text: associative

text: , and non-

text: commutative

text: , the result of the operation correctly obtains a velocity with a magnitude less than . If ordinary vector addition was used, it would be possible to obtain a velocity with a magnitude larger than . The

text: Lorentz factor

text: of both composite velocities are equal,

text: Suppose there are two collinear velocities v and w. How does one find the frame of reference in which the velocities become equal speeds in opposite directions? One solution uses modern algebra to find it:Suppose

text: There are issues to be dealt with to achieve invisibility cloaking. One issue, related to ray tracing, is the anisotropic effects of the material on the electromagnetic rays entering the "system". Parallel bundles of rays, (see above image), headed directly for the center are abruptly curved and, along with neighboring rays, are forced into tighter and tighter arcs. This is due to rapid changes in the now shifting and transforming permittivity ε′ and permeability µ′. The second issue is that, while it has been discovered that the selected metamaterials are capable of working within the parameters of the anisotropic effects and the continual shifting of ε′ and µ′, the values for ε′ and µ′ cannot be very large or very small. The third issue is that the selected metamaterials are currently unable to achieve broad, frequency spectrum capabilities. This is because the rays must curve around the "concealed" sphere, and therefore have longer trajectories than traversing free space, or air. However, the rays must arrive around the other side of the sphere in phase with the beginning radiated light. If this is happening then the phase velocity exceeds the velocity of light in a vacuum, which is the speed limit of the universe. (Note, this does not violate the laws of physics). And, with a required absence of frequency dispersion, the group velocity will be identical with phase velocity. In the context of this experiment, group velocity can never exceed the velocity of light, hence the analytical parameters are effective for only one frequency.

text: There are issues to be dealt with to achieve invisibility cloaking. One issue, related to

text: ray tracing

text: , is the

text: anisotropic

text: effects of the material on the electromagnetic rays entering the "system". Parallel bundles of rays, (see above image), headed directly for the center are abruptly curved and, along with neighboring rays, are forced into tighter and tighter

text: arc

text: s. This is due to rapid changes in the now shifting and transforming

text: permittivity

text: ε′ and

text: permeability

text: µ′. The second issue is that, while it has been discovered that the selected metamaterials are capable of working within the parameters of the anisotropic effects and the continual shifting of ε′ and µ′, the values for ε′ and µ′ cannot be very large or very small. The third issue is that the selected metamaterials are currently unable to achieve broad,

text: frequency spectrum

text: capabilities. This is because the rays must curve around the "concealed"

text: sphere

text: , and therefore have longer trajectories than traversing

text: free space

text: , or air. However, the rays must arrive around the other side of the sphere in

text: phase

text: with the beginning radiated

text: light

text: . If this is happening then the

text: phase velocity

text: exceeds the

text: velocity of light

text: in a

text: vacuum

text: , which is the speed limit of the universe. (Note, this does not violate the laws of physics). And, with a required absence of

text: frequency dispersion

text: , the

text: group velocity

text: will be identical with

text: phase velocity

text: . In the context of this experiment, group velocity can never exceed the velocity of light, hence the

text: analytical parameters

text: are effective for only one

text: frequency

text: Although to the observer low Earth orbit satellites move at about the same apparent speed as aircraft, individual satellites can be faster or slower; they do not all move at the same speed. Individual satellites never deviate in their velocity (speed and direction). They can be distinguished from aircraft because satellites do not leave contrails.  They are lit solely by the reflection of sunlight from solar panels or other surfaces.  A satellite's brightness sometimes changes as it moves across the sky.  Occasionally a satellite will 'flare' as its orientation changes relative to the viewer, suddenly increasing in reflectivity. Satellites often grow dimmer and are more difficult to see toward the horizons. Because reflected sunlight is necessary to see satellites, the best viewing times are for a few hours immediately after nightfall and a few hours before dawn. Given the number of satellites now in orbit, a fifteen-minute session of sky watching will generally yield at least one satellite passing overhead.

text: Although to the observer

text: low Earth orbit

text: satellites move at about the same apparent speed as aircraft, individual satellites can be faster or slower; they do not all move at the same speed. Individual satellites never deviate in their velocity (speed and direction). They can be distinguished from aircraft because satellites do not leave contrails.  They are lit solely by the reflection of sunlight from solar panels or other surfaces.  A satellite's brightness sometimes changes as it moves across the sky.  Occasionally a satellite will '

text: flare

text: ' as its orientation changes relative to the viewer, suddenly increasing in reflectivity. Satellites often grow dimmer and are more difficult to see toward the horizons. Because reflected sunlight is necessary to see satellites, the best viewing times are for a few hours immediately after nightfall and a few hours before dawn. Given the number of satellites now in orbit, a fifteen-minute session of sky watching will generally yield at least one satellite passing overhead.

text: , it should be emphasized that Bradley's result does not merely give the classical limit of the relativistic case, in the sense that it gives incorrect predictions even at low relative velocities. Bradley's explanation cannot account for situations such as the water telescope, nor for many other optical effects (such as interference) that might occur within the telescope. This is because in the Earth's frame it predicts that the direction of propagation of the light beam in the telescope is not normal to the wavefronts of the beam, in contradiction with Maxwell's theory of electromagnetism. It also does not preserve the speed of light c between frames. However, Bradley did correctly infer that the effect was due to relative velocities.

text: , it should be emphasized that Bradley's result does not merely give the classical limit of the relativistic case, in the sense that it gives incorrect predictions even at low relative velocities. Bradley's explanation cannot account for situations such as the water telescope, nor for many other optical effects (such as interference) that might occur within the telescope. This is because in the Earth's frame it predicts that the direction of propagation of the light beam in the telescope is not normal to the wavefronts of the beam, in contradiction with

text: Maxwell's theory of electromagnetism

text: . It also does not preserve the speed of light c between frames. However, Bradley did correctly infer that the effect was due to relative velocities.

text: The wave velocity in one medium not only may differ from that in another, but the velocity typically varies with wavelength. As a result, the change in direction upon entering a different medium changes with the wavelength of the wave.

text: MACHO 176.18833.411 (OGLE BLG-RRLYR-10353) is an RR Lyrae variable star located in the galactic bulge of our Milky Way Galaxy. However, it is not a galactic bulge star, it is a galactic halo star, which is on the part of its elliptical orbit that brings it within the bulge before returning to the outer parts of the galaxy, the halo. The star is located  from the Galactic Center. , this star has the highest velocity of any known RR Lyrae variable located in the bulge, moving at , only slightly below galactic escape velocity, and 5x the average velocity of bulge stars. Its nature was discovered as part of the BRAVA-RR survey.

text: MACHO 176.18833.411 (OGLE BLG-RRLYR-10353) is an

text: RR Lyrae

text: variable

text: star

text: located in the

text: galactic bulge

text: of our

text: Milky Way Galaxy

text: . However, it is not a galactic bulge star, it is a

text: galactic halo

text: star, which is on the part of its elliptical orbit that brings it within the bulge before returning to the outer parts of the galaxy, the halo. The star is located  from the Galactic Center. , this star has the highest velocity of any known RR Lyrae variable located in the bulge, moving at , only slightly below galactic

text: escape velocity

text: , and 5x the average velocity of bulge stars. Its nature was discovered as part of the

text: BRAVA-RR

text: survey.

text: The group velocity is one half the phase velocity.  A wave in which the group and phase velocities differ is called dispersive.

text: A related, and more commonly used, algorithm is the Velocity Verlet algorithm, similar to the leapfrog method, except that the velocity and position are calculated at the same value of the time variable (Leapfrog does not, as the name suggests). This uses a similar approach but explicitly incorporates velocity, solving the first-timestep problem in the Basic Verlet algorithm:

text: A related, and more commonly used, algorithm is the Velocity Verlet algorithm, similar to the

text: leapfrog method

text: , except that the velocity and position are calculated at the same value of the time variable (Leapfrog does not, as the name suggests). This uses a similar approach but explicitly incorporates velocity, solving the first-timestep problem in the Basic Verlet algorithm:

text: A physical field can be thought of as the assignment of a physical quantity at each point of space and time. For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a vector to each point in space.  Each vector represents the direction of the movement of air at that point.  As the day progresses, the directions in which the vectors point change as the directions of the wind change.  From the mathematical viewpoint, classical fields are described by sections of fiber bundles (covariant classical field theory).

text: A physical field can be thought of as the assignment of a

text: physical quantity

text: at each point of

text: space

text: and time. For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a vector to each point in space.  Each vector represents the direction of the movement of air at that point.  As the day progresses, the directions in which the vectors point change as the directions of the wind change.  From the mathematical viewpoint, classical fields are described by sections of

text: fiber bundle

text: s (

text: covariant classical field theory

text: A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry.  Ungar introduced the concept of  gyrovectors that have addition based on gyrogroups instead of vectors which have  addition based on groups.  Ungar developed his concept as a tool for the formulation of special relativity as an alternative to  the use of Lorentz transformations to represent compositions of velocities (also called boosts - "boosts" are aspects of relative velocities, and should not be conflated with "translations"). This is achieved by introducing "gyro operators"; two 3d velocity vectors are used to construct an operator, which acts on another 3d velocity.

text: A gyrovector space is a

text: mathematical

text: concept proposed by Abraham A. Ungar for studying

text: hyperbolic geometry

text: in analogy to the way

text: vector spaces

text: are used in

text: Euclidean geometry

text: .  Ungar introduced the concept of  gyrovectors that have addition based on gyrogroups instead of vectors which have  addition based on

text: group

text: s.  Ungar developed his concept as a tool for the formulation of

text: special relativity

text: as an alternative to  the use of

text: Lorentz transformations

text: to represent compositions of velocities (also called

text: boost

text: s - "boosts" are aspects of

text: relative velocities

text: , and should not be conflated with "

text: translations

text: "). This is achieved by introducing "gyro operators"; two 3d velocity vectors are used to construct an operator, which acts on another 3d velocity.

text: The simplest configuration considered in Ref. 1 consists of an interface between an isotropic material with permittivity ε and a uniaxial crystal with permittivities εo and εe for the ordinary and the extraordinary waves respectively. The crystal C axis is parallel to the interface. For this configuration, the DSW can propagate along the interface within certain angular intervals with respect to the C axis, provided that the condition of  εe > ε > εo is satisfied. Thus DSW are supported by interfaces with positive birefringent crystals only (εe > εo).  The angular interval is defined by the parameter η =εe/εo − 1.  The angular intervals for the DSW phase and group velocities (Δθph and Δθgr) are different. The phase velocity interval is proportional to η^2 and even for the most strongly birefringent natural crystals is very narrow Δθph ≃ 1° (Rutile) and Δθph ≃4° (Calomel). However the physically more important group velocity interval is substantially larger (proportional to  η). Calculations give Δθgr ≃ 7° for Rutile, and Δθgr ≃ 20° for Calomel.

text: The simplest configuration considered in Ref. 1 consists of an interface between an isotropic material with permittivity ε and a uniaxial crystal with permittivities εo and εe for the ordinary and the

text: extraordinary wave

text: s respectively. The crystal C axis is parallel to the interface. For this configuration, the DSW can propagate along the interface within certain angular intervals with respect to the C axis, provided that the condition of  εe > ε > εo is satisfied. Thus DSW are supported by interfaces with positive birefringent crystals only (εe > εo).  The angular interval is defined by the parameter η =εe/εo − 1.  The angular intervals for the DSW phase and group velocities (Δθph and Δθgr) are different. The phase velocity interval is proportional to η^2 and even for the most strongly birefringent natural crystals is very narrow Δθph ≃ 1° (Rutile) and Δθph ≃4° (Calomel). However the physically more important group velocity interval is substantially larger (proportional to  η). Calculations give Δθgr ≃ 7° for Rutile, and Δθgr ≃ 20° for Calomel.

text: Terminal velocity of hail, or the speed at which hail is falling when it strikes the ground, varies. It is estimated that a hailstone of  in diameter falls at a rate of , while stones the size of  in diameter fall at a rate of .  Hailstone velocity is dependent on the size of the stone, friction with air it is falling through, the motion of wind it is falling through, collisions with raindrops or other hailstones, and melting as the stones fall through a warmer atmosphere. As hail stones are not perfect spheres it is  difficult to calculate their speed accurately.

text: Terminal velocity

text: of hail, or the speed at which hail is falling when it strikes the ground, varies. It is estimated that a hailstone of  in diameter falls at a rate of , while stones the size of  in diameter fall at a rate of .  Hailstone velocity is dependent on the size of the stone, friction with air it is falling through, the motion of

text: wind

text: it is falling through, collisions with raindrops or other hailstones, and melting as the stones fall through a warmer

text: atmosphere

text: . As hail stones are not perfect spheres it is  difficult to calculate their speed accurately.

text: For two frames moving at constant relative three-velocity v (not four-velocity, see below), it is convenient to denote and define the relative velocity in units of c by:

text: For two frames moving at constant relative three-velocity v (not four-velocity,

text: see below

text: ), it is convenient to denote and define the relative velocity in units of c by:

text: Several limitations to stepping disks are mentioned in the Ringworld novels. If there is a difference in velocity between two disks, any matter transferred between them must be accelerated by the disk accordingly. If there is not enough energy to do so, the transfer cannot take place. This becomes a problem with disks that are a significant distance apart on the Ringworld surface, as they will have different velocities: same speed, different direction.

text: Several limitations to stepping disks are mentioned in the

text: Ringworld

text: novels. If there is a difference in

text: velocity

text: between two disks, any matter transferred between them must be accelerated by the disk accordingly. If there is not enough energy to do so, the transfer cannot take place. This becomes a problem with disks that are a significant distance apart on the

text: Ringworld

text: surface, as they will have different velocities: same speed, different direction.

text: The neural circuitry underlying smooth pursuit is an object of debate. The first step towards the initiation of pursuit is to see a moving target. Signals from the retina ascend through the lateral geniculate nucleus and activate neurons in primary visual cortex. Primary visual cortex sends the information about the target to the middle temporal visual cortex, which responds very selectively to directions of movement. The processing of motion in this area is necessary for smooth pursuit responses. This sensory area provides the motion signal, which may or may not be smoothly pursued. A region of cortex in the frontal lobe, known as the frontal pursuit area, responds to particular vectors of pursuit, and can be electrically stimulated to induce pursuit movements. Recent evidence suggests that the superior colliculus also responds during smooth pursuit eye movement. These two areas are likely involved in providing the "go"-signal to initiate pursuit, as well as selecting which target to track. The "go"-signal from the cortex and the superior colliculus is relayed to several pontine nuclei, including the dorsolateral pontine nuclei and the nucleus reticularis tegmenti pontis The neurons of the pons are tuned to eye velocity and are directionally selective, and can be stimulated to change the velocity of pursuit. The pontine nuclei project to the cerebellum, specifically the vermis and the paraflocculus. These neurons code for the target velocity and are responsible for the particular velocity profile of pursuit.  The cerebellum, especially the vestibulo-cerebellum, is also involved in the online correction of velocity during pursuit. The cerebellum then projects to optic motoneurons, which control the eye muscles and cause the eye to move.

text: The neural circuitry underlying smooth pursuit is an object of debate. The first step towards the initiation of pursuit is to see a moving target. Signals from the retina ascend through the lateral geniculate nucleus and activate neurons in primary visual cortex. Primary visual cortex sends the information about the target to the middle temporal visual cortex, which responds very selectively to directions of movement. The processing of motion in this area is necessary for smooth pursuit responses. This sensory area provides the motion signal, which may or may not be smoothly pursued. A region of

text: cortex

text: in the

text: frontal lobe

text: , known as the frontal pursuit area, responds to particular vectors of pursuit, and can be electrically stimulated to induce pursuit movements. Recent evidence suggests that the

text: superior colliculus

text: also responds during smooth pursuit eye movement. These two areas are likely involved in providing the "go"-signal to initiate pursuit, as well as selecting which target to track. The "go"-signal from the cortex and the superior colliculus is relayed to several pontine nuclei, including the dorsolateral pontine nuclei and the nucleus reticularis tegmenti pontis The neurons of the

text: pons

text: are tuned to eye velocity and are directionally selective, and can be stimulated to change the velocity of pursuit. The pontine nuclei project to the cerebellum, specifically the vermis and the paraflocculus. These neurons code for the target velocity and are responsible for the particular velocity profile of pursuit.  The

text: cerebellum

text: , especially the vestibulo-cerebellum, is also involved in the online correction of velocity during pursuit. The

text: cerebellum

text: then projects to optic motoneurons, which control the eye muscles and cause the eye to move.

text: This is different from the particle velocity

text: Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has magnitude, has direction, and which adheres to the rules of vector addition. An example is velocity, the magnitude of which is speed. For example, the velocity 5 meters per second upward could be represented by the vector (0,5) (in 2 dimensions with the positive y axis as 'up'). Another quantity represented by a vector is force, since it has a magnitude and direction and follows the rules of vector addition. Vectors also describe many other physical quantities, such as linear displacement, displacement, linear acceleration, angular acceleration, linear momentum, and angular momentum. Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field. Examples of quantities that have magnitude and direction but fail to follow the rules of vector addition: Angular displacement and electric current. Consequently, these are not vectors.

text: Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has magnitude, has direction, and which adheres to the rules of vector addition. An example is

text: velocity

text: , the magnitude of which is

text: speed

text: . For example, the velocity 5 meters per second upward could be represented by the vector (0,5) (in 2 dimensions with the positive y axis as 'up'). Another quantity represented by a vector is

text: force

text: , since it has a magnitude and direction and follows the rules of vector addition. Vectors also describe many other physical quantities, such as linear displacement,

text: displacement

text: , linear acceleration,

text: angular acceleration

text: linear momentum

text: , and

text: angular momentum

text: . Other physical vectors, such as the

text: electric

text: and

text: magnetic field

text: , are represented as a system of vectors at each point of a physical space; that is, a

text: vector field

text: . Examples of quantities that have magnitude and direction but fail to follow the rules of vector addition: Angular displacement and electric current. Consequently, these are not vectors.

text: In a medium, light usually does not propagate at a speed equal to c; further, different types of light wave will travel at different speeds. The speed at which the individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency) propagate is called the phase velocity v. An actual physical signal with a finite extent (a pulse of light) travels at a different speed. The largest part of the pulse travels at the group velocity v, and its earliest part travels at the front velocity v.

text: In a medium, light usually does not propagate at a speed equal to c; further, different types of light wave will travel at different speeds. The speed at which the individual crests and troughs of a

text: plane wave

text: (a wave filling the whole space, with only one

text: frequency

text: ) propagate is called the

text: phase velocity

text: v. An actual physical signal with a finite extent (a pulse of light) travels at a different speed. The largest part of the pulse travels at the

text: group velocity

text: v, and its earliest part travels at the

text: front velocity

text: v.

text: Kirchhoff and Helmholtz showed, that the radiation of sound from a limited source region can be described by enclosing this source region by a control surface - the so-called Kichhoff surface. Then the sound field inside or outside the surface, where no sources are allowed and the wave operator on the left hand side applies, can be produced as a superposition of monopoles and dipoles on the surface. The theory follows directly from the wave equation. The source strength of monopoles and dipoles on the surface can be calculated if the normal velocity (for monopoles) and the pressure (for dipoles) on the surface are known respectively. A modification of the method allows even to calculate the pressure on the surface based on the normal velocity only. The normal velocity could be given by a FE-simulation of a moving structure for instance. However, the modification to avid the acoustic pressure on the surface to be known leads to problems, when considering an enclosed volume at its resonant frequencies, which is a major issue of the implementations of their method. The Kirchhoff integral method finds for instance application in Boundary element methods (BEM). A non-zero flow velocity is accounted by considering a moving frame of reference with the outer flow speed, in which the acoustic wave propagation takes place. Repetitive applications of the method can account for obstacles. First the sound field on the surface of the obstacle is calculated and then the obstacle is introduced by adding sources on its surface to cancel the normal velocity on the surface of the obstacle. Variations of the average flow field (speed of sound, density and velocity) can be taken into account by a similar method (e.g. dual reciprocity BEM).

text: Kirchhoff

text: and

text: Helmholtz

text: Boundary element method

text: s (BEM). A non-zero flow velocity is accounted by considering a moving frame of reference with the outer flow speed, in which the acoustic wave propagation takes place. Repetitive applications of the method can account for obstacles. First the sound field on the surface of the obstacle is calculated and then the obstacle is introduced by adding sources on its surface to cancel the normal velocity on the surface of the obstacle. Variations of the average flow field (speed of sound, density and velocity) can be taken into account by a similar method (e.g. dual reciprocity BEM).

text: In A-scan ultrasound biometry, a crystal oscillates to generate a high-frequency sound wave that penetrates into the eye. When the sound wave encounters a media interface, part of the sound wave is reflected back toward the probe. These echoes allow us to calculate the distance between the probe and various structures in the eye. Ultrasonography does not measure the distance but rather the time required for a sound pulse to travel from the cornea to the retina. The speed of sound varies in different parts of the eye. The eye is divided ultrasonographically into four components:Cornea, Anterior chamber, Lens thickness and Vitreous cavity. The velocity of sound in these compartments are 1620, 1532, 1641, 1532 m/s respectively. Through normal eyes an average velocity of 1555 m/s is accepted for calculation. Modern instruments use separate sound velocities for the different eye components to obtain the total axial length.  The measured transit time is converted to a distance using the formula d=t/v Where d is the distance, t is the time and v is the velocity.

text: In A-scan ultrasound biometry, a crystal oscillates to generate a high-frequency sound wave that penetrates into the eye. When the sound wave encounters a media interface, part of the sound wave is reflected back toward the probe. These echoes allow us to calculate the distance between the probe and various structures in the eye. Ultrasonography does not measure the distance but rather the time required for a sound pulse to travel from the cornea to the

text: retina

text: . The speed of sound varies in different parts of the eye. The eye is divided ultrasonographically into four components:Cornea, Anterior chamber, Lens thickness and Vitreous cavity. The velocity of sound in these compartments are 1620, 1532, 1641, 1532 m/s respectively. Through normal eyes an average velocity of 1555 m/s is accepted for calculation. Modern instruments use separate sound velocities for the different eye components to obtain the total axial length.  The measured transit time is converted to a distance using the formula d=t/v Where d is the distance, t is the time and v is the velocity.

text: Achieving a precise velocity, i.e. a precise energy & de Broglie wavelength, of the neutron beam is important. Such single-energy beams are termed 'monochromatic'. Monochromaticity is achieved either with a crystal monochromator or a time of flight spectrometer. In the time-of-flight technique, neutrons are sent through a sequence of two rotating slits, so that only neutrons of a particular velocity are selected. Recently there has been the development of spallation sources which can create a rapid pulse of neutrons. In this method, the pulse contains neutrons of many different velocities / de Broglie wavelengths. However, the velocities of the scattered neutrons can be determined afterwards by measuring the time of flight of the neutrons between the sample and neutron detector.

text: Achieving a precise velocity, i.e. a precise energy & de Broglie wavelength, of the neutron beam is important. Such single-energy beams are termed 'monochromatic'. Monochromaticity is achieved either with a crystal monochromator or a time of flight spectrometer. In the time-of-flight technique, neutrons are sent through a sequence of two rotating slits, so that only neutrons of a particular velocity are selected. Recently there has been the development of

text: spallation source

text: s which can create a rapid pulse of neutrons. In this method, the pulse contains neutrons of many different velocities / de Broglie wavelengths. However, the velocities of the scattered neutrons can be determined afterwards by measuring the time of flight of the neutrons between the sample and neutron detector.

text: Verification and Validation –Valve –Vector –Vertical strength –Viscosity –Volt –Vibration –Velocity diagrams –

text: Verification and Validation

text: Valve

text: Vector

text: Vertical strength

text: Viscosity

text: Volt

text: Vibration

text: Velocity diagrams

text: In deep water, shock waves form even from slow-moving sources, because waves with short enough wavelengths move slower. These shock waves are at sharper angles than one would naively expect, because it is group velocity that dictates the area of constructive interference and, in deep water, the group velocity is half of the phase velocity.

text: In deep water,

text: shock waves

text: form even from slow-moving sources, because waves with short enough wavelengths move slower. These shock waves are at sharper angles than one would naively expect, because it is

text: group velocity

text: that dictates the area of

text: constructive interference

text: and, in deep water, the

text: group velocity

text: is half of the

text: phase velocity

text: The average velocity is always less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, displacement can increase or decrease in magnitude as well as change direction.

text: A twist represents the velocity of a rigid body as an angular velocity around an axis and a linear velocity along this axis.  All points in the body have the same component of the velocity along the axis, however the greater the distance from the axis the greater the velocity in the plane perpendicular to this axis.  Thus, the helicoidal field formed by the velocity vectors in a moving rigid body flattens out the further the points are radially from the twist axis.

text: Once all of the velocities for the layers are known then it is possible to calculate the amount of time that is needed for the wave to travel the distance down to the midpoint between each geophone and the shot point for each of the layers. As the geophones are farther away from the shot the time taken for the wave to travel there increases which forms a hyperbola in a graph of time vs. distance. The velocity data is used to correct the curves of the hyperbolas and create a flat line where all points are at an equal depth. The final step for the semblance analysis is to sum all of the data that has been corrected for velocity. This is done with the use of a computer filter which will sum together all of the events that the traces share and remove the ones that they do not. The result is a single data set that has all of the primary peaks strongly displayed with most of the noise removed.

text: There are two velocities that are associated with waves, the phase velocity and the group velocity.  To understand them, one must consider several types of waveform. For simplification, examination is restricted to one dimension.

text: There are two velocities that are associated with waves, the

text: phase velocity

text: and the

text: group velocity

text: .  To understand them, one must consider several types of waveform. For simplification, examination is restricted to one dimension.

text: The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source. Wind shear of 4 m/(s · km) can produce refraction equal to a typical temperature lapse rate of . Higher values of wind gradient will refract sound downward toward the surface in the downwind direction, eliminating the acoustic shadow on the downwind side. This will increase the audibility of sounds downwind. This downwind refraction effect occurs because there is a wind gradient; the sound is not being carried along by the wind.

text: The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is

text: refracted

text: upward, away from listeners on the ground, creating an

text: acoustic shadow

text: at some distance from the source. Wind shear of 4 m/(s · km) can produce refraction equal to a typical temperature

text: lapse rate

text: of . Higher values of wind gradient will refract sound downward toward the surface in the downwind direction, eliminating the acoustic shadow on the downwind side. This will increase the audibility of sounds downwind. This downwind refraction effect occurs because there is a wind gradient; the sound is not being carried along by the wind.

text: The classical central-force problem was solved geometrically by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, in which Newton introduced his laws of motion.  Newton used an equivalent of leapfrog integration to convert the continuous motion to a discrete one, so that geometrical methods may be applied.  In this approach, the position of the particle is considered only at evenly spaced time points.  For illustration, the particle in Figure 10 is located at point A at time t = 0, at point B at time t = Δt, at point C at time t = 2Δt, and so on for all times t = nΔt, where n is an integer.  The velocity is assumed to be constant between these time points.  Thus, the vector r = r − r equals Δt times the velocity vector v (red line), whereas r = r − r equals vΔt (blue line).    Since the velocity is constant between points, the force is assumed to act instantaneously at each new position; for example, the force acting on the particle at point B instantly changes the velocity from v to v.  The difference vector Δr = r − r equals ΔvΔt (green line), where Δv = v − v is the change in velocity resulting from the force at point B.  Since the acceleration a is parallel to Δv and since F = ma, the force F must be parallel to Δv and Δr.  If F is a central force, it must be parallel to the vector r from the center O to the point B (dashed green line); in that case, Δr is also parallel to r.

text: The classical central-force problem was solved geometrically by

text: Isaac Newton

text: in his

entity_name: Philosophiæ Naturalis Principia Mathematica

text: Philosophiæ Naturalis Principia Mathematica

text: , in which Newton introduced his

text: laws of motion

text: .  Newton used an equivalent of

text: leapfrog integration

text: In this position-sensing version of product imaging, the position of the ions as they hit the detector is recorded.  One can imagine the ions produced by the dissociation and ionization lasers as expanding outward from the center-of-mass with a particular distribution of velocities.  It is this three-dimensional object that we wish to detect.  Since the ions created should be of the same mass, they will all be accelerated uniformly toward the detector.  It takes very little time for the whole three-dimensional object to be crushed into the detector, so the position of an ion on the detector relative to the center position is given simply by v Δt, where v is its velocity and Δt is the time between when the ions were made and when they hit the detector.  The image is thus a two-dimensional projection of the desired three-dimensional velocity distribution.  Fortunately, for systems with an axis of cylindrical symmetry parallel to the surface of the detector, the three-dimensional distribution may be recovered from the two-dimensional projection by the use of the inverse Abel transform.  The cylindrical axis is the axis containing the polarization direction of the dissociating light.  It is important to note that the image is taken in the center-of-mass frame; no transformation, other than from time to speed, is needed.

text: Abel transform

text: .  The cylindrical axis is the axis containing the polarization direction of the dissociating light.  It is important to note that the image is taken in the center-of-mass frame; no transformation, other than from time to speed, is needed.

text: The most elaborate types of ultrasonic flow meters average speed of sound over multiple paths in the pipe.  The length of each path is precisely measured in the factory.  Each path consists of an ultrasonic transducer at one end and a sensor at the other.  The meter creates a 'ping' with the transducer and measures the time elapsed before the sensor receives the sonic pulse.  Some of these paths point upstream so that the sum of the times of flight of the sonic pulses can be divided by the sum of the flight lengths to provide an average speed of sound in the upstream direction.  This speed differs from the speed of sound in the gas by the velocity at which the gas is moving in the pipe.  The other paths may be identical or similar, except that the sound pulses travel downstream.  The meter then compares the difference between the upstream and downstream speeds to calculate the velocity of gas flow.

text: Typically, microphysics schemes will use a mass-weighted average for the fall velocity. McFarquhar and Black (2004) showed that different parameterizing methods results in dramatically different terminal velocities of the hydrometeors.

text: This wave travels in the +x direction with speed (more specifically, phase velocity)

text: This wave travels in the +x direction with speed (more specifically,

text: phase velocity

text: Out of different masses, tight, heavy, middling—indicated by variations of size or color—directional line—vectors which represent speeds, velocities, accelerations, forces, etc. . . .—these directions making between them meaningful angles, and senses, together defining one big conclusion or many.

text: Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric) system as metres per second (m/s) or as the SI base unit of (m⋅s). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector.

text: Velocity is a physical

text: vector

text: quantity

text: ; both magnitude and direction are needed to define it. The

text: scalar

text: absolute value

text: magnitude

text: ) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the

text: SI

text: metric

text: ) system as

text: metres per second

text: (m/s) or as the SI base unit of (m⋅s). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector.

text: To understand forces and velocities, discussed here, one must understand what is meant by a "vector" and a "scalar." Velocity (V), denoted as boldface in this article, is an example of a vector, because it implies both direction and speed. The corresponding speed (V ), denoted as italics in this article is a scalar value. Likewise, a force vector, F, denotes direction and strength, whereas its corresponding scalar (F ) denotes strength alone. Graphically, each vector is represented with an arrow that shows direction and a length that shows speed or strength. Vectors of consistent units (e.g. V in m/s or F in N) may be added and subtracted, graphically, by positioning tips and tails of the arrows, representing the input variables and drawing the resulting derived vector.

text: To understand forces and velocities, discussed here, one must understand what is meant by a "

text: vector

text: " and a "

text: scalar

text: ." Velocity (V), denoted as

text: boldface

text: in this article, is an example of a vector, because it implies both direction and speed. The corresponding speed (V ), denoted as

text: italics

text: in this article is a scalar value. Likewise, a force vector, F, denotes direction and strength, whereas its corresponding scalar (F ) denotes strength alone. Graphically, each vector is represented with an arrow that shows direction and a length that shows speed or strength. Vectors of consistent units (e.g. V in m/s or F in

text: N

text: ) may be added and subtracted, graphically, by positioning tips and tails of the arrows, representing the input variables and drawing the resulting derived vector.

text: Fluttering is a physical phenomenon in which several degrees of freedom of a structure become coupled in an unstable oscillation driven by the wind. This movement inserts energy to the bridge during each cycle so that it neutralizes the natural damping of the structure; the composed system (bridge-fluid) therefore behaves as if it had an effective negative damping (or had positive feedback), leading to an exponentially growing response. In other words, the oscillations increase in amplitude with each cycle because the wind pumps in more energy than the flexing of the structure can dissipate, and finally drives the bridge toward failure due to excessive deflection and stress. The wind speed that causes the beginning of the fluttering phenomenon (when the effective damping becomes zero) is known as the flutter velocity. Fluttering occurs even in low-velocity winds with steady flow. Hence, bridge design must ensure that flutter velocity will be higher than the maximum mean wind speed present at the site.

text: Fluttering is a physical phenomenon in which several

text: degrees of freedom

text: of a structure become coupled in an unstable oscillation driven by the wind. This movement inserts energy to the bridge during each cycle so that it neutralizes the natural

text: damping

text: of the structure; the composed system (bridge-fluid) therefore behaves as if it had an effective negative damping (or had

text: positive feedback

text: ), leading to an exponentially growing response. In other words, the oscillations increase in

text: amplitude

text: with each cycle because the wind pumps in more energy than the flexing of the structure can dissipate, and finally drives the bridge toward failure due to excessive deflection and stress. The wind speed that causes the beginning of the fluttering phenomenon (when the effective damping becomes zero) is known as the flutter velocity. Fluttering occurs even in low-velocity winds with steady flow. Hence, bridge design must ensure that flutter velocity will be higher than the maximum mean wind speed present at the site.

text: After a cluster has become gravitationally unbound, many of its constituent stars will still be moving through space on similar trajectories, in what is known as a stellar association, moving cluster, or moving group. Several of the brightest stars in the 'Plough' of Ursa Major are former members of an open cluster which now form such an association, in this case, the Ursa Major Moving Group. Eventually their slightly different relative velocities will see them scattered throughout the galaxy. A larger cluster is then known as a stream, if we discover the similar velocities and ages of otherwise unrelated stars.

text: After a cluster has become gravitationally unbound, many of its constituent stars will still be moving through space on similar trajectories, in what is known as a

text: stellar association

text: , moving cluster, or

text: moving group

text: . Several of the brightest stars in the '

text: Plough

text: ' of

text: Ursa Major

text: are former members of an open cluster which now form such an association, in this case, the

text: Ursa Major Moving Group

text: . Eventually their slightly different relative velocities will see them scattered throughout the galaxy. A larger cluster is then known as a stream, if we discover the similar velocities and ages of otherwise unrelated stars.

text: is the Lorentz factor of the velocity  (the vertical bars  indicate the magnitude of the vector). The velocity  can be thought of the velocity of a frame  relative to a frame , and  is the velocity of an object, say a particle or another frame  relative to . In the present context, all velocities are best thought of as relative velocities of frames unless otherwise specified. The result  u ⊕ v}} is then the relative velocity of frame  relative to a frame .

text: is the

text: Lorentz factor

text: of the velocity  (the vertical bars  indicate the

text: magnitude of the vector

text: ). The velocity  can be thought of the velocity of a frame  relative to a frame , and  is the velocity of an object, say a particle or another frame  relative to . In the present context, all velocities are best thought of as relative velocities of frames unless otherwise specified. The result  u ⊕ v}} is then the relative velocity of frame  relative to a frame .

text: Any obstruction within flowing water will produce changes in velocity within the water column. The flow changes that occur in the vicinity of the substrate may cause differential movement in the bed materials near the obstruction. The magnitude of these changes varies with stream velocity, feature shape and substrate character. Generally the stream bed is deepened at the upstream end of the obstruction, and the material removed from the substrate is usually deposited in the sheltered areas behind or adjacent to the obstruction where the local velocity is sufficiently reduced. In conditions of high stream velocities, mobile bed materials, and poorly streamlined structures scour depths can be quite deep.

text: In framework of the MCA approach an object under modeling is considered as a set of interacting elements/automata. The dynamics of the set of automata are defined by their mutual forces and rules for their relationships. This system exists and operates in time and space. Its evolution in time and space is governed by the equations of motion. The mutual forces and rules for inter-elements relationships are defined by the function of the automaton response. This function has to be specified for each automaton. Due to mobility of automata the following new parameters of cellular automata have to be included into consideration: R – radius-vector of automaton; V – velocity of automaton; ω – rotation velocity of automaton; θ – rotation vector of automaton; m – mass of automaton; J – moment of inertia of automaton.

text: A five-speed, all-indirect manual transmission using a "dog-leg" selector pattern was the only transmission offered. Instead of the conventional "H" shift pattern, this arrangement (also known as a "reverse h-gate") has 1st gear situated to the far left and back, behind reverse. This pattern has been popular with racing gearboxes, as it allows quicker, more direct shifts between 2nd and 3rd, and 4th and 5th, gears. Output from the final drive to the rear wheels is via a pair of short, solid drive shafts fitted with constant-velocity joints at each end to allow for suspension articulation.

text: A five-speed,

text: all-indirect

text: manual transmission

text: using a

text: "dog-leg"

text: selector pattern was the only transmission offered. Instead of the conventional "H"

text: shift pattern

text: , this arrangement (also known as a "reverse h-gate") has 1st gear situated to the far left and back, behind reverse. This pattern has been popular with racing gearboxes, as it allows quicker, more direct shifts between 2nd and 3rd, and 4th and 5th, gears. Output from the final drive to the rear wheels is via a pair of short, solid

text: drive shaft

text: s fitted with

text: constant-velocity joint

text: s at each end to allow for suspension articulation.

text: is the velocity vector.

text: is the velocity vector.

text: Once velocity has been calculated, the volume can be calculated by multiplying the velocity by the orifice area times its flow coefficient.

text: is the relative velocity (the difference of the velocities of the bird and the plane, resulting in a lower absolute value if they are flying in the same direction and higher absolute value if they are flying in opposite directions). Therefore, the speed of the aircraft is much more important than the size of the bird when it comes to reducing energy transfer in a collision. The same can be said for jet engines: the slower the rotation of the engine, the less energy which will be imparted onto the engine at collision.

text: A set of sequential indices i may be used to enumerate elements (or subsets) of a set of ratios under study.  For example, in finance, one could define i by assigning consecutive integers to companies, to political subdivisions (such as states), to different investments, etc.  The reason for using indices i, is so a set of ratios (i=0,N) can be used in an equation so as to calculate a function of the rates such as an average of a set of ratios.  For example, the average velocity found from the set of v's mentioned above.  Finding averages may involve using weighted averages and possibly using the Harmonic mean.

text: A set of sequential indices i may be used to enumerate elements (or subsets) of a set of ratios under study.  For example, in finance, one could define i by assigning consecutive integers to companies, to political subdivisions (such as states), to different investments, etc.  The reason for using indices i, is so a set of ratios (i=0,N) can be used in an equation so as to calculate a function of the rates such as an average of a set of ratios.  For example, the average velocity found from the set of v's mentioned above.  Finding averages may involve using weighted averages and possibly using the

text: Harmonic mean

text: For turbulent boundary layer calculations, the time averaged density and velocity at the edge of the boundary layer must be used.  In the equations above,

text: The thickness of the velocity boundary layer is normally defined as the distance from the solid body at which the viscous flow velocity is 99% of the freestream velocity (the surface velocity of an inviscid flow). Displacement Thickness is an alternative definition stating that the boundary layer represents a deficit in mass flow compared to inviscid flow with slip at the wall. It is the distance by which the wall would have to be displaced in the inviscid case to give the same total mass flow as the viscous case. The no-slip condition requires the flow velocity at the surface of a solid object be zero and the fluid temperature be equal to the temperature of the surface. The flow velocity will then increase rapidly within the boundary layer, governed by the boundary layer equations, below.

text: The

text: thickness

text: of the velocity boundary layer is normally defined as the distance from the solid body at which the viscous flow velocity is 99% of the freestream velocity (the surface velocity of an inviscid flow). Displacement Thickness is an alternative definition stating that the boundary layer represents a deficit in mass flow compared to inviscid flow with slip at the wall. It is the distance by which the wall would have to be displaced in the inviscid case to give the same total mass flow as the viscous case. The

text: no-slip condition

text: requires the flow velocity at the surface of a solid object be zero and the fluid temperature be equal to the temperature of the surface. The flow velocity will then increase rapidly within the boundary layer, governed by the boundary layer equations, below.

text: as a function of position and time, write the average fluid velocity as

text: , the velocity difference

text: , the velocity difference

text: Since the discovery of neutrino oscillations, it is assumed that their speed is slightly below the speed of light. Direct velocity measurements indicated an upper limit for relative speed differences between light and neutrinos of

text: As gas velocity in the annulus depends on a calculated velocity of the solids ejected from bubbles, it is more difficult for the solids coming from the annulus with increasing velocity in the nozzle to penetrate into the central gas jet under a constant fluidization velocity. Increasing the central velocity at a height of 25 mm above the nozzle decreases the time-averaged solids concentration. However, an increase in this velocity has no effect on the solids concentration above the annulus. On the other hand, for a low central gas velocity, the solids velocities over the annulus and above the nozzle show nearly the same value with sharp velocity gradient.

text: Note that  is not the kinetic energy of the fluid per unit volume, for the following reasons. Even in the case of laminar flow, where all the flow lines are parallel to the length of the pipe, the velocity of the fluid on the inner surface of the pipe is zero due to viscosity, and the velocity in the center of the pipe must therefore be larger than the average velocity obtained by dividing the volumetric flow rate by the wet area. The average kinetic energy then involves the root mean-square velocity, which always exceeds the mean velocity. In the case of turbulent flow, the fluid acquires random velocity components in all directions, including perpendicular to the length of the pipe, and thus turbulence contributes to the kinetic energy per unit volume but not to the average lengthwise velocity of the fluid.

text: Note that  is not the kinetic energy of the fluid per unit volume, for the following reasons. Even in the case of

text: laminar flow

text: , where all the

text: flow line

text: s are parallel to the length of the pipe, the velocity of the fluid on the inner surface of the pipe is zero due to viscosity, and the velocity in the center of the pipe must therefore be larger than the average velocity obtained by dividing the volumetric flow rate by the wet area. The average kinetic energy then involves the

text: root mean-square velocity

text: , which always exceeds the mean velocity. In the case of

text: turbulent flow

text: , the fluid acquires random velocity components in all directions, including perpendicular to the length of the pipe, and thus turbulence contributes to the kinetic energy per unit volume but not to the average lengthwise velocity of the fluid.

text: The write time may vary (± 30 s) between writer and media used. For high speed, the write strategy changes from constant linear velocity (CLV) to constant angular velocity (CAV), or zoned constant linear velocity (ZCLV).  The table below largely assumes CAV.

text: The write time may vary (± 30 s) between writer and media used. For high speed, the write strategy changes from

text: constant linear velocity

text: (CLV) to

text: constant angular velocity

text: (CAV), or

text: zoned constant linear velocity

text: (ZCLV).  The table below largely assumes CAV.

text: The e'/a' ratio becomes <1 about 60 years of age, which is similar to the E/A ratio of mitral flow. Women has slightly higher S' and e' velocities than men, although the difference disappears with age. The study also did show that velocities were highest in the lateral wall, and lowest in the septum. The E/e' was thus dependent on the site of e' measurement. The ratio was also age dependent.

text: In physics, the angular velocity is defined as the rate of change of angular displacement and is a vector quantity (more precisely, a pseudovector) that specifies the angular speed (rotational speed) of an object and the axis about which the object is rotating. This speed can be measured in the SI unit of angular velocity, radians per second, or in terms of degrees per second, degrees per hour, etc. Angular velocity is usually represented by the symbol omega (ω, rarely Ω).

text: In

text: physics

text: , the angular velocity is defined as the rate of change of

text: angular displacement

text: and is a

text: vector

text: quantity (more precisely, a

text: pseudovector

text: ) that specifies the angular speed (

text: rotational speed

text: ) of an object and the axis about which the object is rotating. This speed can be measured in the

text: SI

text: unit of angular velocity,

text: radians per second

text: , or in terms of degrees per second, degrees per hour, etc. Angular velocity is usually represented by the symbol

text: omega

text: (ω, rarely Ω).

text: Minkowski in his earlier work in 1907 followed Poincaré in representing space and time together in complex form (x,y,z,ict) emphasizing the formal similarity with Euclidean space. He noted that space-time is in a certain sense a four-dimensional non-Euclidean manifold. Sommerfeld (1910) used Minkowski's complex representation to combine non-collinear velocities by spherical geometry and so derive Einstein's addition formula. Subsequent writers, principally Varićak, dispensed with the imaginary time coordinate, and wrote in explicitly non-Euclidean (i.e. Lobachevskian) form reformulating relativity using the concept of rapidity previously introduced by Alfred Robb (1911);  Edwin Bidwell Wilson and Gilbert N. Lewis (1912) introduced a vector notation for spacetime; Émile Borel (1913) showed how parallel transport in non-Euclidean space provides the kinematic basis of Thomas precession twelve years before its experimental discovery by Thomas; Felix Klein (1910) and Ludwik Silberstein (1914) employed such methods as well. One historian argues that the non-Euclidean style had little to show "in the way of creative power of discovery", but it offered notational advantages in some cases, particularly in the law of velocity addition. (So in the years before World War I, the acceptance of the non-Euclidean style was approximately equal to that of the initial spacetime formalism, and it continued to be employed in relativity textbooks of the 20th century. 1

text: Minkowski in his earlier work in 1907 followed Poincaré in representing space and time together in complex form (x,y,z,ict) emphasizing the formal similarity with Euclidean space. He noted that space-time is in a certain sense a four-dimensional non-Euclidean manifold. Sommerfeld (1910) used Minkowski's complex representation to combine non-collinear velocities by spherical geometry and so derive Einstein's addition formula. Subsequent writers, principally

text: Varićak

text: , dispensed with the imaginary time coordinate, and wrote in explicitly non-Euclidean (i.e. Lobachevskian) form reformulating relativity using the concept of

text: rapidity

text: previously introduced by

text: Alfred Robb

text: Edwin Bidwell Wilson

text: and

text: Gilbert N. Lewis

text: (1912) introduced a vector notation for spacetime;

text: Émile Borel

text: (1913) showed how parallel transport in non-Euclidean space provides the kinematic basis of

text: Thomas precession

text: twelve years before its experimental discovery by Thomas;

text: Felix Klein

text: (1910) and

text: Ludwik Silberstein

text: (1914) employed such methods as well. One historian argues that the non-Euclidean style had little to show "in the way of creative power of discovery", but it offered notational advantages in some cases, particularly in the law of velocity addition. (So in the years before

text: World War I

text: , the acceptance of the non-Euclidean style was approximately equal to that of the initial spacetime formalism, and it continued to be employed in relativity textbooks of the 20th century. 1

text: where v is the group velocity. This value should not be confused with n, which is always defined with respect to the phase velocity. When the dispersion is small, the group velocity can be linked to the phase velocity by the relation

text: where v is the

text: group velocity

text: . This value should not be confused with n, which is always defined with respect to the

text: phase velocity

text: . When the

text: dispersion

text: is small, the group velocity can be linked to the phase velocity by the relation

text: As the exponents are additive inverses of each other, the images represent equal speeds in opposite directions.

text: As the exponents are

text: additive inverse

text: s of each other, the images represent equal speeds in opposite directions.

text: The velocity vector of a point A in the wheel is perpendicular to the segment AP and is proportional to the length of this segment.  In particular, the velocities of points in the wheel are determined by the angular velocity of the wheel in rotation around P.  The velocity vectors of a number of points are illustrated in sketch 3.

text: Traditionally sound pressure is measured using microphones. Microphones have a polar pattern describing their sensitivity as a function of the direction of the incident sound. Many microphones have an omnidirectional polar pattern which means their sensitivity is independent of the direction of the incident sound. Microphones with other polar patterns exist that are more sensitive in a certain direction. This however is still no solution for the sound localization problem as one tries to determine either an exact direction, or a point of origin. Besides considering microphones that measure sound pressure, it is also possible to use a particle velocity probe to measure the acoustic particle velocity directly. The particle velocity is another quantity related to acoustic waves however, unlike sound pressure, particle velocity is a vector. By measuring particle velocity one obtains a source direction directly. Other more complicated methods using multiple sensors is also possible. Many of these methods use the time difference of arrival (TDOA) technique.

text: Traditionally

text: sound pressure

text: is measured using microphones. Microphones have a

text: polar pattern

text: describing their sensitivity as a function of the direction of the incident sound. Many microphones have an omnidirectional polar pattern which means their sensitivity is independent of the direction of the incident sound. Microphones with other polar patterns exist that are more sensitive in a certain direction. This however is still no solution for the sound localization problem as one tries to determine either an exact direction, or a point of origin. Besides considering microphones that measure

text: sound pressure

text: , it is also possible to use a

text: particle velocity probe

text: to measure the acoustic

text: particle velocity

text: directly. The particle velocity is another quantity related to

text: acoustic wave

text: s however, unlike sound pressure, particle velocity is a

text: vector

text: . By measuring particle velocity one obtains a source direction directly. Other more complicated methods using multiple sensors is also possible. Many of these methods use the

text: time difference of arrival

text: (TDOA) technique.

text: |Neutron velocity vector||-|

text: |Neutron velocity vector||-|

text: Shock describes matter subject to extreme rates of force with respect to time. Shock is a vector that has units of an acceleration (rate of change of velocity).  The unit g (or g) represents multiples of the acceleration of gravity and is conventionally used.

text: The drift velocity deals with the average velocity of a particle, such as an electron, due to an electric field. In general, an electron will propagate randomly in a conductor at the Fermi velocity. Free electrons in a conductor follow a random path.  Without the presence of an electric field, the electrons have no net velocity.  When a DC voltage is applied, the electron drift velocity will increase in speed proportionally to the strength of the electric field. The drift velocity is on the order of millimeters per hour. AC voltages cause no net movement; the electrons oscillate back and forth in response to the alternating electric field (over a distance of a few micrometers – see example calculation).

text: The

text: drift velocity

text: deals with the average velocity of a particle, such as an electron, due to an electric field. In general, an electron will propagate randomly in a conductor at the

text: Fermi velocity

text: . Free electrons in a conductor follow a random path.  Without the presence of an electric field, the electrons have no net velocity.  When a

text: DC voltage

text: is applied, the electron drift velocity will increase in speed proportionally to the strength of the electric field. The drift velocity is on the order of millimeters per hour.

text: AC voltage

text: s cause no net movement; the electrons oscillate back and forth in response to the alternating electric field (over a distance of a few micrometers – see

text: example calculation

text: The actual velocity of the missile is denoted by V and the missile is subject to both the acceleration due to gravity g and that due to the engines a.  The velocity to be gained is defined as the difference between V and V:

text: The strong dielectric boundary effects that result from this tight confinement substantially alter the optical dispersion relation.  By selecting the waveguide geometry, it is possible to tailor the dispersion to have desired properties, which is of crucial importance to applications requiring ultrashort pulses.  In particular, the group velocity dispersion (that is, the extent to which group velocity varies with wavelength) can be closely controlled.  In bulk silicon at 1.55 micrometres, the group velocity dispersion (GVD) is normal in that pulses with longer wavelengths travel with higher group velocity than those with shorter wavelength.  By selecting a suitable waveguide geometry, however, it is possible to reverse this, and achieve anomalous GVD, in which pulses with shorter wavelengths travel faster.  Anomalous dispersion is significant, as it is a prerequisite for soliton propagation, and modulational instability.

text: The strong

entity_name: Interface conditions for electromagnetic fields

text: dielectric boundary effects

text: that result from this tight confinement substantially alter the

text: optical dispersion relation

text: .  By selecting the waveguide geometry, it is possible to tailor the dispersion to have desired properties, which is of crucial importance to applications requiring ultrashort pulses.  In particular, the group velocity dispersion (that is, the extent to which

text: group velocity

text: varies with wavelength) can be closely controlled.  In bulk silicon at 1.55 micrometres, the group velocity dispersion (GVD) is normal in that pulses with longer wavelengths travel with higher group velocity than those with shorter wavelength.  By selecting a suitable waveguide geometry, however, it is possible to reverse this, and achieve anomalous GVD, in which pulses with shorter wavelengths travel faster.  Anomalous dispersion is significant, as it is a prerequisite for

text: soliton

text: propagation, and

text: modulational instability

text: Apparent wind velocity is the vector sum of the true wind and the headwind an object would experience in still air.  The headwind velocity in still air is inverse of the object's velocity, therefore the apparent wind can also be defined as a vector subtraction: the Velocity of the wind minus the Velocity of the object.

text: Apparent wind

text: velocity

text: is the

text: vector sum

text: of the true wind and the headwind an object would experience in still air.  The headwind velocity in still air is

text: inverse

text: of the object's velocity, therefore the apparent wind can also be defined as a vector subtraction: the Velocity of the wind minus the Velocity of the object.

text: Sound velocity level (SVL) or acoustic velocity level or particle velocity level is a logarithmic measure of the effective particle velocity of a sound relative to a reference value.<br>Sound velocity level, denoted L and measured in dB, is defined by

text: Sound velocity level (SVL) or acoustic velocity level or particle velocity level is a

text: logarithmic measure

text: of the effective particle velocity of a sound relative to a reference value.<br>Sound velocity level, denoted L and measured in

text: dB

text: , is defined by

text: Linear speed is the distance travelled per unit of time, while tangential speed (or tangential velocity) is the linear speed of something moving along a circular path. A point on the outside edge of a merry-go-round or turntable travels a greater distance in one complete rotation than a point nearer the center. Travelling a greater distance in the same time means a greater speed, and so linear speed is greater on the outer edge of a rotating object than it is closer to the axis. This speed along a circular path is known as tangential speed because the direction of motion is tangent to the circumference of the circle. For circular motion, the terms linear speed and tangential speed are used interchangeably, and both use units of m/s, km/h, and others.

text: Linear speed is the distance travelled per unit of time, while tangential speed (or tangential velocity) is the linear speed of something moving along a circular path. A point on the outside edge of a

text: merry-go-round

text: or

text: turntable

text: travels a greater distance in one complete rotation than a point nearer the center. Travelling a greater distance in the same time means a greater speed, and so linear speed is greater on the outer edge of a rotating object than it is closer to the axis. This speed along a circular path is known as tangential speed because the direction of motion is

text: tangent

text: to the

text: circumference

text: of the circle. For circular motion, the terms linear speed and tangential speed are used interchangeably, and both use units of m/s, km/h, and others.

text: The Green-Kubo relations can be used to calculate the thermal transport properties of a mineral.  Since the velocities of the ions are stored at each numerical step, one can calculate the time correlation of later velocities with earlier velocities.  The integral of these correlations is related to the Fourier thermal coefficient.

text: The

text: Green-Kubo

text: relations can be used to calculate the thermal transport properties of a mineral.  Since the velocities of the ions are stored at each numerical step, one can calculate the time correlation of later velocities with earlier velocities.  The integral of these correlations is related to the Fourier thermal coefficient.

text: Any velocity can be interpreted as the slope of a curve; in geometric units, slopes are evidently dimensionless ratios. Physical quantities which can be identified with dimensionless ratios include the components of the electromagnetic potential four-vector and the electromagnetic current four-vector.

text: Any

text: velocity

text: can be interpreted as the

text: slope

text: of a curve; in geometric units, slopes are evidently

text: dimensionless

text: ratios. Physical quantities which can be identified with dimensionless ratios include the components of the

text: electromagnetic potential

text: four-vector and the

text: electromagnetic current

text: four-vector.

text: In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase velocity and group velocity.

text: In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of

text: phase velocity

text: and

text: group velocity

text: is the velocity vector

text: is the velocity vector

text: The measured wind velocity is taken at near sea level, and does not account for effects of wind gradient with reported true wind speed of  at mast head height of over . The measured sea-level wind direction shifted away from 180 degrees between the time of setting of the course and commencement of sailing of the downwind leg, by which time wind direction was reported to be at around 160 degrees. As such the ratio between downwind velocity made good and wind speed is an approximation only.

text: The measured wind velocity is taken at near sea level, and does not account for effects of

text: wind gradient

text: with reported true wind speed of  at mast head height of over . The measured sea-level wind direction shifted away from 180 degrees between the time of setting of the course and commencement of sailing of the downwind leg, by which time wind direction was reported to be at around 160 degrees. As such the ratio between downwind

text: velocity made good

text: and wind speed is an approximation only.

text: An object's average acceleration over a period of time is its change in velocity

text: An object's average acceleration over a period of

text: time

text: is its change in

text: velocity

text: In the case of rigid bodies, the so-called quadratic velocity vector

text: If the average value of a quantity is denoted by an overbar, then the average Eulerian velocity vector ū and average Lagrangian velocity vector ū are:

text: If the

text: average

text: value of a quantity is denoted by an overbar, then the average Eulerian velocity vector ū and average Lagrangian velocity vector ū are:

text: Vectors are fundamental in the physical sciences.  They can be used to represent any quantity that has both a magnitude and direction, such as velocity, the magnitude of which is speed. For example, the velocity 5 meters per second upward could be represented by the vector  (in 2 dimensions with the positive  axis as 'up'). Another quantity represented by a vector is force, since it has a magnitude and direction. Vectors also describe many other physical quantities, such as displacement, acceleration, momentum, and angular momentum.  Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field.

text: Vectors are fundamental in the physical sciences.  They can be used to represent any quantity that has both a magnitude and direction, such as

text: velocity

text: , the magnitude of which is

text: speed

text: . For example, the velocity 5 meters per second upward could be represented by the vector  (in 2 dimensions with the positive  axis as 'up'). Another quantity represented by a vector is

text: force

text: , since it has a magnitude and direction. Vectors also describe many other physical quantities, such as

text: displacement

text: acceleration

text: momentum

text: , and

text: angular momentum

text: .  Other physical vectors, such as the

text: electric

text: and

text: magnetic field

text: vector field

text: is called the group velocity or Lieb-Robinson velocity.

text: More precisely, the vorticity is a pseudovector field , defined as the curl (rotational) of the flow velocity  vector.  The definition can be expressed by the vector analysis formula:

text: More precisely, the vorticity is a

text: pseudovector

text: field

text: , defined as the

text: curl

text: (rotational) of the

text: flow velocity

text: vector.  The definition can be expressed by the

text: vector analysis

text: formula:

text: is the average Cooper pair velocity,

text: is the average Cooper pair velocity,

text: To find the relativistic transformation law, it is useful to introduce the four-velocities  (V, V, 0, 0)}} and  (U, U, U, U)}}. The four-velocity is defined to be a four-vector with relativistic length equal to , future-directed and tangent to the world line of the object in spacetime. Here,  corresponds to the time component and  to the  component of the fly's four-velocity as seen by the ship. It is convenient to take the -axis to be the direction of motion of the ship, and the -axis so that the  plane is the plane spanned by the motion of the ship and the fly. This results in several components of the velocities being zero;  V  U  0}}.

text: To find the relativistic transformation law, it is useful to introduce the four-velocities  (V, V, 0, 0)}} and  (U, U, U, U)}}. The

text: four-velocity

text: is defined to be a

text: four-vector

text: with

text: relativistic length

text: equal to , future-directed and tangent to the

text: world line

text: of the object in spacetime. Here,  corresponds to the time component and  to the  component of the fly's four-velocity as seen by the ship. It is convenient to take the -axis to be the direction of motion of the ship, and the -axis so that the  plane is the plane spanned by the motion of the ship and the fly. This results in several components of the velocities being zero;  V  U  0}}.

text: There are two typical protocols of SMD: one in which pulling velocity is held constant, and one in which applied force is constant. Typically, part of the studied system (e.g., an atom in a protein) is restrained by a harmonic potential. Forces are then applied to specific atoms at either a constant velocity or a constant force. Umbrella sampling is used to move the system along the desired reaction coordinate by varying, for example, the forces, distances, and angles manipulated in the simulation. Through umbrella sampling, all of the system's configurations—both high-energy and low-energy—are adequately sampled. Then, each configuration's change in free energy can be calculated as the potential of mean force. A popular method of computing PMF is through the weighted histogram analysis method (WHAM), which analyzes a series of umbrella sampling simulations.

text: There are two typical protocols of SMD: one in which pulling velocity is held constant, and one in which applied force is constant. Typically, part of the studied system (e.g., an atom in a protein) is restrained by a harmonic potential. Forces are then applied to specific atoms at either a constant velocity or a constant force.

text: Umbrella sampling

text: is used to move the system along the desired reaction coordinate by varying, for example, the forces, distances, and angles manipulated in the simulation. Through umbrella sampling, all of the system's configurations—both high-energy and low-energy—are adequately sampled. Then, each configuration's change in free energy can be calculated as the

text: potential of mean force

text: . A popular method of computing PMF is through the weighted histogram analysis method (WHAM), which analyzes a series of umbrella sampling simulations.

text: To solve a noise and vibration problem with SEA, the system is partitioned into a number of components (such as plates, shells, beams and acoustic cavities) that are coupled together at various junctions. Each component can support a number of different propagating wavetypes (for example,the bending, longitudinal and shear wavefields in a thin isotropic plate).  From an SEA point of view, the reverberant field of each wavefield represents an orthogonal store of energy and so is represented as a separate energy degree of freedom in the SEA equations.  The energy storage capacity of each reverberant field is described by a parameter termed the 'modal density', which depends on the average speed with which waves propagate energy through the subsystem (the average group velocity), and the overall dimension of the subsystem.  The transmission of energy between different wavefields at a given type of junction is described by parameters termed 'coupling loss factors'.  Each coupling loss factor describes the input power to the direct field of a given receiving subsystem per unit energy in the reverberant field of a particular source subsystem.  The coupling loss factors are typically calculated by considering the way in which waves are scattered at different types of junctions (for example, point, line and area junctions).  Strictly, SEA predicts the average response of a population or ensemble of systems and so the coupling loss factors and modal densities represent ensemble average quantities.  To simplify the calculation of the coupling loss factors it is often assumed that there is significant scattering within each subsystem (when viewed across an ensemble) so that direct field transmission between multiple connections to the same subsystem is negligible and reverberant transmission dominates.  In practical terms, this means that SEA is often best suited for problems in which each subsystem is large compared with a wavelength (or from a modal point of view, each subsystem contains several modes in a given frequency band of interest).  The SEA equations contain a relatively small number of degrees of freedom and so can be easily inverted to find the reverberant energy in each subsystem due to a given set of external input powers.  The (ensemble average) sound pressure levels and vibration velocities within each subsystem can then be obtained by superimposing the direct and reverberant fields within each subsystem.

text: To solve a noise and vibration problem with SEA, the system is partitioned into a number of components (such as

text: plate

text: s, shells,

text: beams

text: and acoustic cavities) that are coupled together at various junctions. Each component can support a number of different propagating wavetypes (for example,the

text: bending

text: longitudinal

text: and

text: shear

text: wavefields in a thin isotropic plate).  From an SEA point of view, the

text: reverberant field

text: of each wavefield represents an orthogonal store of energy and so is represented as a separate energy degree of freedom in the SEA equations.  The energy storage capacity of each reverberant field is described by a parameter termed the 'modal density', which depends on the average speed with which waves propagate energy through the subsystem (the average

text: group velocity

text: In some cases, the average velocity field

text: Along with other members of the Feynman team, Ashkin produced technical reports while at Los Alamos. These were classified at the time but have since been made public. One example gives an idea of the work carried out by the group. It is The Calculation of Critical Masses Including the Effects of the Distribution of Neutron Energies, by Feynman, R.P.; Welton, T.A.; Ashkin, J.; Ehrlich, R.; Peshkin, M.; and Reines, F. Report LA-524(Del.) January 21, 1947 (extract from abstract: "Convenient approximate methods are developed for the calculation of critical sizes and multiplication rates of spherical, active cores surrounded by infinite tampers. Special attention is given to those problems arising from the fact that neutrons of different velocities have different properties. The methods consist essentially of approximating the neutron densities at each velocity by fundamental mode shapes for each velocity.")

text: 3.  Calculate the burnout velocity, and sum it with the initial velocity for each individual stage.  Assuming each stage occurs immediately after the previous, the burnout velocity becomes the initial velocity for the following stage.

text: If a stationary box contains many particles, it weighs more in its rest frame, the faster the particles are moving. Any energy in the box (including the kinetic energy of the particles) adds to the mass, so that the relative motion of the particles contributes to the mass of the box. But if the box itself is moving (its center of mass is moving), there remains the question of whether the kinetic energy of the overall motion should be included in the mass of the system. The invariant mass is calculated excluding the kinetic energy of the system as a whole (calculated using the single velocity of the box, which is to say the velocity of the box's center of mass), while the relativistic mass is calculated including invariant mass plus the kinetic energy of the system which is calculated from the velocity of the center of mass.

text: If a stationary box contains many particles, it weighs more in its rest frame, the faster the particles are moving. Any energy in the box (including the kinetic energy of the particles) adds to the mass, so that the relative motion of the particles contributes to the mass of the box. But if the box itself is moving (its

text: center of mass

text: is moving), there remains the question of whether the kinetic energy of the overall motion should be included in the mass of the system. The invariant mass is calculated excluding the kinetic energy of the system as a whole (calculated using the single velocity of the box, which is to say the velocity of the box's center of mass), while the relativistic mass is calculated including invariant mass plus the kinetic energy of the system which is calculated from the velocity of the center of mass.

text: over velocity. These variables are only functions of position and time, which means that some information is lost. In multifluid theory, the different particle species are treated as different fluids with different pressures, densities and flow velocities. The equations governing the plasma moments are called the moment or fluid equations.

text: In the case of engines outputting shaft power, engine speed is measured in revolutions per minute (RPM).  Engines may be classified as low-speed, medium-speed or high-speed but these terms are inexact and depend on the type of engine being described. Generally, diesel engines operate at lower speed compared to gasoline engines. Electric motors and turboshafts are capable of very high speeds. In the case of engines producing thrust, it is rather inaccurate to talk of an 'engine speed' since what is moving is not the engine, but the working medium that the engine is accelerating; in this case one talks of an exhaust velocity, which is exactly the I outside of a gravitational field and therefore makes one jump straight to a discussion of efficiency; see the article on specific impulse for more information.

text: In the case of engines outputting shaft power, engine speed is measured in

text: revolutions per minute

text: (RPM).  Engines may be classified as low-speed, medium-speed or high-speed but these terms are inexact and depend on the type of engine being described. Generally, diesel engines operate at lower speed compared to gasoline engines. Electric motors and turboshafts are capable of very high speeds. In the case of engines producing thrust, it is rather inaccurate to talk of an 'engine speed' since what is moving is not the engine, but the working medium that the engine is accelerating; in this case one talks of an

text: exhaust velocity

text: , which is exactly the

text: I

text: outside of a gravitational field and therefore makes one jump straight to a discussion of efficiency; see the article on

text: specific impulse

text: for more information.

text: The flow velocity difference between adjacent layers can be measured in terms of velocity gradient. It is given by ∆u/∆y

text: The

text: flow velocity

text: difference between adjacent layers can be measured in terms of velocity gradient. It is given by ∆u/∆y

text: are the "course" (azimuth of the velocity vector) and "path angle" (elevation angle of the velocity vector).  Integration of the normal probability density function of the velocity, above, over the course (from 0 to

text: 'Velocity  of  speed       m/sAcceleration                  m/s2Density                           kg/m3Forces                            N

text: The spectral resolution can also be expressed in terms of physical quantities, such as velocity; then it describes the difference between velocities

text: In studying the trajectory, it is the direction of the velocity vector, rather than that of the body, which is of interest.  The direction of the velocity vector when projected on to the horizontal will be called the track, denoted

text: The Lorentz factor here applies to the velocity v, the relative velocity between the frames. This is not necessarily the same as the velocity u of an object.

text: As the turbine rotates, in this case in a clockwise direction, the motion of the foil through the fluid changes the apparent velocity and angle of attack (speed and direction) of the fluid with respect to the frame of reference of the foil.  The combined effect of these two flow components (i.e. the vector sum), yields the net total "Apparent flow velocity" as shown in the next figure.

text: As the turbine rotates, in this case in a clockwise direction, the motion of the foil through the fluid changes the

text: apparent velocity

text: and

text: angle of attack

text: (speed and direction) of the fluid with respect to the

text: frame of reference

text: of the foil.  The combined effect of these two flow components (i.e. the

text: vector

text: sum), yields the net total "Apparent flow velocity" as shown in the next figure.

text: A pulse with different group and phase velocities (which occurs if the phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as dispersion. Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light, which has been confirmed in various experiments.The opposite, group velocities exceeding c, has also been shown in experiment. It should even be possible for the group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time.

text: A pulse with different group and phase velocities (which occurs if the phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as

text: dispersion

text: . Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called

text: slow light

text: , which has been confirmed in various experiments.The opposite, group velocities exceeding c, has also been shown in experiment. It should even be possible for the group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time.

text: Variations include common velocity obstacles (CVO), finite-time-interval velocity obstacles (FVO), generalized velocity obstacles (GVO), hybrid reciprocal velocity obstacles (HRVO), nonlinear velocity obstacles (NLVO),  reciprocal velocity obstacles (RVO), and recursive probabilistic velocity obstacles (PVO).

text: Variations include common velocity obstacles (CVO), finite-time-interval velocity obstacles (FVO),

text: generalized

text: velocity obstacles (GVO),

text: hybrid

text: reciprocal velocity obstacles (HRVO),

text: nonlinear

text: velocity obstacles (NLVO),  reciprocal velocity obstacles (RVO), and

text: recursive

text: probabilistic

text: velocity obstacles (PVO).

text: The table above shows typical muzzle velocities available in commercial 30-06 loads along with maximum 30-06 muzzle velocities reported by several reloading manuals for common bullet weights. Hodgdon, Nosler, and Barnes report velocities for  barrels. Hornady and Speer report velocities for  barrels. The data are all for barrels with a twist rate of 1 turn in  which is needed to stabilize the heaviest bullets. The higher muzzle velocities reported by Nosler for  and heavier bullets use loads employing a slow-burning, double-base powder (Alliant Reloder 22).

text: In the case of nanotube nanomotors however, the intershell friction in the multi-walled nanotubes (MWNT) is remarkably small. Molecular dynamics studies show that, with the exception of small peaks, the frictional force remains almost negligible for all sliding velocities until a special sliding velocity is reached. Simulations relating the sliding velocity, induced rotation, inter-shell frictional force to the applied force provide explanations for the low inter-wall friction. Contrary to macroscale expectations the speed at which an inner tube travels within an outer tube does not follow a linear relationship with the applied force. Instead, the speed remains constant (as in a plateau) despite increasing applied force occasionally jumping in value to the next plateau. No real rotation is noticed in nonchiral inner tubes. In the case of chiral tubes a true rotation is noticed and the angular velocity also jumps to plateaus along with the jumps in the linear velocity. These plateaus and jumps can be explained as a natural outcome of frictional peaks for growing velocity, the stable (rising) side of the peak leading to a plateau, the dropping (unstable) side leading to a jump. These peaks occur due to parametric excitation of vibrational modes in the walls of the tubes due to the sliding of the inner tube. With the exception of small peaks, that correspond to the speed plateaus, the frictional force remains almost negligible for all sliding velocities until a special sliding velocity. These velocity plateaus correspond to the peaks in the frictional force. The sudden rise in sliding velocity is due to a resonance condition between a frequency that is dependent on the inter-tube corrugation period and particular phonon frequencies of the outer tube which happen to possess a group velocity approximately equal to the sliding velocity.

text: In the case of nanotube nanomotors however, the intershell friction in the multi-walled nanotubes (MWNT) is remarkably small.

text: Molecular dynamics

text: The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves.

text: The phase velocity is the speed at which the crests or the

text: phase

text: of the

text: wave

text: moves, which may be different from the

text: group velocity

text: , the speed at which the pulse of light or the

text: envelope

text: of the wave moves.

text: Even though angular velocity, angular frequency and the unit hertz all have the dimension 1/s, angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate angular unit such as radians per second. Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2 rad/s or 1 Hz, where the former measures the angular velocity and the latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second is

text: Even though

text: angular velocity

text: angular frequency

text: and the unit hertz all have the dimension 1/s, angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate angular unit such as

text: radians per second

text: . Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2 rad/s or 1 Hz, where the former measures the

text: angular velocity

text: and the latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular velocity ω measured in

text: radians

text: per second is

text: In The Flash episode "Legends of Today", a drug called Velocity 6 is developed by Earth-2's Harrison Wells and Caitlin Snow to make Barry Allen faster against Zoom by improving his ability to take in oxygen using the heat he generated via lightning when he runs. Jay Garrick uses the drug to save Wells' life after he was shot; the drug temporarily restores Jay's speed so that he can remove a bullet preventing Caitlin from operating on Wells. However, Jay states that he will never use the drug again, nor wants Barry to ever take it. In the episode "Welcome to Earth Two", Jay reveals that he had experimented with Velocity 6 on Earth-Two to make himself faster, but it ended up making him sick, slowly killing him. Caitlin makes a serum called Velocity 7 to give Jay his speed without the negative side effects. It appears effective until it stops working during Jay's fight against Geomancer. Later, Caitlin says that she plans to make more versions of the drug to help Jay. In the next episode, "Escape from Earth Two", Caitlin creates Velocity 8, which is made to last longer. However, after simulations show the same long term effects, she makes Velocity 9 instead to correct the problems. During Velocity 9's development, Caitlin had asked Eliza Harmon for help, as she was having trouble with the synthesis. She sent information on 3 of the 8 components to Eliza. After Geomancer damages a building to draw him out, Jay takes V9, giving him his speed back long enough to save the people inside. It's then shown that V9 is beginning to restore Jay's regenerative abilities, repairing the cells damaged from using Velocity 6. In episode 16 ("Trajectory"), a new speedster calling herself "Trajectory" appears. She turns out to be a colleague of Caitlin Snow's who used a reverse-engineered V9 to gain superhuman speed and wreak havoc on Central City. The drug caused Eliza to develop an immoral split personality which became Trajectory. This version of V9 is a highly addictive drug that causes rapid cellular decay if overused. When Trajectory is nearly defeated by the Flash, she takes more V9. As she runs off, her lightning turns blue, like Zoom's, and she dissolves into dust (possibly due to the accelerated cellular degeneration). During the conflict, Barry finds out about V9's existence and considers using it to increase his own speed and defeat Zoom. However, after some advice from Wells, he decides not to use the drug and destroys the only remaining sample.

text: In

text: The Flash

text: episode "Legends of Today", a drug called Velocity 6 is developed by Earth-2's Harrison Wells and Caitlin Snow to make Barry Allen faster against Zoom by improving his ability to take in oxygen using the heat he generated via lightning when he runs. Jay Garrick uses the drug to save Wells' life after he was shot; the drug temporarily restores Jay's speed so that he can remove a bullet preventing Caitlin from operating on Wells. However, Jay states that he will never use the drug again, nor wants Barry to ever take it. In the episode "Welcome to Earth Two", Jay reveals that he had experimented with Velocity 6 on Earth-Two to make himself faster, but it ended up making him sick, slowly killing him. Caitlin makes a serum called Velocity 7 to give Jay his speed without the negative side effects. It appears effective until it stops working during Jay's fight against

text: Geomancer

text: . Later, Caitlin says that she plans to make more versions of the drug to help Jay. In the next episode, "Escape from Earth Two", Caitlin creates Velocity 8, which is made to last longer. However, after simulations show the same long term effects, she makes Velocity 9 instead to correct the problems. During Velocity 9's development, Caitlin had asked

text: Eliza Harmon

text: for help, as she was having trouble with the synthesis. She sent information on 3 of the 8 components to Eliza. After Geomancer damages a building to draw him out, Jay takes V9, giving him his speed back long enough to save the people inside. It's then shown that V9 is beginning to restore Jay's regenerative abilities, repairing the cells damaged from using Velocity 6. In episode 16 ("Trajectory"), a new speedster calling herself "

text: Trajectory

text: " appears. She turns out to be a colleague of Caitlin Snow's who used a reverse-engineered V9 to gain superhuman speed and wreak havoc on Central City. The drug caused Eliza to develop an immoral split personality which became Trajectory. This version of V9 is a highly addictive drug that causes rapid cellular decay if overused. When Trajectory is nearly defeated by the Flash, she takes more V9. As she runs off, her lightning turns blue, like Zoom's, and she dissolves into dust (possibly due to the accelerated cellular degeneration). During the conflict, Barry finds out about V9's existence and considers using it to increase his own speed and defeat Zoom. However, after some advice from Wells, he decides not to use the drug and destroys the only remaining sample.

text: where r is air density, A is rotor area, and V is wind velocity. This means that the amount of energy available in the wind is directly proportional to the wind speed cubed. For example, assuming that all other variables are held constant, doubling the wind speed would increase the available energy in the wind by 8 times. A slight increase in wind speed results in dramatic increases in wind power. Unfortunately, this also means that if the wind speeds were to slow down even slightly, it’d drastically reduce wind power.

text: The velocity is calculated by measuring the travel time from the piezoelectric transmitter to the receiver, normally with the units microsecond per foot (a measure of slowness).  To compensate for the variations in the drilling mud thickness, there are actually two receivers, one near and one far.  This is because the travel time within the drilling mud will be common for both, so the travel time within the formation is given by:

text: The velocity is calculated by measuring the travel time from the

text: piezoelectric

text: transmitter to the receiver, normally with the units microsecond per foot (a measure of

text: slowness

text: ).  To compensate for the variations in the

text: drilling mud

text: thickness, there are actually two receivers, one near and one far.  This is because the travel time within the drilling mud will be common for both, so the travel time within the formation is given by:

text: In general for three objects A (e.g. Galilei), B (e.g. ship), C (e.g. falling body on ship) the velocity vector  of C relative to A (velocity of falling object as Galilei sees it) is the sum of the velocity  of C relative to B (velocity of falling object relative to ship) plus the velocity  of B relative to A (ships velocity relative to the shore). The addition here is the vector addition of vector algebra and the resulting velocity is usually represented in the form

text: Unlike spectral Doppler, Colour tissue Doppler samples velocities from all points of the sector, by shooting two pulses successively, and calculating the velocity from the phase shift between them by autocorrelation. The calculation is slightly different from the true Doppler effect, but the result becomes identical. This results in a single velocity value per sample volume. The result is a velocity field of (nearly) simultaneous velocity vectors towards the probe. The advantage of colour Doppler over spectral Doppler is that all velocities can be sampled simultaneously. The disadvantage is that if there is clutter noise (stationary reverberations), the stationary echoes will be integrated in the velocity calculation, resulting in an under estimate. As pulsed wave Doppler are displayed as a spectrum, the colour Doppler values will correspond to the mean of the spectrum (in the absence of clutter), giving slightly lower values. In the HUNT study, the difference in peak systolic values were about 1.5 cm/s.

text: Unlike spectral Doppler, Colour tissue Doppler samples velocities from all points of the sector, by shooting two pulses successively, and calculating the velocity from the phase shift between them by

text: autocorrelation

text: . The calculation is slightly different from the true

text: Doppler effect

text: , but the result becomes identical. This results in a single velocity value per sample volume. The result is a velocity field of (nearly) simultaneous velocity vectors towards the probe. The advantage of colour Doppler over spectral Doppler is that all velocities can be sampled simultaneously. The disadvantage is that if there is clutter noise (stationary reverberations), the stationary echoes will be integrated in the velocity calculation, resulting in an under estimate. As pulsed wave Doppler are displayed as a spectrum, the colour Doppler values will correspond to the mean of the spectrum (in the absence of clutter), giving slightly lower values. In the HUNT study, the difference in peak systolic values were about 1.5 cm/s.

text: An analysis of the propagation speed indicates that the rupture propagated at a normal velocity along the original segment, but increased in velocity to above the S-wave velocity after the jump across the extensional stepover and continued at that speed until propagation stopped. This makes the Kunlun earthquake the best documented example of a supershear earthquake. It has been suggested that the unusually wide zone of co-seismic deformation is a direct result of the supershear rupture propagation.

text: An analysis of the propagation speed indicates that the rupture propagated at a normal velocity along the original segment, but increased in velocity to above the

text: S-wave

text: velocity after the jump across the extensional stepover and continued at that speed until propagation stopped. This makes the Kunlun earthquake the best documented example of a

text: supershear earthquake

text: . It has been suggested that the unusually wide zone of co-seismic deformation is a direct result of the supershear rupture propagation.

text: where a is the local speed of sound. The flow velocity  is again equal to , with  the velocity potential. The full potential equation is valid for sub-, trans- and supersonic flow at arbitrary angle of attack, as long as the assumption of irrotationality is applicable.

text: where a is the local

text: speed of sound

text: . The flow velocity  is again equal to , with  the velocity potential. The full potential equation is valid for

text: sub-

text: trans-

text: and

text: supersonic flow

text: at arbitrary

text: angle of attack

text: , as long as the assumption of irrotationality is applicable.

text: A variable named velocity with a Vector composite type would be declared as Vector velocity; Members of the velocity would be accessed using a dot notation.  For example, velocity.x = 5; would set the x component of velocity equal to 5.

text: Also indirect constraints on neutrino velocity, on the basis of effective field theories such as SME, can be achieved by searching for threshold effects such as Vacuum Cherenkov radiation. For example, neutrinos should exhibit Bremsstrahlung in the form of electron-positron pair production. Another possibility in the same framework is the investigation of the decay of pions into muons and neutrinos. Superluminal neutrinos would considerably delay those decay processes. The absence of those effects indicate tight limits for velocity differences between light and neutrinos.

text: Also indirect constraints on neutrino velocity, on the basis of effective field theories such as SME, can be achieved by searching for threshold effects such as Vacuum Cherenkov radiation. For example, neutrinos should exhibit

text: Bremsstrahlung

text: in the form of electron-positron

text: pair production

text: . Another possibility in the same framework is the investigation of the decay of

text: pion

text: s into muons and neutrinos. Superluminal neutrinos would considerably delay those decay processes. The absence of those effects indicate tight limits for velocity differences between light and neutrinos.

text: Based on this star's kinematic properties, it appears to belong to a stellar association called the Castor Moving Group. However, Vega may be much older than this group, so the membership remains uncertain. This group contains about 16 stars, including Alpha Librae, Alpha Cephei, Castor, Fomalhaut and Vega. All members of the group are moving in nearly the same direction with similar space velocities. Membership in a moving group implies a common origin for these stars in an open cluster that has since become gravitationally unbound. The estimated age of this moving group is , and they have an average space velocity of 16.5 km/s.

text: Based on this star's kinematic properties, it appears to belong to a stellar association called the

text: Castor Moving Group

text: . However, Vega may be much older than this group, so the membership remains uncertain. This group contains about 16 stars, including

text: Alpha Librae

text: Alpha Cephei

text: Castor

text: Fomalhaut

text: and Vega. All members of the group are moving in nearly the same direction with similar

text: space velocities

text: . Membership in a moving group implies a common origin for these stars in an

text: open cluster

text: that has since become gravitationally unbound. The estimated age of this moving group is , and they have an average space velocity of 16.5 km/s.

text: The relativistic four-velocity, that is the four-vector representing velocity in relativity, is defined as follows:

text: The following example concerns definitions of quantities and units. The (average) velocity (v) of an object is defined as the quantitative physical property of the object that is directly proportional to the distance (d) traveled by the object and inversely proportional to the time (t) of travel, i.e., v = kd/t, where k is a constant that depends on the units used. Suppose that the meter (m) and the second (s) are base units; then the kilometer (km) and the hour (h) are noncoherent derived units. The meter per second (mps) is defined as the velocity of an object that travels one meter in one second, and the kilometer per hour (kmph) is defined as the velocity of an object that travels one kilometer in one hour. Substituting from the definitions of the units into the defining equation of velocity we obtain, 1 mps = k m/s and 1 kmph = k km/h = 1/3.6 k m/s = 1/3.6 mps. Now choose k = 1; then the meter per second is a coherent derived unit, and the kilometer per hour is a noncoherent derived unit. Suppose that we choose to use the kilometer per hour as the unit of velocity in the system. Then the system becomes noncoherent, and the numerical value equation for velocity becomes {v} = 3.6 {d}/{t}. Coherence may be restored, without changing the units, by choosing k = 3.6; then the kilometer per hour is a coherent derived unit, with 1 kmph = 1 m/s, and the meter per second is a noncoherent derived unit, with 1 mps = 3.6 m/s.

text: The velocity of a sound wave at different temperatures:-

text: In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space.

text: In

text: physics

text: , in particular in

text: special relativity

text: and

text: general relativity

text: , a four-velocity is a

text: four-vector

text: in four-dimensional

text: spacetime

text: that represents the relativistic counterpart of

text: velocity

text: , which is a three-dimensional vector in space.

text: The hexagonal grid model was first introduced in 1986, in a paper by Uriel Frisch, Brosl Hasslacher and Yves Pomeau, and this has become known as the FHP model after its inventors. The model has six or seven velocities, depending on which variation is used. In any case, six of the velocities represent movement to each of the neighboring sites. In some models (called FHP-II and FHP-III), a seventh velocity representing particles "at rest" is introduced. The "at rest" particles do not propagate to neighboring sites, but they are capable of colliding with other particles. The FHP-III model allows all possible collisions that conserve density and momentum. Increasing the number of collisions raises the Reynolds number, so the FHP-II and FHP-III models can simulate less viscous flows than the six-speed FHP-I model.

text: The hexagonal grid model was first introduced in 1986, in a paper by

text: Uriel Frisch

text: Brosl Hasslacher

text: and Yves Pomeau, and this has become known as the FHP model after its inventors. The model has six or seven velocities, depending on which variation is used. In any case, six of the velocities represent movement to each of the neighboring sites. In some models (called FHP-II and FHP-III), a seventh velocity representing particles "at rest" is introduced. The "at rest" particles do not propagate to neighboring sites, but they are capable of colliding with other particles. The FHP-III model allows all possible collisions that conserve density and momentum. Increasing the number of collisions raises the

text: Reynolds number

text: , so the FHP-II and FHP-III models can simulate less viscous flows than the six-speed FHP-I model.

text: Suppose a particle moves at a uniform rate along a line from A to B (Figure 2) in a given time (say, one second), while in the same time, the line AB moves uniformly from its position at AB to a position at DC, remaining parallel to its original orientation throughout. Accounting for both motions, the particle traces the line AC. Because a displacement in a given time is a measure of velocity, the length of AB is a measure of the particle's velocity along AB, the length of AD is a measure of the line's velocity along AD, and the length of AC is a measure of the particle's velocity along AC. The particle's motion is the same as if it had moved with a single velocity along AC.

text: Suppose a

text: particle

text: moves at a uniform rate along a line from A to B (Figure 2) in a given time (say, one

text: second

text: ), while in the same time, the line AB moves uniformly from its position at AB to a position at DC, remaining parallel to its original orientation throughout. Accounting for both motions, the particle traces the line AC. Because a displacement in a given time is a measure of

text: velocity

text: , the length of AB is a measure of the particle's velocity along AB, the length of AD is a measure of the line's velocity along AD, and the length of AC is a measure of the particle's velocity along AC. The particle's motion is the same as if it had moved with a single velocity along AC.

text: If v is the velocity of the ultrasonic wave in the liquid  we can calculate the velocity of the wave with:

text: Traditionally, the injection portion of the moulding process was done at one constant pressure to fill and pack the cavity. This method, however, allowed for a large variation in dimensions from cycle-to-cycle. More commonly used now is scientific or decoupled moulding, a method pioneered by RJG Inc. In this the injection of the plastic is "decoupled" into stages to allow better control of part dimensions and more cycle-to-cycle (commonly called shot-to-shot in the industry) consistency. First the cavity is filled to approximately 98% full using velocity (speed) control.  Although the pressure should be sufficient to allow for the desired speed, pressure limitations during this stage are undesirable. Once the cavity is 98% full, the machine switches from velocity control to pressure control, where the cavity is "packed out" at a constant pressure, where sufficient velocity to reach desired pressures is required. This allows part dimensions to be controlled to within thousandths of an inch or better.

text: Traditionally, the injection portion of the moulding process was done at one constant pressure to fill and pack the cavity. This method, however, allowed for a large variation in dimensions from cycle-to-cycle. More commonly used now is scientific or decoupled moulding, a method pioneered by

text: RJG Inc.

text: In this the injection of the plastic is "decoupled" into stages to allow better control of part dimensions and more cycle-to-cycle (commonly called shot-to-shot in the industry) consistency. First the cavity is filled to approximately 98% full using velocity (speed) control.  Although the pressure should be sufficient to allow for the desired speed, pressure limitations during this stage are undesirable. Once the cavity is 98% full, the machine switches from velocity control to pressure control, where the cavity is "packed out" at a constant pressure, where sufficient velocity to reach desired pressures is required. This allows part dimensions to be controlled to within thousandths of an inch or better.

text: is the unit vector pointing in the radial direction outwards from the center. This means that the unbalanced centripetal force felt by any object is always directed toward the center of the curving path. Such forces act perpendicular to the velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. The unbalanced force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates the object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction.

text: is the

text: unit vector

text: pointing in the radial direction outwards from the center. This means that the unbalanced centripetal force felt by any object is always directed toward the center of the curving path. Such forces act perpendicular to the velocity vector associated with the motion of an object, and therefore do not change the

text: speed

text: of the object (magnitude of the velocity), but only the direction of the velocity vector. The unbalanced force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates the object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction.

text: Metre per second (American English: meter per second) is an SI derived unit of both speed (scalar) and velocity (vector quantity which specifies both magnitude and a specific direction), defined by distance in metres divided by time in seconds.

text: Metre per second (

text: American English

text: : meter per second) is an

text: SI derived unit

text: of both

text: speed

text: scalar

text: ) and

text: velocity

text: vector quantity

text: which specifies both magnitude and a specific direction), defined by

text: distance

text: in

text: metre

text: s divided by

text: time

text: in

text: second

text: s.

text: Example Simple examples of this include the velocity vector in Euclidean space, which is the tangent vector of the position vector (considered as a function of time). Also, the acceleration is the tangent vector of the velocity.

text: Example Simple examples of this include the

text: velocity

text: vector in

text: Euclidean space

text: , which is the

text: tangent vector

text: of the

text: position

text: vector (considered as a function of time). Also, the

text: acceleration

text: is the tangent vector of the velocity.

text: Crystallographically, zorite belongs in the orthorhombic group, which has 3 axes, a, b, and c that are of unequal lengths (a≠b≠c) that form 90° with each other. It also belongs in the point group 2/m2/m2/m. The state of aggregation for zorite is acicular. Zorite has perfect cleavage along the planes {010} and {001}, while having poor cleavage along the plane {110}. Zorite is anisotropic, which means that the velocity of light is not the same in all directions. It belongs in the biaxial group, because it is an orthorhombic mineral. Under plane polarized light, zorite displays different colors depending on the angle that the light hits the mineral. This quality is called pleochroism and zorite is rose along the x-axis, colorless along the y-axis, and bluish along the z-axis. The index of refraction of zorite is 1.59, which is the velocity of light through vacuum over the velocity of light through zorite. Zorite is studied to better understand silicate structures.

text: Shear velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow.

text: Shear velocity, also called friction velocity, is a form by which a

text: shear stress

text: may be re-written in units of

text: velocity

text: . It is useful as a method in

text: fluid mechanics

text: to compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow.

text: is the range from missile to target. This acceleration depends explicitly on the velocity difference vector, which may be difficult to obtain in practice. By contrast, in the expressions that follow, dependence is only on the change of the line of sight and the magnitude of the  closing velocity. If acceleration normal to the instantaneous line of sight is desired (as in the initial description), then the following expression is valid:

text: This is a substantially simpler calculation of the momenta of both particles; the reduced mass and relative velocity can be calculated from the initial velocities in the lab frame and the masses, and the momentum of one particle is simply the negative of the other. The calculation can be repeated for final velocities v and v in place of the initial velocities u and u, since after the collision the velocities still satisfy the above equations:

text: The fact that the catch mechanism relies on elastic structures used as power amplifiers implies a series of conditions much convenient for the bullfrog. Sonomicrometry and electromyographic recordings of the plantaris muscle corroborate a relationship between presence of muscle-tendon units and decreasing, variable gearing. By supplying additional work output through the coupling of elastic strain energy, elastic structures relieve the musculature from the need of shortening at velocities that would otherwise hinder the amount of force generated and thus, the magnitude of power output. This is also aided by a decreasing gearing, which makes it possible for the bullfrog to generate the desired velocity of movement by relieving the plantaris from strennous shortening velocities, achieving the velocity desired by slower, forceful contractions. Like in the case of its ballistic tongue projection, elastic structures in the plantaris muscle also confer it thermal independence. Studies show that jumping peak power output and mechanical efficiency of high elevation frogs of the families Hyla, Eleutherodactylus,Colostethus and Atelopus, which achieve these at temperatures as low as 5C, are not statistically different from those achieved by tropical Bufo frogs at 35C.

text: The fact that the catch mechanism relies on elastic structures used as power amplifiers implies a series of conditions much convenient for the bullfrog.

text: Sonomicrometry

text: and

text: electromyographic recordings

text: of the plantaris muscle corroborate a relationship between presence of muscle-tendon units and decreasing, variable

text: gearing

text: . By supplying additional work output through the coupling of elastic strain energy, elastic structures relieve the musculature from the need of shortening at velocities that would otherwise hinder the amount of force generated and thus, the magnitude of power output. This is also aided by a decreasing gearing, which makes it possible for the bullfrog to generate the desired velocity of movement by relieving the plantaris from strennous shortening velocities, achieving the velocity desired by slower, forceful contractions. Like in the case of its

text: ballistic tongue projection

text: , elastic structures in the plantaris muscle also confer it thermal independence. Studies show that jumping peak power output and mechanical efficiency of high elevation frogs of the families

text: Hyla

text: Eleutherodactylus

text: Colostethus

text: and

text: Atelopus

text: , which achieve these at temperatures as low as 5C, are not statistically different from those achieved by tropical

text: Bufo

text: frogs at 35C.

text: Momentum is defined as mass times velocity. Conservation of momentum applies to velocity terms, usually described in a two dimensional plane with a vector diagram. A vector representing velocity has both direction and magnitude. A requirement for determining conservation of momentum is that an inertial frame or frame of reference for the observer be fixed. Inertial frames are well defined for constant velocity and conservation of momentum holds for all such frames. During acceleration or a change in acceleration, conservation of momentum applies to the local inertial frame (LIF) of instantaneous velocity, not to the proper acceleration a.k.a. coordinate acceleration), as measured by the accelerated observer.

text: Momentum

text: is defined as mass times velocity. Conservation of momentum applies to velocity terms, usually described in a two dimensional plane with a

text: vector

text: diagram. A vector representing velocity has both direction and magnitude. A requirement for determining conservation of momentum is that an

text: inertial frame

text: or

text: frame of reference

text: for the observer be fixed.

text: Inertial frames

text: are well defined for constant velocity and conservation of momentum holds for all such frames. During acceleration or a change in acceleration, conservation of momentum applies to the local inertial frame (LIF) of instantaneous velocity, not to the

text: proper acceleration

text: a.k.a. coordinate acceleration), as measured by the accelerated observer.

text: . This important requirement is what distinguishes a contravariant vector from any other triple of physically meaningful quantities.  For example, if v consists of the x, y, and z-components of velocity, then v is a contravariant vector: if the coordinates of space are stretched, rotated, or twisted, then the components of the velocity transform in the same way.  Examples of contravariant vectors include displacement, velocity and acceleration.  On the other hand, for instance, a triple consisting of the length, width, and height of a rectangular box could make up the three components of an abstract vector, but this vector would not be contravariant, since a change in coordinates on the space does not change the box's length, width, and height: instead these are scalars.

text: . This important requirement is what distinguishes a contravariant vector from any other triple of physically meaningful quantities.  For example, if v consists of the x, y, and z-components of

text: velocity

text: , then v is a contravariant vector: if the coordinates of space are stretched, rotated, or twisted, then the components of the velocity transform in the same way.  Examples of contravariant vectors include

text: displacement

text: velocity

text: and

text: acceleration

text: .  On the other hand, for instance, a triple consisting of the length, width, and height of a rectangular box could make up the three components of an abstract

text: vector

text: , but this vector would not be contravariant, since a change in coordinates on the space does not change the box's length, width, and height: instead these are

text: scalars

text: is the average velocity at the inlet,

text: is the average velocity at the inlet,

text: Another consequence of dispersion manifests itself as a temporal effect. The formula v =  calculates the phase velocity of a wave; this is the velocity at which the phase of any one frequency component of the wave will propagate. This is not the same as the group velocity of the wave, that is the rate at which changes in amplitude (known as the envelope of the wave) will propagate. For a homogeneous medium, the group velocity v is related to the phase velocity v by (here λ is the wavelength in vacuum, not in the medium):

text: Another consequence of dispersion manifests itself as a temporal effect. The formula v =  calculates the phase velocity of a wave; this is the

text: velocity

text: at which the

text: phase

text: of any one frequency component of the wave will propagate. This is not the same as the

text: group velocity

text: of the wave, that is the rate at which changes in

text: amplitude

text: (known as the envelope of the wave) will propagate. For a homogeneous medium, the group velocity v is related to the phase velocity v by (here λ is the wavelength in vacuum, not in the medium):

text: Neutron spin echo is a time-of-flight technique. Concerning the neutron spins it has a strong analogy to the so-called Hahn echo,  well known in thefield of NMR. In both cases the loss of polarization (magnetization) due to dephasing of the spins in time is restored by an effective time reversal operation,that leads to a restituation of polarization (rephasing). In NMR the dephasing happens due to variation in the local fields at positions of thenuclei, in NSE the dephasing is due to different neutron velocities in the incoming neutron beam.The Larmor precession of the neutron spin in a preparation zone with a magnetic field before the sample encodesthe individual velocities of neutrons in the beam into precession angles. Close to the sample the time reversal is effected by a so-calledflipper. A symmetric decoding zone follows such that at its end the precession angle accumulated in the preparation zone is exactly compensated(provided the sample did not change the neutron velocity, i.e. elastic scattering), all spins rephase to form the "spin-echo". Ideally the full polarization is restored. This effect does not depend on the velocity/energy/wavelength of the incoming neutron. If the scattering at the sample is not elastic but changes the neutron velocity, the rephasing will become incomplete and a loss of finalpolarization results, which depends on the distribution of differences in the time, which the neutrons need to fly through the symmetric first (coding) and second (decoding)precession zones. The time differences occur due to a velocity change acquired by non-elastic scattering at the sample. The distribution of these time differences is proportional (in the linearization approximation which is appropriate for quasi-elastic high resolution spectroscopy) to the spectral part of the scattering function S(Q,ω). The effect on the measured beam polarization is proportionalto the cos-Fourier transform of the spectral function, the intermediate scattering function F(Q,t). The time parameter depends on the neutronwavelength and the factor connecting precession angle with (reciprocal) velocity, which can e.g. be controlled by setting a certain magneticfield in the preparation and decoding zones. Scans of t may then be performed by varying the magnetic field.

text: Neutron spin echo is a

text: time-of-flight

text: technique. Concerning the neutron spins it has a strong analogy to the so-called

text: Hahn echo

text: ,  well known in thefield of

text: NMR

text: . In both cases the loss of polarization (magnetization) due to dephasing of the spins in time is restored by an effective time reversal operation,that leads to a restituation of polarization (rephasing). In NMR the dephasing happens due to variation in the local fields at positions of thenuclei, in NSE the dephasing is due to different neutron velocities in the incoming neutron beam.The

text: Larmor precession

text: scattering function

text: S(Q,ω). The effect on the measured beam polarization is proportionalto the cos-Fourier transform of the spectral function, the

text: intermediate scattering function

text: F(Q,t). The time parameter depends on the neutronwavelength and the factor connecting precession angle with (reciprocal) velocity, which can e.g. be controlled by setting a certain magneticfield in the preparation and decoding zones. Scans of t may then be performed by varying the magnetic field.

text: Figure 1 illustrates velocity and acceleration vectors for uniform motion at four different points in the orbit. Because the velocity v is tangent to the circular path, no two velocities point in the same direction. Although the object has a constant speed, its direction is always changing. This change in velocity is caused by an acceleration a, whose magnitude is (like that of the velocity) held constant, but whose direction also is always changing. The acceleration points radially inwards (centripetally) and is perpendicular to the velocity. This acceleration is known as centripetal acceleration.

text: Figure 1 illustrates velocity and acceleration vectors for uniform motion at four different points in the orbit. Because the velocity v is tangent to the circular path, no two velocities point in the same direction. Although the object has a constant speed, its direction is always changing. This change in velocity is caused by an acceleration a, whose magnitude is (like that of the velocity) held constant, but whose direction also is always changing. The

text: acceleration

text: points radially inwards (

text: centripetal

text: ly) and is perpendicular to the velocity. This acceleration is known as centripetal acceleration.

text: On a graph of atom velocities (atoms moving rapidly to the right correspond with stationary dots far to the right, atoms moving rapidly to the left correspond with stationary dots far to the left), there is a narrow band on the left edge corresponding to the speed those atoms start absorbing photons from the left laser. Atoms in that band are the only ones that interact with the left laser. When a photon from the left laser slams into one of those atoms, it suddenly slows down an amount corresponding to the momentum of that photon (the dot would be redrawn some fixed "quantum" distance further to the right). If the atom releases the photon directly to the right, then the dot is redrawn that same distance to the left, putting it back in the narrow band of interaction. But usually the atom releases the photon in some other random direction, and the dot is redrawn that quantum distance in the opposite direction.

text: Other techniques used to measure flows are laser Doppler velocimetry  and hot-wire anemometry. The main difference between PIV and those techniques is that PIV produces two-dimensional or even three-dimensional vector fields, while the other techniques measure the velocity at a point. During PIV, the particle concentration is such that it is possible to identify individual particles in an image, but not with certainty to track it between images. When the particle concentration is so low that it is possible to follow an individual particle it is called Particle tracking velocimetry, while Laser speckle velocimetry is used for cases where the particle concentration is so high that it is difficult to observe individual particles in an image.

text: Other techniques used to measure flows are

text: laser Doppler velocimetry

text: and

text: hot-wire anemometry

text: . The main difference between PIV and those techniques is that PIV produces two-dimensional or even three-dimensional

text: vector field

text: s, while the other techniques measure the velocity at a point. During PIV, the particle

text: concentration

text: is such that it is possible to identify individual particles in an image, but not with certainty to track it between images. When the particle concentration is so low that it is possible to follow an individual particle it is called

text: Particle tracking velocimetry

text: , while

text: Laser speckle velocimetry

text: is used for cases where the particle concentration is so high that it is difficult to observe individual particles in an image.

text: Fox suggested that better experiments were possible, in order to close that "small gap".  Since photons with higher energies will, on average, travel much farther in any material before being extinguished and re-emitted, experiments using gamma rays instead of lower-energy visible light or x-rays would be dramatically less sensitive to the extinction problem.  In 1963, along with T. A. Filippas (also of Carnegie Tech), Fox examined 68 MeV gamma rays emitted in the forward and backward directions by neutral pions moving at 0.2c, i.e., two-tenths the speed of light.  The classical velocities of those photons should have been 1.2c and 0.8c, respectively, but this was not the case.  The experiment, perhaps the earliest to be considered free of extinction effects, was successful:  "We conclude that our results provide strong evidence that the velocity of radiation from a moving source is not the classical vector sum of c and the velocity of the source.  Within our accuracy, the resultant sum is c as required by special relativity."

text: Fox suggested that better experiments were possible, in order to close that "small gap".  Since photons with higher energies will, on average, travel much farther in any material before being extinguished and re-emitted, experiments using gamma rays instead of lower-energy visible light or x-rays would be dramatically less sensitive to the extinction problem.  In 1963, along with T. A. Filippas (also of Carnegie Tech), Fox examined 68 MeV gamma rays emitted in the forward and backward directions by

text: neutral pions

text: moving at 0.2c, i.e., two-tenths the speed of light.  The classical velocities of those photons should have been 1.2c and 0.8c, respectively, but this was not the case.  The experiment, perhaps the earliest to be considered free of extinction effects, was successful:  "We conclude that our results provide strong evidence that the velocity of radiation from a moving source is not the classical vector sum of c and the velocity of the source.  Within our accuracy, the resultant sum is c as required by special relativity."

text: Early observations have revealed a few genuinely hyperbolic (i.e. non-periodic) trajectories, but no more than could be accounted for by perturbations from Jupiter. If comets pervaded interstellar space, they would be moving with velocities of the same order as the relative velocities of stars near the Sun (a few tens of km per second). If such objects entered the Solar System, they would have positive specific orbital energy and would be observed to have genuinely hyperbolic trajectories. A rough calculation shows that there might be four hyperbolic comets per century within Jupiter's orbit, give or take one and perhaps two orders of magnitude.

text: Early observations have revealed a few genuinely hyperbolic (i.e. non-periodic) trajectories, but no more than could be accounted for by perturbations from Jupiter. If comets pervaded

text: interstellar space

text: , they would be moving with velocities of the same order as the relative velocities of stars near the Sun (a few tens of km per second). If such objects entered the Solar System, they would have positive

text: specific orbital energy

text: and would be observed to have genuinely hyperbolic trajectories. A rough calculation shows that there might be four hyperbolic comets per century within Jupiter's orbit, give or take one and perhaps two orders of

text: magnitude

text: In plasma physics, a wave can be collisionlessly damped by particles in the plasma whose velocity matches the wave's phase velocity. This is typically represented as a spatially dispersive loss in the plasma's permittivity.

text: Since different projectile shapes will respond differently to changes in velocity (particularly between supersonic and subsonic velocities), a BC provided by a bullet manufacturer will be an average BC that represents the common range of velocities for that bullet. For rifle bullets, this will probably be a supersonic velocity, for pistol bullets it will probably be subsonic. For projectiles that travel through the supersonic, transonic and subsonic flight regimes BC is not well approximated by a single constant, but is considered to be a function BC(M) of the Mach number M; here M equals the projectile velocity divided by the speed of sound. During the flight of the projectile the M will decrease, and therefore (in most cases) the BC will also decrease.

text: Since different projectile shapes will respond differently to changes in velocity (particularly between

text: supersonic

text: and

text: subsonic

text: velocities), a BC provided by a bullet manufacturer will be an average BC that represents the common range of velocities for that bullet. For

text: rifle

text: bullets, this will probably be a

text: supersonic

text: velocity, for pistol bullets it will probably be subsonic. For projectiles that travel through the

text: supersonic

text: transonic

text: and subsonic flight regimes BC is not well approximated by a single constant, but is considered to be a

text: function

text: BC(M) of the

text: Mach number

text: M; here M equals the projectile velocity divided by the

text: speed of sound

text: . During the flight of the projectile the M will decrease, and therefore (in most cases) the BC will also decrease.

text: ζ Ophiuchi is moving through space with a peculiar velocity of 30 km s. Based upon the age and direction of motion of this star, it is a member of the Upper Scorpius sub-group of the Scorpius-Centaurus Association of stars that share a common origin and space velocity. Such runaway stars may be ejected by dynamic interactions between three or four stars. However, in this case the star may be a former component of a binary star system in which the more massive primary was destroyed in a Type II supernova explosion. The pulsar PSR B1929+10 may be the leftover remnant of this supernova, as it too was ejected from the association with a velocity vector that fits the scenario.

text: ζ Ophiuchi is moving through space with a

text: peculiar velocity

text: of 30 km s. Based upon the age and direction of motion of this star, it is a member of the Upper Scorpius sub-group of the

text: Scorpius-Centaurus Association

text: of stars that share a common origin and

text: space velocity

text: . Such

text: runaway star

text: s may be ejected by dynamic interactions between three or four stars. However, in this case the star may be a former component of a

text: binary star

text: system in which the more massive primary was destroyed in a

text: Type II supernova

text: explosion. The pulsar

text: PSR B1929+10

text: may be the leftover remnant of this supernova, as it too was ejected from the association with a velocity vector that fits the scenario.

text: The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion (e.g.  to the north).  Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

text: The velocity of an object is the

text: rate of change

text: of its

text: position

text: with respect to a

text: frame of reference

text: , and is a function of time. Velocity is equivalent to a specification of its

text: speed

text: and direction of motion (e.g.  to the north).  Velocity is an important concept in

text: kinematics

text: , the branch of

text: classical mechanics

text: that describes the

text: motion

text: of bodies.

text: The group velocity is often thought of as the velocity at which energy or information is conveyed along a wave. In most cases this is accurate, and the group velocity can be thought of as the signal velocity of the waveform. However, if the wave is travelling through an absorptive or gainful medium, this does not always hold. In these cases the group velocity may not be a well-defined quantity, or may not be a meaningful quantity.

text: The group velocity is often thought of as the velocity at which

text: energy

text: or

text: information

text: is conveyed along a wave. In most cases this is accurate, and the group velocity can be thought of as the

text: signal velocity

text: of the

text: wave

text: form. However, if the wave is travelling through an absorptive or gainful medium, this does not always hold. In these cases the group velocity may not be a well-defined quantity, or may not be a meaningful quantity.

text: Frederick Thomas Trouton, (after conducting the Trouton–Noble experiment in 1903), instead did the calculations using his own interpretation of electrodynamics, calculating the length contraction according to the velocity of the experimental apparatus in the aether frame, but calculating the electrodynamics by applying Maxwell's equations and Ohm's law in the lab frame. According to Trouton's view of electrodynamics, the calculations then predicted a measurable effect of the length contraction in the lab frame. Together with Alexander Oliver Rankine, he set out to verify this in 1908 by attempting to measure the change of the resistance of a coil as they changed its orientation to the "aether velocity" (the velocity of the lab through the luminiferous aether).  This was done by putting four identical such coils in a Wheatstone bridge configuration which allowed them to precisely measure any change in resistance.  The circuit was then rotated through 90 degrees about its axis as the resistance was measured.  Because the Lorentz–FitzGerald contraction is only in the direction of motion, from the point of view of the "Aether frame" the length of the coils depended on their angle with respect to their Aether velocity.  Trouton and Rankine therefore believed that the resistance as measured in the rest frame of the experiment should change as the device was rotated.  However their careful measurements showed no detectable change in resistance.

text: Frederick Thomas Trouton

text: , (after conducting the

text: Trouton–Noble experiment

text: in 1903), instead did the calculations using his own interpretation of electrodynamics, calculating the length contraction according to the velocity of the experimental apparatus in the aether frame, but calculating the electrodynamics by applying Maxwell's equations and

text: Ohm's law

text: in the lab frame. According to Trouton's view of electrodynamics, the calculations then predicted a measurable effect of the length contraction in the lab frame. Together with

text: Alexander Oliver Rankine

text: , he set out to verify this in 1908 by attempting to measure the change of the resistance of a coil as they changed its orientation to the "aether velocity" (the velocity of the lab through the luminiferous aether).  This was done by putting four identical such coils in a

text: Wheatstone bridge

text: configuration which allowed them to precisely measure any change in resistance.  The circuit was then rotated through 90 degrees about its axis as the resistance was measured.  Because the Lorentz–FitzGerald contraction is only in the direction of motion, from the point of view of the "Aether frame" the length of the coils depended on their angle with respect to their Aether velocity.  Trouton and Rankine therefore believed that the resistance as measured in the rest frame of the experiment should change as the device was rotated.  However their careful measurements showed no detectable change in resistance.

text: a direction there is a continuous dynamical system called a billiard. The trajectory of a point inside the polygon is defined as follows: as long as it does not touch the boundary it proceeds in a straight line at unit speed; when it touches the interior of an edge it bounces back (i.e. its direction changes with an orthogonal reflection in the perpendicular of the edge), and when it touches a vertex it stops.

text: a direction there is a continuous dynamical system called a

text: billiard

text: . The trajectory of a point inside the polygon is defined as follows: as long as it does not touch the boundary it proceeds in a straight line at unit speed; when it touches the interior of an edge it bounces back (i.e. its direction changes with an orthogonal reflection in the perpendicular of the edge), and when it touches a vertex it stops.

text: An example of a scalar quantity is temperature: the temperature at a given point is a single number. Velocity, on the other hand, is a vector quantity: velocity in three-dimensional space is specified by three values; in a Cartesian coordinate system the values are the speeds relative to each coordinate axis. The associated fields describe the temperature and velocity in each point of some space. Considering the norms of the velocity vectors results in a scalar field of the speeds in each point of the space.

text: An example of a scalar quantity is

text: temperature

text: : the temperature at a given point is a single number. Velocity, on the other hand, is a vector quantity: velocity in three-dimensional space is specified by three values; in a

text: Cartesian coordinate system

text: the values are the speeds relative to each

text: coordinate axis

text: . The associated fields describe the temperature and velocity in each point of some space. Considering the norms of the velocity vectors results in a scalar field of the speeds in each point of the space.

text: To properly understand spacecraft rendezvous it is essential to understand the relation between spacecraft velocity and orbit. A spacecraft in a certain orbit cannot arbitrarily alter its velocity. Each orbit correlates to a certain orbital velocity. If the spacecraft fires thrusters and increases (or decreases) its velocity it will obtain a different orbit, one that correlates to the higher (or lower) velocity. For circular orbits, higher orbits have a lower orbital velocity. Lower orbits have a higher orbital velocity. This might seem counter-intuitive, but an orbit is nothing else but a state of equilibrium between the force of the gravitational body (the Earth) and the force due to circular motion. At higher orbits the force of the gravity becomes weaker, therefore the balancing force of the circular motion can be lower, corresponding to a lower velocity.  (It's actually about angular momentum, not "weaker gravity.")

text: This equation is very similar to the equation for the reduction in surface velocity with longitude stated above.This is equivalent to stating that the angular velocity that is imparted to the pendulum bob decreases with the sine of the latitude of the location (the sine of 90 degrees latitude equals 1; the sine of zero degrees latitude equals 0). The time to observe a complete rotation is inversely proportional to the angular velocity that is imparted to the pendulum bob in comparison to the angular velocity of the Earth. The statements above are thus equivalent to the inverse sine law for the observed time for a full rotation of the pendulum in relation to the rotation of the Earth.

text: The group velocity also turns out to be the energy transport velocity. This is the velocity with which the mean wave energy is transported horizontally in a narrow-band wave field.<ref>

text: The group velocity also turns out to be the energy transport velocity. This is the velocity with which the mean wave energy is transported horizontally in a

text: narrow-band

text: wave field.<ref>

text: Typically, the average velocity is directly proportional to the applied force, giving the equation:

text: His most enduring work began in 1919, when he was working at the Carnegie Institution for Science to develop new methods for high-pressure measurement. In the late 19th century the prevailing view of the Earth was that it was made up of a thin crust floating on a molten interior. By Adams' day, this view was being challenged, especially by the findings of some seismologists who had found the wave velocities of the Earth at different depths. Wave velocities depend upon the elastic constants of the materials through which they pass, in particular the bulk modulus and stiffness.

text: His most enduring work began in 1919, when he was working at the Carnegie Institution for Science to develop new methods for high-pressure measurement. In the late 19th century the prevailing view of the Earth was that it was made up of a thin crust floating on a molten interior. By Adams' day, this view was being challenged, especially by the findings of some

text: seismologists

text: who had found the

text: wave velocities

text: of the Earth at different depths. Wave velocities depend upon the

text: elastic constants

text: of the materials through which they pass, in particular the

text: bulk modulus

text: and

text: stiffness

text: The average velocity can be obtained by integrating over the pipe cross section:

text: The average velocity can be obtained by integrating over the pipe

text: cross section

text: The "force-mediating particle" picture (FMPP) is used because the classical two-body interaction (Coulomb's law for example), depending on six spatial dimensions, is incompatible with the Lorentz invariance of Dirac's equation.  The use of the FMPP is unnecessary in nonrelativistic quantum mechanics, and Coulomb's law is used as given in atomic physics and quantum chemistry to calculate both bound and scattering states.  A nonperturbative relativistic quantum theory, in which Lorentz invariance is preserved, is achievable by evaluating Coulomb's law as a 4-space interaction using the 3-space position vector of a reference electron obeying Dirac's equation and the quantum trajectory of a second electron which depends only on the scaled time ct.  The quantum trajectory of each electron in an ensemble is inferred from the Dirac current for each electron by setting it equal to a velocity field times a quantum density, calculating a position field from the time integral of the velocity field, and finally calculating a quantum trajectory from the expectation value of the position field.  The quantum trajectories are of course spin dependent, and the theory can be validated by checking that Pauli's Exclusion Principle is obeyed for a collection of fermions.

text: pair that gives the lowest D for SAD and SSD, or the largest ρ for the cross correlation, is selected as the estimation of the movement. The velocity is then calculated as the movement divided by the time difference between the frames. Usually the median or average of multiple estimations is taken to give more accurate result.

text: Note that effective exhaust velocity and actual exhaust velocity can be significantly different, for example when a rocket is run within the atmosphere, atmospheric pressure on the outside of the engine causes a retarding force that reduces the specific impulse, and the effective exhaust velocity goes down, whereas the actual exhaust velocity is largely unaffected. Also, sometimes rocket engines have a separate nozzle for the turbo-pump turbine gas, and then calculating the effective exhaust velocity requires averaging the two mass flows as well as accounting for any atmospheric pressure.

text: Lift is produced by the changing direction of the flow around a wing. The change of direction results in a change of velocity (even if there is no speed change, just as seen in uniform circular motion), which is an acceleration. To change the direction of the flow therefore requires that a force be applied to the fluid; lift is simply the reaction force of the fluid acting on the wing.

text: Lift

text: is produced by the changing direction of the flow around a wing. The change of direction results in a change of velocity (even if there is no speed change, just as seen in uniform circular motion), which is an acceleration. To change the direction of the flow therefore requires that a force be applied to the fluid; lift is simply the reaction force of the fluid acting on the wing.

text: The R-bar approach consists of the chaser moving below or above the target spacecraft, along its radial vector. The motion is orthogonal to the orbital velocity of the passive spacecraft.When below the target the chaser fires radial thrusters to close in on the target. By this it increases its altitude. However, the orbital velocity of the chaser remains unchanged (thruster firings in the radial direction have no effect on the orbital velocity). Now in a slightly higher position, but with an orbital velocity that does not correspond to the local circular velocity, the chaser slightly falls behind the target. Small rocket pulses in the orbital velocity direction are necessary to keep the chaser along the radial vector of the target. If these rocket pulses are not executed (for example due to a thruster failure), the chaser will move away from the target. This is a natural braking effect. For the R-bar approach, this effect is stronger than for the V-bar approach, making the R-bar approach the safer one of the two.Generally, the R-bar approach from below is preferable, as the chaser is in a lower (faster) orbit than the target, and thus "catches up" with it. For the R-bar approach from above, the chaser is in a higher (slower) orbit than the target, and thus has to wait for the target to approach it.

text: The R-bar approach consists of the chaser moving below or above the target spacecraft, along its radial vector. The motion is

text: orthogonal

text: When introduced in 2005, Velocity differed from most other frequent flyer programs with points earned being based on the cost of a flight, rather than distance. On domestic VA flights, Red Velocity members earn 5 points per dollar spent, Silver members earn a bonus of 50%, Gold members earn a bonus of 75% and Platinum members earn a bonus of 100%. On international flights (previously V Australia), as well as the majority of Velocity's airline partners, including 'VA' codeshare flights, points are based on fare class and distance, with the same bonus points applying.

text: When introduced in 2005, Velocity differed from most other frequent flyer programs with points earned being based on the cost of a flight, rather than distance. On domestic VA flights, Red Velocity members earn 5 points per dollar spent, Silver members earn a bonus of 50%, Gold members earn a bonus of 75% and Platinum members earn a bonus of 100%. On international flights (previously

text: V Australia

text: ), as well as the majority of Velocity's airline partners, including 'VA'

text: codeshare flights

text: , points are based on fare class and distance, with the same bonus points applying.

text: The pressure of a fluid is different when it flows than when it is not flowing. This is why static pressure and dynamic pressure are never the same in a system in which the fluid is in motion. This pressure difference arises from a change in fluid velocity that produces velocity head, which is a term of the Bernoulli equation that is zero when there is no bulk motion of the fluid. In the picture on the right, the pressure differential is entirely due to the change in velocity head of the fluid, but it can be measured as a pressure head because of the Bernoulli principle. If, on the other hand, we could measure the velocity of the fluid, the pressure head could be calculated from the velocity head. See the Derivations of Bernoulli equation.

text: The pressure of a fluid is different when it flows than when it is not flowing. This is why

text: static pressure

text: and

text: dynamic pressure

text: are never the same in a system in which the fluid is in motion. This pressure difference arises from a change in fluid velocity that produces

text: velocity head

text: , which is a term of the Bernoulli equation that is zero when there is no bulk motion of the fluid. In the picture on the right, the pressure differential is entirely due to the change in velocity head of the fluid, but it can be measured as a pressure head because of the Bernoulli principle. If, on the other hand, we could measure the velocity of the fluid, the pressure head could be calculated from the velocity head. See the

text: Derivations of Bernoulli equation

text: the depth-averaged flow velocities upstream and downstream, and

text: the depth-

text: averaged

text: flow velocities upstream and downstream, and

text: The radial and angular velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components. The transverse velocity is the component of velocity along a circle centered at the origin.

text: The radial and angular velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components. The

text: transverse

text: velocity is the component of velocity along a circle centered at the origin.

text: The seismic noise includes a small amount of body waves (P- and S-waves), but  surface waves (Love and Rayleigh waves) predominate. Theses waves are dispersive, meaning that their phase velocity varies with frequency (generally, it decreases with increasing frequency). Since the dispersion curve (phase velocity or slowness as a function of frequency) is tightly related to the variations of the shear-wave velocity with depth in the different ground layers, it can be used as a non-invasive tool to investigate the underground structure.

text: The seismic noise includes a small amount of

text: body waves

text: (P- and S-waves), but

text: surface wave

text: s (

text: Love

text: and

text: Rayleigh wave

text: s) predominate. Theses waves are

text: dispersive

text: , meaning that their

text: phase velocity

text: varies with frequency (generally, it decreases with increasing frequency). Since the

text: dispersion curve

text: (phase velocity or slowness as a function of frequency) is tightly related to the variations of the shear-wave velocity with depth in the different ground layers, it can be used as a non-invasive tool to investigate the underground structure.

text: In robotics and motion planning, a velocity obstacle, commonly abbreviated VO, is the set of all velocities of a robot that will result in a collision with another robot at some moment in time, assuming that the other robot maintains its current velocity.  If the robot chooses a velocity inside the velocity obstacle then the two robots will eventually collide, if it chooses a velocity outside the velocity obstacle, such a collision is guaranteed not to occur.

text: In

text: robotics

text: and

text: motion planning

text: , a velocity obstacle, commonly abbreviated VO, is the set of all

text: velocities

text: of a

text: robot

text: that will result in a

text: collision

text: with another robot at some moment in time, assuming that the other robot maintains its current velocity.  If the robot chooses a velocity inside the velocity obstacle then the two robots will eventually collide, if it chooses a velocity outside the velocity obstacle, such a collision is guaranteed not to occur.

text: While this technology does appear to provide higher velocities, the main drawback with gaseous or liquid propellants for gun systems is the difficulty in getting uniform and predictable ignition and muzzle velocities. Variance with muzzle velocities affects precision in range, and the further a weapon shoots, the more significant these variances become. If an artillery system cannot maintain uniform and predictable muzzle velocities it will be of no use at longer ranges. Another issue is the survival of projectile payloads at higher accelerations. Fuzes, explosive fill, and guidance systems all must be "hardened" against the significant acceleration loads of conventional artillery to survive and function properly. Higher velocity weapons, like the CLGG, face these engineering challenges as they edge the boundaries of firing accelerations higher.

text: While this technology does appear to provide higher velocities, the main drawback with gaseous or liquid propellants for gun systems is the difficulty in getting uniform and predictable ignition and muzzle velocities. Variance with muzzle velocities affects precision in range, and the further a weapon shoots, the more significant these variances become. If an artillery system cannot maintain uniform and predictable muzzle velocities it will be of no use at longer ranges. Another issue is the survival of projectile payloads at higher accelerations.

text: Fuze

text: s, explosive fill, and guidance systems all must be "hardened" against the significant acceleration loads of conventional artillery to survive and function properly. Higher velocity weapons, like the CLGG, face these engineering challenges as they edge the boundaries of firing accelerations higher.

text: An average retardation coefficient can be calculated for any given slope constant factor if velocity data points are known and distance between said velocity measurements is known. Obviously this is true only within the same flight regime. With velocity actual speed is meant, as velocity is a vector quantity and speed is the magnitude of the velocity vector. Because the power function does not have constant curvature a simple chord average cannot be used. The Pejsa model uses a weighted average retardation coefficient weighted at 0.25 range.The closer velocity is more heavily weighted. The retardation coefficient is measured in feet whereas range is measured in yards hence 0.25 * 3.0 = 0.75, in some places 0.8 rather than 0.75 is used. The 0.8 comes from rounding in order to allow easy entry on hand calculators. Since the Pejsa model does not use a simple chord weighted average, two velocity measurements are used to find the chord average retardation coefficient at midrange between the two velocity measurements points. In order to find the starting retardation coefficient Dr. Pejsa provides two separate equations in his two books. The first involves the power function. The second equation is identical to the one used to find the weighted average at R / 4; add N * (R/2) where R is the range in feet to the chord average retardation coefficient at midrange and where N is the slope constant factor. After the starting retardation coefficient is found the opposite procedure is used in order find the weighted average at R / 4; the starting retardation coefficient minus N * (R/4). In other words, N is used as the slope of the chord line. Dr. Pejsa states that he expanded his drop formula in a power series in order to prove that the weighted average retardation coefficient at R / 4 was a good approximation. For this Dr. Pejsa compared the power series expansion of his drop formula to some other unnamed drop formula’s power expansion to reach his conclusions. The fourth term in both power series matched when the retardation coefficient at 0.25 range was used in Pejsa’s drop formula. The fourth term was also the first term to use N. The higher terms involving N where insignificant and disappeared at N = 0.36, which according to Dr. Pejsa was a lucky coincidence making for an exceedingly accurate linear approximation, especially for N’s around 0.36. If a retardation coefficient function is used exact average values for any N can be obtained because from calculus it is trivial to find the average of any integrable function. Dr. Pejsa states that the retardation coefficient can be modeled by C * V where C is a fitting coefficient which disappears during the derivation of the drop formula and N the slope constant factor.The retardation coefficient equals the velocity squared divided by the retardation rate A. Using an average retardation coefficient allows the Pejsa model to be a closed-form expression within a given flight regime.

text: An average retardation coefficient can be calculated for any given slope constant factor if velocity data points are known and distance between said velocity measurements is known. Obviously this is true only within the same flight regime. With velocity actual

text: speed

text: is meant, as velocity is a vector quantity and speed is the magnitude of the velocity vector. Because the

text: power function

text: does not have constant

text: curvature

text: a simple

text: chord

text: average of any integrable function

text: . Dr. Pejsa states that the retardation coefficient can be modeled by C * V where C is a fitting coefficient which disappears during the derivation of the drop formula and N the slope constant factor.The retardation coefficient equals the velocity squared divided by the retardation rate A. Using an average retardation coefficient allows the Pejsa model to be a

text: closed-form expression

text: within a given flight regime.

text: In 1911 Laue also discussed a situation where on a platform a beam of light is split and the two beams are made to follow a trajectory in opposite directions. On return to the point of entry the light is allowed to exit the platform in such a way that an interference pattern is obtained. Laue calculated a displacement of the interference pattern if the platform is in rotation –  because the speed of light is independent of the velocity of the source, so one beam has covered less distance than the other beam. An experiment of this kind was performed by Georges Sagnac in 1913, who actually measured a displacement of the interference pattern (Sagnac effect). While Sagnac himself concluded that his theory confirmed the theory of an aether at rest, Laue's earlier calculation showed that it is compatible with special relativity as well because in both theories the speed of light is independent of the velocity of the source. This effect can be understood as the electromagnetic counterpart of the mechanics of rotation, for example in analogy to a Foucault pendulum. Already in 1909–11, Franz Harress (1912) performed an experiment which can be considered as a synthesis of the experiments of Fizeau and Sagnac. He tried to measure the dragging coefficient within glass. Contrary to Fizeau he used a rotating device so he found the same effect as Sagnac. While Harress himself misunderstood the meaning of the result, it was shown by Laue that the theoretical explanation of Harress' experiment is in accordance with the Sagnac effect. Eventually, the Michelson–Gale–Pearson experiment (1925, a variation of the Sagnac experiment) indicated the angular velocity of the Earth itself in accordance with special relativity and a resting aether.

text: In 1911 Laue also discussed a situation where on a platform a beam of light is split and the two beams are made to follow a trajectory in opposite directions. On return to the point of entry the light is allowed to exit the platform in such a way that an interference pattern is obtained. Laue calculated a displacement of the interference pattern if the platform is in rotation –  because the speed of light is independent of the velocity of the source, so one beam has covered less distance than the other beam. An experiment of this kind was performed by

text: Georges Sagnac

text: in 1913, who actually measured a displacement of the interference pattern (

text: Sagnac effect

text: ). While Sagnac himself concluded that his theory confirmed the theory of an aether at rest, Laue's earlier calculation showed that it is compatible with special relativity as well because in both theories the speed of light is independent of the velocity of the source. This effect can be understood as the electromagnetic counterpart of the mechanics of rotation, for example in analogy to a

text: Foucault pendulum

text: . Already in 1909–11, Franz Harress (1912) performed an experiment which can be considered as a synthesis of the experiments of Fizeau and Sagnac. He tried to measure the dragging coefficient within glass. Contrary to Fizeau he used a rotating device so he found the same effect as Sagnac. While Harress himself misunderstood the meaning of the result, it was shown by Laue that the theoretical explanation of Harress' experiment is in accordance with the Sagnac effect. Eventually, the

text: Michelson–Gale–Pearson experiment

text: (1925, a variation of the Sagnac experiment) indicated the angular velocity of the Earth itself in accordance with special relativity and a resting aether.

text: are calculated so that for eachpoint in the velocity field

text: In a consistent way with the general definition, the angular velocity of a frame is defined as the angular velocity of each of the three vectors of the frame (it will be the same for any of them). The addition of angular velocity vectors for frames is also defined by movement composition, and can be useful to decompose the movement as in a gimbal. Components of the vector can be calculated as derivatives of the parameters defining the moving frames (Euler angles or rotation matrices). As in the general case, addition is commutative:

text: In a consistent way with the general definition, the angular velocity of a frame is defined as the angular velocity of each of the three vectors of the frame (it will be the same for any of them). The addition of angular velocity vectors for frames is also defined by movement composition, and can be useful to decompose the movement as in a

text: gimbal

text: . Components of the vector can be calculated as derivatives of the parameters defining the moving frames (Euler angles or rotation matrices). As in the general case, addition is commutative:

text: Travel time instruments determine water velocity by at least two acoustic signals, one up stream and one down stream.  By precisely measuring the time to travel from the emitter to the receiver, in both directions, the average water speed can be determined between the two points.  By using multiple paths, the water velocity can be determined in three dimensions.

text: This mode begins at the point where one of the motor/generators reaches zero speed; at this point some clutches within the system engage while others disengage to alter the physical configuration of the transmission, and the velocity is Vshift. Immediately after the shift, both electric machines operate as motors and the first gear ratio is employed. At a given velocity above Vshift, the second gear ratio is employed, and M/G 2 begins to operate as a generator, while also slowing down its angular speed.

text: The acceleration entering the Coriolis force arises from two sources of change in velocity that result from rotation: the first is the change of the velocity of an object in time. The same velocity (in an inertial frame of reference where the normal laws of physics apply) is seen as different velocities at different times in a rotating frame of reference. The apparent acceleration is proportional to the angular velocity of the reference frame (the rate at which the coordinate axes change direction), and to the component of velocity of the object in a plane perpendicular to the axis of rotation. This gives a term

text: An airfoil affects the speed and direction of the flow over a wide area.  When an airfoil produces lift, the flow ahead of the airfoil is deflected upward, the flow above and below the airfoil is deflected downward, and the flow behind the airfoil is deflected upward again, leaving the air far behind the airfoil flowing in the same direction as the oncoming flow far ahead.  The flow above the upper surface is always speeded up, and the flow below the airfoil is usually slowed down.  The downward deflection and the changes in flow speed are pronounced and extend over a wide area, as can be seen in the flow animation on the right.  These differences in the direction and speed of the flow are greatest close to the airfoil and decrease  gradually far above and below.  All of these features of the velocity field also appear in theoretical models for lifting flows.

text: The United States Army has created a plethora of different types of 40 mm grenades in both the low-velocity 40×46mm and high-velocity 40×53mm calibers which uses what it calls High-Low Propulsion System which keeps recoil forces within the boundaries of an infantry weapon. Presented on this page is a basic overview.

text: The

text: United States Army

text: has created a plethora of different types of

text: 40 mm grenade

text: s in both the low-velocity 40×46mm and high-velocity 40×53mm calibers which uses what it calls

text: High-Low Propulsion System

text: which keeps recoil forces within the boundaries of an infantry weapon. Presented on this page is a basic overview.

text: can be a four-vector representing position, velocity, or momentum, and the same Λ can be used when transforming between the same two frames. The most general Lorentz transformation includes boosts and rotations; the components are complicated and the transformation requires spinors.

text: can be a four-vector representing position, velocity, or momentum, and the same Λ can be used when transforming between the same two frames. The most general Lorentz transformation includes boosts and rotations; the components are complicated and the transformation requires

text: spinor

text: s.

text: Similarly the relative velocity of object B moving with velocity w, relative to object A moving with velocity v is:

text: This is the same formula as the group velocity of a wave. More specifically, due to the Heisenberg uncertainty principle, an electron in a crystal cannot have both an exactly-defined k and an exact position in the crystal. It can, however, form a wave packet centered on momentum k (with slight uncertainty), and centered on a certain position (with slight uncertainty). The center position of this wave packet changes as the wave propagates, moving through the crystal at the velocity v given by the formula above. In a real crystal, an electron moves in this way—traveling in a certain direction at a certain speed—for only a short period of time, before colliding with an imperfection in the crystal that causes it to move in a different, random direction. These collisions, called electron scattering, are most commonly caused by crystallographic defects, the crystal surface, and random thermal vibrations of the atoms in the crystal (phonons).

text: This is the same formula as the

text: group velocity of a wave

text: . More specifically, due to the

text: Heisenberg uncertainty principle

text: , an electron in a crystal cannot have both an exactly-defined k and an exact position in the crystal. It can, however, form a

text: wave packet

text: centered on momentum k (with slight uncertainty), and centered on a certain position (with slight uncertainty). The center position of this wave packet changes as the wave propagates, moving through the crystal at the velocity v given by the formula above. In a real crystal, an electron moves in this way—traveling in a certain direction at a certain speed—for only a short period of time, before colliding with an imperfection in the crystal that causes it to move in a different, random direction. These collisions, called

text: electron scattering

text: , are most commonly caused by

text: crystallographic defect

text: s, the crystal surface, and random thermal vibrations of the atoms in the crystal (

text: phonon

text: s).

text: The velocities

text: The velocities

text: The second is the change of velocity in space. Different positions in a rotating frame of reference have different velocities (as seen from an inertial frame of reference). For an object to move in a straight line, it must accelerate so that its velocity changes from point to point by the same amount as the velocities of the frame of reference. The force is proportional to the angular velocity (which determines the relative speed of two different points in the rotating frame of reference), and to the component of the velocity of the object in a plane perpendicular to the axis of rotation (which determines how quickly it moves between those points). This also gives a term

text: Velocity is defined as the rate of change of position with respect to time, which may also be referred to as the instantaneous velocity to emphasize the distinction from the average velocity. In some applications the "average velocity" of an object might be needed, that is to say, the constant velocity that would provide the same resultant displacement as a variable velocity in the same time interval, , over some time period . Average velocity can be calculated as:

text: where v̂ is the velocity unit vector.

text: where v̂ is the velocity

text: unit vector

text: The interpretation of this equation is that the velocity of the particle seen by observers in frame A consists of what observers in frame B call the velocity, namely v, plus two extra terms related to the rate of change of the frame-B coordinate axes. One of these is simply the velocity of the moving origin v. The other is a contribution to velocity due to the fact that different locations in the non-inertial frame have different apparent velocities due to rotation of the frame; a point seen from a rotating frame has a rotational component of velocity that is greater the further the point is from the origin.

text: The thermal velocity or thermal speed is a typical velocity of the thermal motion of particles which make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature. Technically speaking it is a measure of the width of the peak in the Maxwell–Boltzmann particle velocity distribution. Note that in the strictest sense thermal velocity is not a velocity, since velocity usually describes a vector rather than simply a scalar speed.

text: The thermal velocity or thermal speed is a typical velocity of the

text: thermal motion

text: of particles which make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature. Technically speaking it is a measure of the width of the peak in the

text: Maxwell–Boltzmann particle velocity distribution

text: . Note that in the strictest sense thermal velocity is not a

text: velocity

text: , since velocity usually describes a

text: vector

text: rather than simply a

text: scalar

text: speed

text: The local velocities are not the result of the local function, as segments are moved by the action of neighbouring segments. Thus the velocity differences velocity gradient are the main measure of regional contraction, and has become the most important employment of colour tissue Doppler, in the method of strain rate imaging.

text: The local velocities are not the result of the local function, as segments are moved by the action of neighbouring segments. Thus the velocity differences

text: velocity gradient

text: are the main measure of regional contraction, and has become the most important employment of colour tissue Doppler, in the method of

text: strain rate imaging

text: Surface currents flow at a 45° angle to the wind due to a balance between the Coriolis force and the drags generated by the wind and the water. If the ocean is divided vertically into thin layers, the magnitude of the velocity (the speed) decreases from a maximum at the surface until it dissipates. The direction also shifts slightly across each subsequent layer (right in the northern hemisphere and left in the southern hemisphere). This is called the Ekman spiral. The layer of water from the surface to the point of dissipation of this spiral is known as the Ekman layer. If all flow over the Ekman layer is integrated, the net transportation is at 90° to the right (left) of the surface wind in the northern (southern) hemisphere.

text: Surface currents flow at a 45° angle to the wind due to a balance between the

text: Coriolis

text: force and the

text: drags

text: generated by the wind and the water. If the ocean is divided vertically into thin layers, the magnitude of the velocity (the speed) decreases from a maximum at the surface until it dissipates. The direction also shifts slightly across each subsequent layer (right in the northern hemisphere and left in the southern hemisphere). This is called the

text: Ekman spiral

text: . The layer of water from the surface to the point of dissipation of this spiral is known as the

text: Ekman layer

text: . If all flow over the Ekman layer is integrated, the net transportation is at 90° to the right (left) of the surface wind in the northern (southern) hemisphere.

text: The extra coil or helical resonator can be physically separated from the two close-coupled coils, which comprise the master oscillator or driver section.  The power from the master oscillator is fed to the lower end of the extra coil resonator through a large diameter electrical conductor or pipe to minimize corona discharge. The magnifying transmitter's base-driven extra coil behaves as a slow-wave helical resonator, the axial disturbance propagating at a velocity of less than 1% up to around 10% the speed of light in free space.  The axial velocity of the resonator's charge-coupled electromagnetic field is established by the coil pitch and electrical charge propagation speed through the circuit.

text: The extra coil or

text: helical resonator

text: can be physically separated from the two close-coupled coils, which comprise the

text: master oscillator

text: or driver section.  The power from the master oscillator is fed to the lower end of the extra coil resonator through a large diameter

text: electrical conductor

text: or pipe to minimize

text: corona discharge

text: . The magnifying transmitter's base-driven extra coil behaves as a slow-wave

text: helical resonator

text: , the axial disturbance propagating at a velocity of less than 1% up to around 10% the speed of light in free space.  The axial velocity of the resonator's charge-coupled

text: electromagnetic field

text: is established by the coil pitch and electrical charge propagation speed through the circuit.

text: Meteorologists typically express the three vector components of velocity  (

text: The Gauckler–Manning formula is used to estimate the average velocity of water flowing in an open channel in locations where it is not practical to construct a weir or flume to measure flow with greater accuracy.  The friction coefficients across weirs and orifices are less subjective than n along a natural (earthen, stone or vegetated) channel reach.  Cross sectional area, as well as n, will likely vary along a natural channel.  Accordingly, more error is expected in estimating the average velocity by assuming a Manning's n, than by direct sampling (i.e., with a current flowmeter), or measuring it across weirs, flumes or orifices. Manning's equation is also commonly used as part of a numerical step method, such as the Standard Step Method, for delineating the free surface profile of water flowing in an open channel.

text: The Gauckler–Manning formula is used to estimate the average velocity of water flowing in an open channel in locations where it is not practical to construct a weir or flume to measure flow with greater accuracy.  The friction coefficients across weirs and orifices are less subjective than n along a natural (earthen, stone or vegetated) channel reach.  Cross sectional area, as well as n, will likely vary along a natural channel.  Accordingly, more error is expected in estimating the average velocity by assuming a Manning's n, than by direct sampling (i.e., with a current flowmeter), or measuring it across

text: weir

text: s,

text: flume

text: s or

text: orifice

text: s. Manning's equation is also commonly used as part of a numerical step method, such as the

text: Standard Step Method

text: , for delineating the free surface profile of water flowing in an open channel.

text: With the velocity vector expanded as

text: With the velocity vector expanded as

text: Velocity-encoded MRI is based on the detection of changes in the phase of proton precession. These changes are proportional to the velocity of the protons' movement through a magnetic field with a known gradient. When using velocity-encoded MRI, the result is two sets of images, one for each time point in the cardiac cycle. One is an anatomical image and the other is an image in which the signal intensity in each pixel is directly proportional to the through-plane velocity. The average velocity in a vessel, i.e., the aorta or the pulmonary artery, is quantified by measuring the average signal intensity of the pixels in the cross-section of the vessel then multiplying by a known constant. The flow is calculated by multiplying the mean velocity by the cross-sectional area of the vessel. This flow data can be used in a flow-versus-time graph. The area under the flow-versus-time curve for one cardiac cycle is the stroke volume. The length of the cardiac cycle is known and determines heart rate; Q can be calculated using equation (). MRI is typically used to quantify the flow over one cardiac cycle as the average of several heart beats. It is also possible to quantify the stroke volume in real-time on a beat-for-beat basis.

text: Velocity-encoded MRI is based on the detection of changes in the phase of proton

text: precession

text: . These changes are proportional to the velocity of the protons' movement through a magnetic field with a known gradient. When using velocity-encoded MRI, the result is two sets of images, one for each time point in the cardiac cycle. One is an anatomical image and the other is an image in which the signal intensity in each

text: pixel

text: is directly proportional to the through-plane velocity. The average velocity in a vessel, i.e., the

text: aorta

text: or the

text: pulmonary artery

text: , is quantified by measuring the average signal intensity of the pixels in the cross-section of the vessel then multiplying by a known constant. The flow is calculated by multiplying the mean velocity by the cross-sectional area of the vessel. This flow data can be used in a flow-versus-time graph. The area under the flow-versus-time curve for one

text: cardiac cycle

text: is the stroke volume. The length of the cardiac cycle is known and determines heart rate; Q can be calculated using equation (). MRI is typically used to quantify the flow over one cardiac cycle as the average of several heart beats. It is also possible to quantify the stroke volume in real-time on a beat-for-beat basis.

text: is the velocity of the particle with respect to the rotating system, and Ω is the angular velocity vector having magnitude equal to the rotation rate ω, with direction along the axis of rotation of the rotating reference frame, and the × symbol represents the cross product operator.

text: is the velocity of the particle with respect to the rotating system, and Ω is the

text: angular velocity

text: vector having magnitude equal to the rotation rate ω, with direction along the axis of rotation of the rotating reference frame, and the × symbol represents the

text: cross product

text: operator.

text: Depth and velocity have also been raised as a concern with regards to effecting results, however Stark (1993) investigated the influences of the sampling method, water depth, current velocity and substratum on the results and found that both MCI and QMCI are independent of depth, velocity, and substratum from macroinvertebrate samples collected from stony riffles. This finding is an advantage for the assessment of water pollution.

text: Depth and velocity have also been raised as a concern with regards to effecting results, however Stark (1993) investigated the influences of the sampling method, water depth, current velocity and

text: substratum

text: on the results and found that both MCI and QMCI are independent of depth, velocity, and substratum from macroinvertebrate samples collected from stony riffles. This finding is an advantage for the assessment of water pollution.

text: into the velocity vector equation and simplifying, the final form of the velocity vector equation is obtained as:

text: A relatively fast fluid velocity (10–30 m/s) is usually required in FR operations to encourage a continuous particle distribution throughout the reactor’s vessel. This minimizes the column’s slip velocity (average velocity difference of different fluids in a pipe), providing a positive impact on heat and mass transfer rates and allowing for the use of smaller diameter vessels which can lower operating costs. Also, the use of a vertical fluid flow configuration will result in a lack of feed particle mixing in the horizontal and vertical direction, as such, discouraging particle interactions that would decrease product impurity.

text: Though in a semiconductor such as Si saturation velocity of a carrier is same as the peak velocity of the carrier, for some other materials with more complex energy band structures, this is not true.  In GaAs or InP for example the carrier drift velocity reaches to a maximum as a function of field and then it begins to actually decrease as the electric field applied is increased further.  Carriers which have gained enough energy are kicked up to a different conduction band which presents a lower drift velocity and eventually a lower saturation velocity in these materials.  This results in an overall decrease of current for higher voltage until all electrons are in the "slow" band and this is the principle behind operation of a Gunn diode, which can display negative differential resistivity.  Due to the transfer of electrons to a different conduction band involved, such devices, usually single terminal, are referred to as Transferred electron devices, or TEDs.

text: Though in a semiconductor such as Si saturation velocity of a carrier is same as the peak velocity of the carrier, for some other materials with more complex

text: energy band

text: structures, this is not true.  In

text: GaAs

text: or

text: InP

text: for example the carrier drift velocity reaches to a maximum as a function of field and then it begins to actually decrease as the electric field applied is increased further.  Carriers which have gained enough energy are kicked up to a different

text: conduction band

text: which presents a lower drift velocity and eventually a lower saturation velocity in these materials.  This results in an overall decrease of current for higher voltage until all electrons are in the "slow" band and this is the principle behind operation of a

text: Gunn diode

text: , which can display negative differential resistivity.  Due to the transfer of electrons to a different conduction band involved, such devices, usually single terminal, are referred to as

text: Transferred electron device

text: s, or TEDs.

text: The velocity of one point relative to another is simply the difference between their velocities

text: The radial velocity of the component A is , and the radial velocity of the component B is . Since values of the radial velocity are positive, the system currently is moving away from us.

text: The

text: radial velocity

text: of the component A is , and the radial velocity of the component B is . Since values of the radial velocity are positive, the system currently is moving away from us.

text: Relative velocity is a measurement of velocity between two objectsas determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles. In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with special relativity in which velocities depend on the choice of reference frame.

text: Relative velocity is a measurement of velocity between two objectsas determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles. In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with

text: special relativity

text: in which velocities depend on the choice of reference frame.

text: By definition of Average velocity,

text: By definition of Average velocity,

text: Based on measurements of proper motion and radial velocity, astronomers know that this star and AE Aurigae are moving away from each other at a relative velocity of over 200 km/s. Their common point of origin intersects with Iota Orionis in the Trapezium cluster, some two and half million years in the past. The most likely scenario that could have created these runaway stars is a collision between two binary star systems, with the stars being ejected along different trajectories radial to the point of intersection.

text: Based on measurements of

text: proper motion

text: and

text: radial velocity

text: , astronomers know that this star and

text: AE Aurigae

text: are moving away from each other at a

text: relative velocity

text: of over 200 km/s. Their common point of origin intersects with

text: Iota Orionis

text: in the

text: Trapezium cluster

text: , some two and half million years in the past. The most likely scenario that could have created these

text: runaway star

text: s is a collision between two

text: binary star

text: systems, with the stars being ejected along different trajectories radial to the point of intersection.

text: Although conduction velocity itself is not directly measured, calculating conduction velocities from NCS measurements is trivial. The distance between the stimulating and receiving electrodes is divided by the impulse latency, resulting in conduction velocity.

text: Manning did not receive any education or formal training in fluid mechanics or engineering. His accounting background and pragmatism influenced his work and drove him to reduce problems to their simplest form. He compared and evaluated seven best known formulae of the time for the flow of water in a channel: Du Buat (1786), Eyelwein (1814), Weisbach (1845), St. Venant (1851), Neville (1860), Darcy and Bazin (1865), and Ganguillet and Kutter (1869). He calculated the velocity obtained from each formula for a given slope and for hydraulic radii varying from 0.25 m to 30 m. Then, for each condition, he found the mean value of the seven velocities and developed a formula that best fitted the data.

text: The definition of Ekman velocity is the difference between the total horizontal velocity (

text: Wind velocity (/WV) must contain both the wind speed and direction. Direction is reported as a three-digit value in whole degrees true and the wind speed in knots also in three digits.

text: Wind velocity (/WV) must contain both the wind speed and direction. Direction is reported as a three-digit value in whole degrees true and the wind speed in

text: knots

text: also in three digits.

text: Another technique used to estimate the anisotropy parameter is directly measure them from the core which is extracted through a special hollow drill bit during drill process. Since coring a sample will generate large extra cost, only limited number of core samples can be obtained for each well. Thus the anisotropy parameter obtained through core measurement technique only represent the anisotropy property of rock near the borehole at just several specific  depth, rending this technique often provides little help on the field seismic survey application. The measurements on each shale plug require at least one week.From the context of this article, wave propagation in a vertically transverse medium can be described with five elastic constants, and ratios among these parameters define the rock anisotropy . This anisotropy parameter can be obtained in the laboratory by measuring the velocity travel speed with transducer ultrasonic systems at variable saturation and pressure conditions. Usually, three directions of wave propagation on core samples are the minimum requirement to estimate the five elastic coefficients of the stiffness tensor. Each direction in core plug measurement yields three velocities (one P and two S).

text: Neutrino velocities exceeding the speed of light by more than

text: The Moon train starts with gear b1 and proceeds through c1, c2, d1, d2, e2, e5, k1, k2, e6, e1, and b3 to the moon pointer on the front face. The gears k1 and k2 form an epicyclic gear system; they are an identical pair of gears that don't mesh, but rather, they operate face-to-face, with a short pin on k1 inserted into a slot in k2. The two gears have different centres of rotation, so the pin must move back and forth in the slot. That increases and decreases the radius at which k2 is driven, also necessarily varying its angular velocity (presuming the velocity of k1 is even) faster in some parts of the rotation than others.  Over an entire revolution the average velocities are the same, but the fast-slow variation models the effects of the elliptical orbit of the moon, in consequence of Kepler's second and third laws. The modelled rotational period of the moon pointer (averaged over a year) is 27.321 days, compared to the modern length of a lunar sidereal month of 27.321661 days. As mentioned, the pin/slot driving of the k1/k2 gears varies the displacement over a year's time, and the mounting of those two gears on the e3 gear supplies a precessional advancement to the ellipticity modelling with a period of 8.8826 years, compared with the current value of precession period of the moon of 8.85 years.

text: The Moon train starts with gear b1 and proceeds through c1, c2, d1, d2, e2, e5, k1, k2, e6, e1, and b3 to the moon pointer on the front face. The gears k1 and k2 form an

text: epicyclic gear system

text: ; they are an identical pair of gears that don't mesh, but rather, they operate face-to-face, with a short pin on k1 inserted into a slot in k2. The two gears have different centres of rotation, so the pin must move back and forth in the slot. That increases and decreases the radius at which k2 is driven, also necessarily varying its angular velocity (presuming the velocity of k1 is even) faster in some parts of the rotation than others.  Over an entire revolution the average velocities are the same, but the fast-slow variation models the effects of the elliptical orbit of the moon, in consequence of

text: Kepler's second and third laws

text: . The modelled rotational period of the moon pointer (averaged over a year) is 27.321 days, compared to the modern length of a lunar sidereal month of 27.321661 days. As mentioned, the pin/slot driving of the k1/k2 gears varies the displacement over a year's time, and the mounting of those two gears on the e3 gear supplies a precessional advancement to the ellipticity modelling with a period of 8.8826 years, compared with the current value of precession period of the

text: moon

text: of 8.85 years.

text: The local physical velocity can still be different than the advection velocity because the vector of the local fluid flow does not have to be parallel to that of average flow. Also, there may be local constriction in the flow channel.

text: Signal velocity is usually equal to group velocity (the speed of a short "pulse" or of a wave-packet's middle or "envelope"). However, in a few special cases (e.g., media designed to amplify the front-most parts of a pulse and then attenuate the back section of the pulse), group velocity can exceed the speed of light in vacuum, while the signal velocity will still be less than or equal to the speed of light in vacuum.

text: Signal velocity is usually equal to

text: group velocity

text: (the speed of a short "pulse" or of a wave-packet's middle or "envelope"). However, in a few special cases (e.g., media designed to amplify the front-most parts of a pulse and then attenuate the back section of the pulse), group velocity can exceed the speed of light in vacuum, while the signal velocity will still be less than or equal to the speed of light in vacuum.

text: In principle, velocity cannot be directly perceived by relative cues alone, like those from the vestibular system. For such a system, flying in space with some constant velocity is not different from sitting in a chair. However, changing the velocity is perceived as acceleration, or force acting on the human body. For the case of constant linear acceleration, a substitute for the real situation is simple. Since the amplitude of the acceleration is not very well perceived by humans, one can tilt the subject backwards and use the gravity vector as a replacement for correct resulting force from gravity and forward acceleration. In this case, leaning backwards is therefore not perceived differently from being constantly accelerated forwards.

text: 1971 saw the Spider Veloce get a new, larger powerplant—a 1962 cc,  unit—and consequently the name was changed from 1750 Spider Veloce to 2000 Spider Veloce.  The 1600 Spider restarted production a year later as the Spider 1600 Junior, and was visually identical to the 1300.

text: A velocity consists of a speed combined with a direction; the speed part of the velocity takes units of speed.

text: A

text: velocity

text: consists of a speed combined with a direction; the speed part of the velocity takes units of speed.

text: c    outlet absolute velocity vector

text: c    outlet absolute velocity vector

text: If we consider  as velocity and  as the displacement (change in position) vector, then we can express the (instantaneous) velocity of a particle or object, at any particular time , as the derivative of the position with respect to time:

text: If we consider  as velocity and  as the displacement (change in position) vector, then we can express the (instantaneous) velocity of a particle or object, at any particular time , as the

text: derivative

text: of the position with respect to time:

text: McCarthy et al. (2010) explain that each of the velocity regimes they propose is suited to a different temporal orientation, which they define as “a cognitive concept that describes how individuals and teams conceive of time". Specially, they argue that when velocity dimensions are tightly coupled to each (i.e., “the relationship between the velocities of different dimensions involve significant immediate, direct causal effects”), an organization’s capabilities would benefit from a polychronic orientation. In contrast, when velocity regimes are loosely coupled (i.e., “changes in the velocity of one dimension have relatively little immediate, direct impact on the velocities of other dimensions”) an organization’s capabilities would benefit from a monochronic orientation.

text: McCarthy et al. (2010) explain that each of the velocity regimes they propose is suited to a different temporal orientation, which they define as “a cognitive concept that describes how individuals and teams conceive of time". Specially, they argue that when velocity dimensions are tightly coupled to each (i.e., “the relationship between the velocities of different dimensions involve significant immediate, direct causal effects”), an organization’s capabilities would benefit from a

text: polychronic

text: orientation. In contrast, when velocity regimes are loosely coupled (i.e., “changes in the velocity of one dimension have relatively little immediate, direct impact on the velocities of other dimensions”) an organization’s capabilities would benefit from a

text: monochronic

text: orientation.

text: of the velocity vector

text: of the

text: velocity

text: vector

text: The magnitude of the transverse velocity is that of the cross product of the unit vector in the direction of the displacement and the velocity vector. It is also the product of the angular speed

text: The magnitude of the transverse velocity is that of the

text: cross product

text: of the unit vector in the direction of the displacement and the velocity vector. It is also the product of the

text: angular speed

text: Here,  is the parameter of the transformation, for a given boost it is a constant number, but can take a continuous range of values. In the setup used here, positive relative velocity  is motion along the positive directions of the  axes, zero relative velocity  0}} is no relative motion, while negative relative velocity  is relative motion along the negative directions of the  axes. The magnitude of relative velocity  cannot equal or exceed , so only subluminal speeds  are allowed. The corresponding range of  is .

text: Here,  is the

text: parameter

text: of the transformation, for a given boost it is a constant number, but can take a continuous range of values. In the setup used here, positive relative velocity  is motion along the positive directions of the  axes, zero relative velocity  0}} is no relative motion, while negative relative velocity  is relative motion along the negative directions of the  axes. The magnitude of relative velocity  cannot equal or exceed , so only subluminal speeds  are allowed. The corresponding range of  is .

text: Note that "velocity" in this context is defined as a vector, thus Newton's "constant velocity" implies both constant speed and constant direction (and also includes the case of zero speed, or no motion).  Since initial publication, Newton's Laws of Motion (and by inclusion, this first law) have come to form the basis for the branch of physics known as classical mechanics.

text: Note that "velocity" in this context is defined as a

text: vector

text: , thus Newton's "constant velocity" implies both constant speed and constant direction (and also includes the case of zero speed, or no motion).  Since initial publication, Newton's Laws of Motion (and by inclusion, this first law) have come to form the basis for the branch of

text: physics

text: known as

text: classical mechanics

text: In relativity, proper velocity, also known as celerity, is an alternative to velocity for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured distance by the time elapsed on the clocks of the traveling object. Proper velocity equals velocity at low speeds.  Proper velocity at high speeds, moreover, retains many of the properties that velocity loses in relativity compared with Newtonian theory.

text: In

text: relativity

text: , proper velocity, also known as celerity, is an alternative to

text: velocity

text: for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured distance by the time elapsed on the clocks of the traveling object. Proper velocity equals velocity at low speeds.  Proper velocity at high speeds, moreover, retains many of the properties that velocity loses in relativity compared with Newtonian theory.

text: Suppose the vector field describes the velocity field of a fluid flow (such as a large tank of liquid or gas) and a small ball is located within the fluid or gas (the centre of the ball being fixed at a certain point). If the ball has a rough surface, the fluid flowing past it will make it rotate. The rotation axis (oriented according to the right hand rule) points in the direction of the curl of the field at the centre of the ball, and the angular speed of the rotation is half the magnitude of the curl at this point.

text: Suppose the vector field describes the

text: velocity field

text: of a

text: fluid flow

text: (such as a large tank of

text: liquid

text: or

text: gas

text: ) and a small ball is located within the fluid or gas (the centre of the ball being fixed at a certain point). If the ball has a rough surface, the fluid flowing past it will make it rotate. The rotation axis (oriented according to the right hand rule) points in the direction of the curl of the field at the centre of the ball, and the angular speed of the rotation is half the magnitude of the curl at this point.

text: The group velocity ∂Ω/∂k of capillary waves – dominated by surface tension effects – is greater than the phase velocity Ω/k. This is opposite to the situation of surface gravity waves (with surface tension negligible compared to the effects of gravity) where the phase velocity exceeds the group velocity.

text: The

text: group velocity

text: ∂Ω/∂k of capillary waves – dominated by surface tension effects – is greater than the

text: phase velocity

text: Ω/k. This is opposite to the situation of surface gravity waves (with surface tension negligible compared to the effects of gravity) where the phase velocity exceeds the group velocity.

text: Suppose two forces act on a particle at the origin (the "tails" of the vectors) of Figure 1. Let the lengths of the vectors F and F represent the velocities the two forces could produce in the particle by acting for a given time, and let the direction of each represent the direction in which they act. Each force acts independently and will produce its particular velocity whether the other force acts or not. At the end of the given time, the particle has both velocities. By the above proof, they are equivalent to a single velocity, F. By Newton's second law, this vector is also a measure of the force which would produce that velocity, thus the two forces are equivalent to a single force.

text: Suppose two

text: force

text: s act on a

text: particle

text: at the origin (the "tails" of the

text: vector

text: s) of Figure 1. Let the lengths of the vectors F and F represent the

text: velocities

text: the two forces could produce in the particle by acting for a given time, and let the direction of each represent the direction in which they act. Each force acts independently and will produce its particular velocity whether the other force acts or not. At the end of the given time, the particle has both velocities. By the above proof, they are equivalent to a single velocity, F. By

text: Newton's second law

text: , this vector is also a measure of the force which would produce that velocity, thus the two forces are equivalent to a single force.

text: . In this specific case, the relationship between the linear velocity vector and the angular velocity vector is

text: determines a velocity 4-vector

text: determines a velocity 4-vector

text: Unlike 1D Doppler imaging, which can only provide one-dimensional velocity and has dependency on the beam to flow angle, 2D velocity estimation using Doppler ultrasound is able to generate velocity vectors with axial and lateral velocity components. 2D velocity is useful even if complex flow conditions such as stenosis and bifurcation exist. There are two major methods of 2D velocity estimation using ultrasound: Speckle tracking and crossed beam Vector Doppler, which are based on measuring the time shifts and phase shifts respectively.

text: According to this hypothesis, Earth and the aether are in relative motion, implying that a so-called "aether wind" (Fig. 2) should exist. Although it would be possible, in theory, for the Earth's motion to match that of the aether at one moment in time, it was not possible for the Earth to remain at rest with respect to the aether at all times, because of the variation in both the direction and the speed of the motion. At any given point on the Earth's surface, the magnitude and direction of the wind would vary with time of day and season. By analyzing the return speed of light in different directions at various different times, it was thought to be possible to measure the motion of the Earth relative to the aether. The expected relative difference in the measured speed of light was quite small, given that the velocity of the Earth in its orbit around the Sun has a magnitude of about one hundredth of one percent of the speed of light.

text: There is controversy over whether the Castor Moving Group constitutes a physical group of stars of shared origin (e.g. an "association") or a group of stars of heterogeneous age and chemical composition that happen to have somewhat similar velocities (e.g. a "dynamical stream"). In their 2013 paper describing the discovery of Fomalhaut C, Mamajek et al. point out that the 3D velocities of the famous Castor Moving Group members Fomalhaut, Vega, Castor, and LP 944-20 are now very well-determined. They find that the star-to-star velocity differences are so large (typically ~5–10 km/s) that the stars were not within 100 pc of each other as recently as 10 Myr ago, let alone at the purported group age of ~200 million years. The local density of purported Castor Moving Group members is very low (roughly 0.4% of the mass density of the local Galactic disk), hence the systems are not bound to one another, and the high velocity dispersion can not be attributed to the dynamical interactions amongst the moving group members themselves. They conclude that at least those famous "members" of the Castor Moving Group (Fomalhaut, Vega, Castor, LP 944-20) are extremely unlikely to have shared a common origin.

text: There is controversy over whether the Castor Moving Group constitutes a physical group of stars of shared origin (e.g. an "association") or a group of stars of heterogeneous age and chemical composition that happen to have somewhat similar velocities (e.g. a "dynamical stream"). In their 2013 paper describing the discovery of

text: Fomalhaut

text: C, Mamajek et al. point out that the 3D velocities of the famous Castor Moving Group members

text: Fomalhaut

text: Vega

text: Castor

text: , and

text: LP 944-20

text: are now very well-determined. They find that the star-to-star velocity differences are so large (typically ~5–10 km/s) that the stars were not within 100 pc of each other as recently as 10 Myr ago, let alone at the purported group age of ~200 million years. The local density of purported Castor Moving Group members is very low (roughly 0.4% of the mass density of the local Galactic disk), hence the systems are not bound to one another, and the high velocity dispersion can not be attributed to the dynamical interactions amongst the moving group members themselves. They conclude that at least those famous "members" of the Castor Moving Group (

text: Fomalhaut

text: Vega

text: Castor

text: LP 944-20

text: ) are extremely unlikely to have shared a common origin.

text: From kinetic theory it is known that a molecule of A has an average velocity (different from root mean square velocity) of

text: From

text: kinetic theory

text: it is known that a molecule of A has an

text: average velocity

text: (different from

text: root mean square

text: velocity) of

text: Tomography is a method of producing a three-dimensional image of the internal structures of a solid object (such as the human body or the earth) by the observation and recording of differences in the effects on the passage of energy waves impinging on those structures. The waves of energy are P-waves generated by earthquakes and are recording the wave velocities. The high quality data that is being collected by the permanent seismic stations of USArray and the Advanced National Seismic System (ANSS) will allow the creation of high resolution seismic imaging of the Earth’s interior below the United States. Seismic tomography helps constrain mantle velocity structure and aids in the understanding of chemical and geodynamic processes that are at work. With the use of the data collected by USArray and global travel-time data, a global tomography model of P-wave velocity heterogeneity in the mantle can be created. The range and resolution of this technique will allow investigation into the suite of problems that are of concern in the North American mantle lithosphere, including the nature of the major tectonic features. This method gives evidence for differences in thickness and the velocity anomaly of the mantle lithosphere between the stable center of the continent and the more active western North America. This data is vital for the understanding of local lithosphere evolution, and when combined with additional global data, will allow the mantle to be imaged beyond the current extent of USArray.

text: Tomography

text: mantle lithosphere

text: between the stable center of the continent and the more active western North America. This data is vital for the understanding of local lithosphere evolution, and when combined with additional global data, will allow the mantle to be imaged beyond the current extent of USArray.

text: In physics, many quantities are naturally represented by alternating operators. For example, if the motion of a charged particle is described by velocity and acceleration vectors in four-dimensional spacetime, then normalization of the velocity vector requires that the electromagnetic force must be an alternating operator on the velocity. Its six degrees of freedom are identified with the electric and magnetic fields.

text: Consider the reversed configuration, namely, frame  moves with velocity  relative to frame , and frame , in turn, moves with velocity  relative to frame . In short,  and  by EPVR. Then the velocity of  relative to  is . By EPVR again, the velocity of  relative to  is then  v ⊕ u}}.

text: McCarthy et al. (2010) developed a framework that describes the relationships between these multiple velocity dimensions, noting that they may each have a distinct and often different velocity. They define “velocity homology” as the degree to which velocity dimensions have similar rates and directions of change and “velocity coupling” as the degree to which the velocities of different dimensions affect one another. This multidimensional treatment of environmental velocity results in four “velocity regimes” - simple, divergent, conflicted and integrated - based on the patterns of velocity homology and velocity coupling. A key implication of the framework is that firms should not necessarily focus on being uniformly fast (or slow) to suit industry conditions. Each of the four velocity regimes requires firms to maintain different forms of temporal fit (i.e., the entrainment of multiple organizational paces) and temporal coordination (i.e., managing the interdependences between organizational paces).

text: McCarthy et al. (2010) developed a framework that describes the relationships between these multiple velocity dimensions, noting that they may each have a distinct and often different velocity. They define “velocity homology” as the degree to which velocity dimensions have similar rates and directions of change and “velocity coupling” as the degree to which the velocities of different dimensions affect one another. This multidimensional treatment of environmental velocity results in four “velocity regimes” - simple, divergent, conflicted and integrated - based on the patterns of velocity homology and velocity coupling. A key implication of the framework is that firms should not necessarily focus on being uniformly fast (or slow) to suit industry conditions. Each of the four velocity regimes requires firms to maintain different forms of temporal fit (i.e., the

text: entrainment

text: of multiple organizational paces) and temporal coordination (i.e., managing the interdependences between organizational paces).

text: To evaluate the velocity, the derivative of the unit vector u is needed. Because u is a unit vector, its magnitude is fixed, and it can change only in direction, that is, its change du has a component only perpendicular to u. When the trajectory r(t) rotates an amount dθ, u, which points in the same direction as r(t), also rotates by dθ. See image above. Therefore, the change in u is

text: Low-velocity objects usually cause penetrating injuries in the regions of the skull's temporal bones or orbital surfaces, where the bones are thinner and thus more likely to break.  Damage from lower-velocity penetrating injuries is restricted to the tract of the stab wound, because the lower-velocity object does not create as much cavitation.  However, low-velocity penetrating objects, such as slow bullets, may ricochet inside the skull, continuing to cause damage until they stop moving.

text: Low-velocity objects usually cause penetrating injuries in the regions of the

text: skull

text: 's

text: temporal bone

text: s or

text: orbital surface

text: s, where the bones are thinner and thus more likely to break.  Damage from lower-velocity penetrating injuries is restricted to the tract of the stab wound, because the lower-velocity object does not create as much cavitation.  However, low-velocity penetrating objects, such as slow bullets, may ricochet inside the skull, continuing to cause damage until they stop moving.

text: The velocity of a particle is a vector quantity that describes the direction of motion and the magnitude of the motion of particle. More mathematically, the rate of change of the position vector of a point, with respect to time is the velocity of the point. Consider the ratio of the difference of two positions of a particle divided by the time interval, which is called the average velocity over that time interval. This average velocity is defined as

text: The

text: velocity

text: of a particle is a vector quantity that describes the direction of motion and the magnitude of the motion of particle. More mathematically, the rate of change of the position vector of a point, with respect to time is the velocity of the point. Consider the ratio of the difference of two positions of a particle divided by the time interval, which is called the average velocity over that time interval. This average velocity is defined as

text: In the case of a group velocity different from the phase velocity, a consequence is that the number of waves counted in a wave group is different when counted from a snapshot in space at a certain moment, from when counted in time from the measured surface elevation at a fixed position. Consider a wave group of length Λ and group duration of τ. The group velocity is:

text: Velocity Gradient = velocity/distance.

text: Velocity Gradient = velocity/distance.

text: Specific impulse includes the contribution to impulse provided by external air that has been used for combustion and is exhausted with the spent propellant. Jet engines use outside air, and therefore have a much higher specific impulse than rocket engines. The specific impulse in terms of propellant mass spent (multiplying the weight-based I in seconds by g) is in units of distance per time, which is an artificial velocity called the "effective exhaust velocity". This is higher than the actual exhaust velocity because the mass of the combustion air is not being accounted for. Actual and effective exhaust velocity are the same in rocket engines not utilizing air.

text: For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames. As the relative velocity approaches the speed of light, γ → ∞.

text: A superprism is a photonic crystal in which an entering beam of light will lead to an extremely large angular dispersion. The ability of the photonic crystal to send optical beams with different wavelengths to considerably different angles in space in superprisms has been used to demonstrate wavelength demultiplexing in these structures. The first superprism also modified group velocity rather than phase velocity in order to achieve the "superprism phenomena". This effect was interpreted as anisotropic dispersion in contrast to an isotropic dispersion. Furthermore, the two beams of light appear to show negative bending within the crystal.

text: A superprism is a

text: photonic crystal

text: in which an entering beam of light will lead to an extremely large angular

text: dispersion

text: . The ability of the photonic crystal to send optical beams with different wavelengths to considerably different angles in space in superprisms has been used to demonstrate wavelength demultiplexing in these structures. The first superprism also modified

text: group velocity

text: rather than

text: phase velocity

text: in order to achieve the "superprism phenomena". This effect was interpreted as

text: anisotropic

text: dispersion in contrast to an isotropic dispersion. Furthermore, the two beams of light appear to show negative bending within the crystal.

text: Relativistic speed refers to speed at which relativistic effects become significant to the desired accuracy of measurement of the phenomenon being observed. Relativistic effects are those discrepancies between values calculated by models considering and not considering relativity. Related words are velocity, rapidity, and celerity which is proper velocity. Speed is a scalar, being the magnitude of the velocity vector which in relativity is the four-velocity and in three-dimension Euclidian space a three-velocity. Speed is empirically measured as average speed, although current devices in common use can estimate speed over very small intervals and closely approximate instantaneous speed. Non-relativistic discrepancies include cosine error which occurs in speed detection devices when only one scalar component of the three-velocity is measured and the Doppler effect which may affect observations of wavelength and frequency.

text: Relativistic speed refers to speed at which relativistic effects become significant to the desired accuracy of measurement of the phenomenon being observed. Relativistic effects are those discrepancies between values calculated by models considering and not considering

text: relativity

text: . Related words are

text: velocity

text: rapidity

text: , and

text: celerity

text: which is

text: proper velocity

text: Speed

text: is a

text: scalar

text: , being the

text: magnitude

text: of the velocity

text: vector

text: which in relativity is the

text: four-velocity

text: and in three-dimension Euclidian space a three-velocity. Speed is

text: empirically

text: measured as average speed, although

text: current devices in common use

text: can estimate speed over very small

text: intervals

text: and closely approximate

text: instant

text: aneous speed. Non-relativistic discrepancies include

text: cosine error

text: which occurs in

text: speed detection devices

text: when only one scalar component of the three-velocity is measured and the

text: Doppler effect

text: which may affect observations of wavelength and frequency.

text: In addition bullets there are several hard cast  diameter bullets that are compatible with the .460 Weatherby Magnum. Such bullets, unlike jacketed bullets, are designed to be driven at reduced velocities. Driving these bullets at .460 Weatherby velocities can cause lead to be deposited in the barrel. Regular cast bullets are not recommended with the .460 Weatherby as the upper end of the permissible velocities for these cast bullets is lower than the lowest velocities obtainable from the .460 Weatherby Magnum.

text: In an Esophageal Doppler Monitor (EDM) or Oesophageal Doppler Monitor (ODM), during the time the aortic valve is open (ejection time or flow time), the average aortic blood velocity is calculated. The product of average velocity and ejection time gives the stroke distance (how far the blood travels in each heart cycle). Flow time (FT) is the time difference between the sudden increase in velocity (T0) and the return to near zero velocity (T1). Stroke distance (SD) can calculated from the plug flow like velocity (v(t)):

text: In an Esophageal Doppler Monitor (EDM) or Oesophageal Doppler Monitor (ODM), during the time the

text: aortic valve

text: is open (ejection time or flow time), the average aortic blood velocity is calculated. The product of average velocity and ejection time gives the stroke distance (how far the blood travels in each heart cycle). Flow time (FT) is the time difference between the sudden increase in velocity (T0) and the return to near zero velocity (T1). Stroke distance (SD) can calculated from the plug flow like velocity (v(t)):

text: A distinctive feature of sub-swarms is that their initial positions and initial velocities are not randomly selected as in normal swarms. Instead, they maintain some information from the previous trajectories of the particles. In general, the development of multi-swarm systems leads to design decisions which did not exist during the original development of particle swarm optimization, such as the number of particles to use in each sub-swarm, the optimal value for the constriction factor  and the effects of non-random initial positions and initial velocities. These design decisions have been thoroughly studied and have well-established guidelines – e.g. the use of non-random initial positions and initial velocities leads to improved results in multi-swarm systems, which is not the case for single-swarms. Other design decisions, such as which diversification method to use or which specific search strategy will select the initial positions and initial velocities of a sub-swarm, have less established guidelines and constitute open questions in the field of multi-swarm systems.

text: Ultrasonic flow meters measure the difference of the transit time of ultrasonic pulses propagating in and against flow direction. This time difference is a measure for the average velocity of the fluid along the path of the ultrasonic beam. By using the absolute transit times both the averaged fluid velocity and the speed of sound can be calculated. Using the two transit times

text: When the ionocraft is turned on, the corona wire becomes charged with high voltage, usually between 20 and 50 kV. The user must be extremely careful not to touch the device at this point, as it can give a nasty shock. At extremely high current, well over the amount usually used for a small model, contact could be fatal. When the corona wire is at approximately 30 kV, it causes the air molecules nearby to become ionised by stripping the electrons away from them. As this happens, the ions are strongly repelled away from the anode but are also strongly attracted towards the collector, causing the majority of the ions to begin accelerating in the direction of the collector. These ions travel at a constant average velocity termed the drift velocity. Such velocity depends on the mean free path between collisions, the external electric field, and on the mass of ions and neutral air molecules.

text: When the ionocraft is turned on, the corona wire becomes charged with

text: high voltage

text: , usually between 20 and 50

text: kV

text: . The user must be extremely careful not to touch the device at this point, as it can give a nasty shock. At extremely high current, well over the amount usually used for a small model, contact could be fatal. When the corona wire is at approximately 30 kV, it causes the air molecules nearby to become

text: ion

text: ised by stripping the

text: electrons

text: away from them. As this happens, the ions are strongly repelled away from the anode but are also strongly attracted towards the collector, causing the majority of the ions to begin accelerating in the direction of the collector. These ions travel at a constant average velocity termed the

text: drift velocity

text: . Such velocity depends on the

text: mean free path

text: between collisions, the external electric field, and on the mass of ions and neutral air molecules.

text: The lift on an airfoil is primarily the result of its angle of attack and shape. When oriented at a suitable angle, the airfoil deflects the oncoming air (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and can be resolved into two components: lift and drag.  Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack. This "turning" of the air in the vicinity of the airfoil creates curved streamlines, resulting in lower pressure on one side and higher pressure on the other.  This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface.  The lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta-Joukowski theorem.

text: The lift on an airfoil is primarily the result of its

text: angle of attack

text: and shape. When oriented at a suitable angle, the airfoil deflects the oncoming air (for fixed-wing aircraft, a downward force), resulting in

text: a force on the airfoil in the direction opposite to the deflection

text: . This force is known as

text: aerodynamic force

text: and can be resolved into two components:

text: lift

text: and

text: drag

text: .  Most foil shapes require a positive angle of attack to generate lift, but

text: cambered

text: airfoils can generate lift at zero angle of attack. This "turning" of the air in the vicinity of the airfoil creates curved

text: streamlines

text: , resulting in lower pressure on one side and higher pressure on the other.  This pressure difference is accompanied by a velocity difference, via

text: Bernoulli's principle

text: , so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface.  The lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of

text: circulation

text: and the

text: Kutta-Joukowski theorem

text: Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get  a circular motion. For this centripetal acceleration we have

text: Transverse

text: acceleration (

text: perpendicular

text: to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get  a

text: circular motion

text: . For this

text: centripetal acceleration

text: we have

text: The group velocity v is often thought of as the velocity at which energy or information is conveyed along the wave. In most cases this is true, and the group velocity can be thought of as the signal velocity of the waveform. In some unusual circumstances, called cases of anomalous dispersion, the rate of change of the index of refraction with respect to the wavelength changes sign (becoming negative), in which case it is possible for the group velocity to exceed the speed of light (v > c). Anomalous dispersion occurs, for instance, where the wavelength of the light is close to an absorption resonance of the medium. When the dispersion is anomalous, however, group velocity is no longer an indicator of signal velocity. Instead, a signal travels at the speed of the wavefront, which is c irrespective of the index of refraction. Recently, it has become possible to create gases in which the group velocity is not only larger than the speed of light, but even negative. In these cases, a pulse can appear to exit a medium before it enters. Even in these cases, however, a signal travels at, or less than, the speed of light, as demonstrated by Stenner, et al.

text: The group velocity v is often thought of as the velocity at which energy or information is conveyed along the wave. In most cases this is true, and the group velocity can be thought of as the

text: signal velocity

text: of the waveform. In some unusual circumstances, called cases of anomalous dispersion, the rate of change of the index of refraction with respect to the wavelength changes sign (becoming negative), in which case it is possible for the group velocity to exceed the speed of light (v > c). Anomalous dispersion occurs, for instance, where the wavelength of the light is close to an

text: absorption

text: resonance of the medium. When the dispersion is anomalous, however, group velocity is no longer an indicator of signal velocity. Instead, a signal travels at the speed of the wavefront, which is c irrespective of the index of refraction. Recently, it has become possible to create gases in which the group velocity is not only larger than the speed of light, but even negative. In these cases, a pulse can appear to exit a medium before it enters. Even in these cases, however, a signal travels at, or less than, the speed of light, as demonstrated by Stenner, et al.

text: with  as the velocity at time  and  as the velocity at time . By combining this equation with the suvat equation , it is possible to relate the displacement and the average velocity by

text: is an invariable constant for each measurement. Therefore the average velocity

text: , the angular velocity tensor represents a linear map between the position vectors

text: Vector –Viscosity –Vibration –vacuum concreting –voids—Velocity--

text: Vector

text: Viscosity

text: Vibration

text: vacuum concreting

text: –voids—Velocity--

text: Length contraction is the phenomenon of a decrease in length of an object as measured by an observer who is traveling at any non-zero velocity relative to the object. This contraction (more formally called Lorentz contraction or Lorentz–FitzGerald contraction after Hendrik Lorentz and George Francis FitzGerald) is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction parallel to the direction in which the observed body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes. Only at greater speeds, or for electron motion, does it become significant. At a speed of 13,400,000 m/s (30 million mph, 0.0447) contracted length is 99.9% of the length at rest; at a speed of 42,300,000 m/s (95 million mph, 0.141), the length is still 99%. As the magnitude of the velocity approaches the speed of light, the effect becomes dominant, as can be seen from the formula:

text: Length contraction is the phenomenon of a decrease in

text: length

text: of an object as measured by an observer who is traveling at any non-zero

text: velocity relative

text: to the object. This contraction (more formally called Lorentz contraction or Lorentz–FitzGerald contraction after

text: Hendrik Lorentz

text: and

text: George Francis FitzGerald

text: ) is usually only noticeable at a substantial fraction of the

text: speed of light

text: . Length contraction is only in the direction parallel to the direction in which the observed body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes. Only at greater speeds, or for electron motion, does it become significant. At a speed of 13,400,000 m/s (30 million mph, 0.0447) contracted length is 99.9% of the length at rest; at a speed of 42,300,000 m/s (95 million mph, 0.141), the length is still 99%. As the magnitude of the velocity approaches the speed of light, the effect becomes dominant, as can be seen from the formula:

text: A key concept in the dynamics of vortices is the vorticity, a vector that describes the local rotary motion at a point in the fluid, as would be perceived by an observer that moves along with it.  Conceptually, the vorticity could be observed by placing a tiny rough ball at the point in question, free to move with the fluid, and observing how it rotates about its center.   The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball (according to the right-hand rule) while its length is twice the ball's angular velocity.  Mathematically, the vorticity is defined as the curl (or rotational) of the velocity field of the fluid, usually denoted by

text: A key concept in the dynamics of vortices is the

text: vorticity

text: , a

text: vector

text: that describes the local rotary motion at a point in the fluid, as would be perceived by an observer that moves along with it.  Conceptually, the vorticity could be observed by placing a tiny rough ball at the point in question, free to move with the fluid, and observing how it rotates about its center.   The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball (according to the

text: right-hand rule

text: ) while its length is twice the ball's

text: angular velocity

text: .  Mathematically, the vorticity is defined as the curl (or rotational) of the

text: velocity field

text: of the fluid, usually denoted by

text: When an object is pushed in the direction of motion, it gains momentum and energy, but when the object is already traveling near the speed of light, it cannot move much faster, no matter how much energy it absorbs. Its momentum and energy continue to increase without bounds, whereas its speed approaches a constant value—the speed of light. This implies that in relativity the momentum of an object cannot be a constant times the velocity, nor can the kinetic energy be a constant times the square of the velocity.

text: When an object is pushed in the direction of motion, it gains

text: momentum

text: and energy, but when the object is already traveling near the speed of light, it cannot move much faster, no matter how much energy it absorbs. Its momentum and energy continue to increase without bounds, whereas its speed approaches a constant value—the speed of light. This implies that in relativity the momentum of an object cannot be a constant times the

text: velocity

text: , nor can the

text: kinetic energy

text: be a constant times the square of the velocity.

text: The third description of the flow field's state is swirl. Swirl is the tangential flow component of the velocity vector. The velocity profile should be referred to as the axial velocity profile. As the velocity vector can be resolved into three mutually orthogonal components, the velocity profile only represents the axial component of velocity. fig.(2) showing the Swirl Angle which explains the definition of flow swirl and swirl angle. Note that swirl is usually referenced to full body rotation (that which the full pipeline flow follows one axis of swirl). In real pipeline conditions, such as downstream of elbows two or more mechanisms of swirl may be present.

text: Unlike all other measurements, which are made near between 3 and 9 feet (1 and 3 meters) above the ground, wind speed and direction are measured at 30 feet (10 meters).

text: A sinusoidal wave, of small surface-elevation amplitude and with a constant wavelength, propagates with the phase velocity, also called celerity or phase speed. While the phase velocity is a vector and has an associated direction, celerity or phase speed refer only to the magnitude of the phase velocity. According to linear theory for waves forced by gravity, the phase speed depends on the wavelength and the water depth. For a fixed water depth, long waves (with large wavelength) propagate faster than shorter waves.

text: A

text: sinusoidal

text: wave, of small surface-elevation

text: amplitude

text: and with a constant

text: wavelength

text: , propagates with the

text: phase velocity

text: , also called celerity or phase speed. While the phase velocity is a vector and has an associated direction, celerity or phase speed refer only to the magnitude of the phase velocity. According to linear theory for waves forced by gravity, the phase speed depends on the wavelength and the water depth. For a fixed water depth, long waves (with large wavelength) propagate faster than shorter waves.

text: Only measured quantities figure into the determination of the number of significant figures in calculated quantities.  Exact mathematical quantities like the  in the formula for the area of a circle with radius ,  has no effect on the number of significant figures in the final calculated area.  Similarly the  in the formula for the kinetic energy of a mass  with velocity , , has no bearing on the number of significant figures in the final calculated kinetic energy.  The constants  and  are considered to have an infinite number of significant figures.

text: Only measured quantities figure into the determination of the number of significant figures in calculated quantities.  Exact mathematical quantities like the  in the formula for the

text: area of a circle

text: with radius ,  has no effect on the number of significant figures in the final calculated area.  Similarly the  in the formula for the

text: kinetic energy

text: of a mass  with velocity , , has no bearing on the number of significant figures in the final calculated kinetic energy.  The constants  and  are considered to have an infinite number of significant figures.

text: Moreover, the velocity that must be exceeded is the phase velocity of light rather than the group velocity of light. The phase velocity can be altered dramatically by employing a periodic medium, and in that case one can even achieve Cherenkov radiation with no minimum particle velocity, a phenomenon known as the Smith-Purcell effect. In a more complex periodic medium, such as a photonic crystal, one can also obtain a variety of other anomalous Cherenkov effects, such as radiation in a backwards direction (whereas ordinary Cherenkov radiation forms an acute angle with the particle velocity).

text: Moreover, the velocity that must be exceeded is the

text: phase velocity

text: of light rather than the

text: group velocity

text: of light. The phase velocity can be altered dramatically by employing a periodic medium, and in that case one can even achieve Cherenkov radiation with no minimum particle velocity, a phenomenon known as the

text: Smith-Purcell effect

text: . In a more complex periodic medium, such as a

text: photonic crystal

text: , one can also obtain a variety of other anomalous Cherenkov effects, such as radiation in a backwards direction (whereas ordinary Cherenkov radiation forms an acute angle with the particle velocity).

text: A reference velocity (c) known as the isentropic velocity, spouting velocity or stage terminal velocity is defined as that velocity which will be obtained during an isentropic expansion of the gas between the entry and exit pressures of the stage.

text: In nearby objects (within our Milky Way galaxy) observed redshifts are almost always related to the line-of-sight velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure velocities and parametrize the masses of the orbiting stars in spectroscopic binaries, a method first employed in 1868 by British astronomer William Huggins. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to diagnose and measure the presence and characteristics of planetary systems around other stars and have even made very detailed differential measurements of redshifts during planetary transits to determine precise orbital parameters. Finely detailed measurements of redshifts are used in helioseismology to determine the precise movements of the photosphere of the Sun. Redshifts have also been used to make the first measurements of the rotation rates of planets, velocities of interstellar clouds, the rotation of galaxies, and the dynamics of accretion onto neutron stars and black holes which exhibit both Doppler and gravitational redshifts. Additionally, the temperatures of various emitting and absorbing objects can be obtained by measuring Doppler broadening – effectively redshifts and blueshifts over a single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter hydrogen line in different directions, astronomers have been able to measure the recessional velocities of interstellar gas, which in turn reveals the rotation curve of our Milky Way. Similar measurements have been performed on other galaxies, such as Andromeda. As a diagnostic tool, redshift measurements are one of the most important spectroscopic measurements made in astronomy.

text: In nearby objects (within our

text: Milky Way

text: galaxy) observed redshifts are almost always related to the

text: line-of-sight

text: velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure

text: velocities

text: and parametrize the

text: mass

text: es of the

text: orbiting

text: star

text: s in

text: spectroscopic binaries

text: , a method first employed in 1868 by British astronomer

text: William Huggins

text: . Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to

text: diagnose and measure

text: the presence and characteristics of

text: planetary systems

text: around other stars and have even made very

text: detailed differential measurements

text: of redshifts during

text: planetary transits

text: to determine precise orbital parameters. Finely detailed measurements of redshifts are used in

text: helioseismology

text: to determine the precise movements of the

text: photosphere

text: of the

text: Sun

text: . Redshifts have also been used to make the first measurements of the

text: rotation rates

text: of

text: planet

text: s, velocities of

text: interstellar cloud

text: s, the

text: rotation of galaxies

text: , and the

text: dynamics

text: of

text: accretion

text: onto

text: neutron star

text: s and

text: black hole

text: s which exhibit both Doppler and gravitational redshifts. Additionally, the

text: temperature

text: s of various emitting and absorbing objects can be obtained by measuring

text: Doppler broadening

text: – effectively redshifts and blueshifts over a single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter

text: hydrogen line

text: in different directions, astronomers have been able to measure the

text: recessional velocities

text: of

text: interstellar gas

text: , which in turn reveals the

text: rotation curve

text: of our Milky Way. Similar measurements have been performed on other galaxies, such as

text: Andromeda

text: . As a diagnostic tool, redshift measurements are one of the most important

text: spectroscopic measurements

text: made in astronomy.

text: To maintain conservation of momentum, ships under Bergenholm drive retain a (temporarily suspended) 'intrinsic velocity' as well as the actual velocity they move at. When a Bergenholm is switched off (or disabled), an inertialess ("free") object resumes its 'intrinsic velocity', the velocity it had when the Bergenholm was activated. As a result, a ship must use its jets for some time while in a non-inertialess ("inert") condition to match speed with destination planets. Matching velocities is usually and more easily done after arrival, but if the velocity of the destination is known it may be done before engaging the Bergenholm. Also, and for the same reasons, two ships that make a rendezvous must match intrinsic velocities. It can be very dangerous for any object or substance to come aboard a ship while the ship is under Bergenholm drive. Once the Bergenholm is deactivated, the foreign object will resume its own intrinsic velocity, which may be very different from that of the ship. In such a case it will become a very dangerous projectile.

text: To maintain

text: conservation of momentum

text: , ships under Bergenholm drive retain a (temporarily suspended) 'intrinsic velocity' as well as the actual velocity they move at. When a Bergenholm is switched off (or disabled), an inertialess ("free") object resumes its 'intrinsic velocity', the velocity it had when the Bergenholm was activated. As a result, a ship must use its jets for some time while in a non-inertialess ("inert") condition to match speed with destination

text: planets

text: . Matching velocities is usually and more easily done after arrival, but if the velocity of the destination is known it may be done before engaging the Bergenholm. Also, and for the same reasons, two ships that make a rendezvous must match intrinsic velocities. It can be very dangerous for any object or substance to come aboard a ship while the ship is under Bergenholm drive. Once the Bergenholm is deactivated, the foreign object will resume its own intrinsic velocity, which may be very different from that of the ship. In such a case it will become a very dangerous projectile.

text: Equation [3] involves the average velocity . Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from  to , as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows from solving [1] for

text: The Dry Mesa Dinosaur Quarry of western Colorado yields one of the most diverse Upper Jurassic vertebrate assemblages in the world. This fossil assemblage was deposited within a poorly sorted sandstone bed that is stratigraphically situated in the lower portion of the upper Brushy Basin Member of the Morrison Formation. The bone accumulation, consisting of thousands of bones, was the consequence of two cataclysmic events, a drought, and flash flood. In the Dry Mesa area, a severe drought resulted in the mass mortality of dinosaurs and other vertebrates. These animals were attracted to a remnant water hole of the dry Lake T'oo'dichi' lake bed where they died of starvation and dehydration. This mass mortality produced a considerable accumulation of disarticulated vertebrate remains.  Subsequently, a short-lived flash flood traversed the dry lake beds. The quarry sandstone bed is a 2 meter thick, 121 meter wide, very poorly sorted pebble-rich sublitharenite. The channel sandstone shows abundant trough cross-stratification and a possible antidune bedform composed of gravel and sand which indicates flow velocities as high as 200 cm/s (5 miles/hour). Measured bone volumes can be equated to flow velocities. These calculated bone volume velocities are in agreement with flow velocities determined from grain size and bedforms. The river flow direction, based upon bedform orientations and bone elongation statistics, was to the east-northeast. Geologic and taphonomic characteristics indicate a short transport distance for the bone accumulation (Richmond and Morris, 1999).

text: The Dry Mesa Dinosaur Quarry of western Colorado yields one of the most diverse Upper

text: Jurassic

text: vertebrate assemblages in the world. This fossil assemblage was deposited within a poorly sorted

text: sandstone

text: bed that is stratigraphically situated in the lower portion of the upper Brushy Basin Member of the

text: Morrison Formation

text: . The bone accumulation, consisting of thousands of bones, was the consequence of two cataclysmic events, a

text: drought

text: , and

text: flash flood

text: . In the Dry Mesa area, a severe drought resulted in the mass mortality of

text: dinosaur

text: s and other

text: vertebrates

text: . These animals were attracted to a remnant water hole of the dry Lake T'oo'dichi' lake bed where they died of starvation and dehydration. This mass mortality produced a considerable accumulation of disarticulated vertebrate remains.  Subsequently, a short-lived flash flood traversed the dry lake beds. The quarry sandstone bed is a 2 meter thick, 121 meter wide, very poorly sorted pebble-rich sublith

text: arenite

text: . The channel

text: sandstone

text: shows abundant trough cross-stratification and a possible

text: antidune

text: bedform composed of gravel and sand which indicates flow velocities as high as 200 cm/s (5 miles/hour). Measured bone volumes can be equated to flow

text: velocities

text: . These calculated bone volume velocities are in agreement with flow

text: velocities

text: determined from

text: grain size

text: and bedforms. The river flow direction, based upon bedform orientations and bone elongation statistics, was to the east-northeast.

text: Geologic

text: and

text: taphonomic

text: characteristics indicate a short transport distance for the bone accumulation (Richmond and Morris, 1999).

text: The magnitude of the radial velocity is the dot product of the velocity vector and the unit vector in the direction of the displacement.

text: The magnitude of the radial velocity is the

text: dot product

text: of the velocity vector and the unit vector in the direction of the displacement.

text: Since the motion of the particles is random and there is no bias applied in any direction, the average squared speed in each direction is identical:

text: For example, when a car starts from a standstill (zero relative velocity) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the car turns, there is an acceleration toward the new direction. In this example, we can call the forward acceleration of the car a "linear acceleration", which passengers in the car might experience as a force pushing them back into their seats. When changing direction, we might call this "non-linear acceleration", which passengers might experience as a sideways force. If the speed of the car decreases, this is an acceleration in the opposite direction from the direction of the vehicle, sometimes called deceleration. Passengers may experience deceleration as a force lifting them forwards.  Mathematically, there is no separate formula for deceleration: both are changes in velocity. Each of these accelerations (linear, non-linear, deceleration) might be felt by passengers until their velocity (speed and direction) matches that of the car.

text: The apparent wind on board (a boat) is often quoted as a speed measured by a masthead transducer containing an anemometer and wind vane that measures wind speed in knots and wind direction in degrees relative to the heading of the boat. Modern instrumentation can calculate the true wind velocity when the apparent wind and boat velocity and direction are input.

text: The apparent wind on board (a boat) is often quoted as a speed measured by a

text: masthead

text: transducer

text: containing an

text: anemometer

text: and

text: wind vane

text: that measures wind speed in

text: knots

text: and wind direction in degrees relative to the

text: heading

text: of the boat. Modern instrumentation can calculate the true wind velocity when the apparent wind and boat velocity and direction are input.

text: There are two different versions of the 25mm grenade: the 25×40mm low-velocity round developed for the XM25, and the 25×59mm high-velocity round developed for the XM109 and XM307.

text: Escape velocity is actually a speed (not a velocity) because it does not specify a direction: no matter what the direction of travel is, the object can escape the gravitational field (provided its path does not intersect the planet). The simplest way of deriving the formula for escape velocity is to use conservation of energy. Imagine that a spaceship of mass m is at a distance r from the center of mass of the planet, whose mass is M. Its initial speed is equal to its escape velocity,

text: In typical free-fall, the acceleration of gravity acts along the direction of an object's velocity, linearly increasing its speed as it falls toward the Earth, or slowing it down if it is moving away from the Earth.  In the case of an orbiting spacecraft, which has a velocity vector largely perpendicular to the force of gravity, gravitational acceleration does not produce a net change in the object's speed, but instead acts centripetally, to constantly "turn" the spacecraft's velocity as it moves around the Earth. Because the acceleration vector turns along with the velocity vector, they remain perpendicular to each other. Without this change in the direction of its velocity vector, the spacecraft would move in a straight line, leaving the Earth altogether.

text: In typical free-fall, the acceleration of gravity acts along the direction of an object's velocity, linearly increasing its

text: speed

text: as it falls toward the Earth, or slowing it down if it is moving away from the Earth.  In the case of an orbiting spacecraft, which has a velocity vector largely perpendicular to the force of gravity, gravitational acceleration does not produce a net change in the object's speed, but instead acts

text: centripetally

text: , to constantly "turn" the spacecraft's velocity as it moves around the Earth. Because the acceleration vector turns along with the velocity vector, they remain perpendicular to each other. Without this change in the direction of its velocity vector, the spacecraft would move in a straight line, leaving the Earth altogether.

text: for arbitrary constants  and . This is a solution in a non-viscous gas (compressible fluid) whose density, velocities and pressure goes to zero far from the origin. (Note this is not a solution to the Clay Millennium problem because that refers to incompressible fluids where  is a constant, neither does it deal with the uniqueness of the Navier–Stokes equations with respect to any turbulence properties.) It is also worth pointing out that the components of the velocity vector are exactly those from the Pythagorean quadruple parametrization. Other choices of density and pressure are possible with the same velocity field:

text: for arbitrary constants  and . This is a solution in a non-viscous gas (compressible fluid) whose density, velocities and pressure goes to zero far from the origin. (Note this is not a solution to the Clay Millennium problem because that refers to incompressible fluids where  is a constant, neither does it deal with the uniqueness of the Navier–Stokes equations with respect to any

text: turbulence

text: properties.) It is also worth pointing out that the components of the velocity vector are exactly those from the

text: Pythagorean quadruple

text: parametrization. Other choices of density and pressure are possible with the same velocity field:

text: For high velocities (or more precisely, at high Reynolds number) drag will vary as the square of velocity. Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half

text: For high velocities (or more precisely, at high

text: Reynolds number

text: ) drag will vary as the square of

text: velocity

text: . Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half

text: Instead of the standard low-velocity 40 x 46 mm grenade used by the M203 and M79 grenade launchers or the standard high-velocity 40 x 53 mm grenade used by the Mk 19, the EX 41 used a hybrid of the two developed by Indiana Ordnance.  High-velocity ammunition such as the M430 HEDP and M918 practice grenades were fitted to the low-velocity cartridge cases, in order to have a longer effective range with a lower recoil.  An optical sight of unknown manufacture was added to the top of the receiver to take advantage of the extended range of the ammunition.

text: Instead of the standard low-velocity

text: 40 x 46 mm grenade

text: used by the

text: and

text: grenade launchers or the standard high-velocity 40 x 53 mm grenade used by the Mk 19, the EX 41 used a hybrid of the two developed by Indiana Ordnance.  High-velocity ammunition such as the M430 HEDP and M918 practice grenades were fitted to the low-velocity cartridge cases, in order to have a longer effective range with a lower recoil.  An optical sight of unknown manufacture was added to the top of the receiver to take advantage of the extended range of the ammunition.

text: This basis is not orthonormal and it is difficult to use, but now the velocity vector can be changed to the fixed frame or to the moving frame with just a change of bases. For example, changing to the mobile frame:

text: .This speed is called the radial Doppler velocity because it gives only the radial variation of distance versus time between the radar and the target. The real speed and direction of motion has to be extracted by the process described below.

text: .This speed is called the radial Doppler velocity because it gives only the

text: radial

text: variation of distance versus time between the radar and the target. The real speed and direction of motion has to be extracted by the process described below.

text: The radial velocity of an object with respect to a given point is the rate of change of the distance between the object and the point. That is, the radial velocity is the component of the object's velocity that points in the direction of the radius connecting the object and the point. In astronomy, the point is usually taken to be the observer on Earth, so the radial velocity then denotes the speed with which the object moves away from or approaches the Earth.

text: The radial velocity of an object with respect to a given point is the rate of change of the distance between the object and the point. That is, the radial velocity is the component of the object's

text: velocity

text: that points in the direction of the radius connecting the object and the point. In astronomy, the point is usually taken to be the observer on Earth, so the radial velocity then denotes the speed with which the object moves away from or approaches the Earth.

text: In optical storage, constant angular velocity (CAV) is a qualifier for the rated speed of an optical disc drive, and may also be applied to the writing speed of recordable discs. A drive or disc operating in CAV mode maintains a constant angular velocity, contrasted with a constant linear velocity (CLV).

text: In

text: optical storage

text: , constant angular velocity (CAV) is a qualifier for the rated speed of an

text: optical disc drive

text: , and may also be applied to the writing speed of recordable

text: discs

text: . A drive or disc operating in CAV mode maintains a constant

text: angular velocity

text: , contrasted with a

text: constant linear velocity

text: (CLV).

text: which is simply the magnitude of the change in velocity. However, this relation does not hold in the general case: if, for instance, a constant, unidirectional acceleration is reversed after (t − t)/2 then the velocity difference is 0, but delta-v is the same as for the non-reversed thrust.

text: which is simply the magnitude of the

text: change in velocity

text: . However, this relation does not hold in the general case: if, for instance, a constant, unidirectional acceleration is reversed after (t − t)/2 then the velocity difference is 0, but delta-v is the same as for the non-reversed thrust.

text: We begin with relative motion in the classical, (or non-relativistic, or  the Newtonian approximation) that all speeds are much less than the speed of light.  This limit is associated with the Galilean transformation.  The figure shows a man on top of a train, at the back edge.  At 1:00 pm he begins to walk forward at a walking speed of 10 km/hr (kilometers per hour).  The train is moving at 40 km/hr.  The figure depicts the man and train at two different times: first, when the journey began, and also one hour later at 2:00 pm.  The figure suggests that the man is 50 km from the starting point after having traveled (by walking and by train) for one hour.  This, by definition, is 50 km/hour, which suggests that the prescription for calculating relative velocity in this fashion is to add the two velocities.

text: We begin with relative motion in the

text: classical

text: , (or non-

text: relativistic

text: , or  the

text: Newtonian approximation

text: ) that all speeds are much less than the speed of light.  This limit is associated with the

text: Galilean transformation

text: .  The figure shows a man on top of a train, at the back edge.  At 1:00 pm he begins to walk forward at a walking speed of 10 km/hr (kilometers per hour).  The train is moving at 40 km/hr.  The figure depicts the man and train at two different times: first, when the journey began, and also one hour later at 2:00 pm.  The figure suggests that the man is 50 km from the starting point after having traveled (by walking and by train) for one hour.  This, by definition, is 50 km/hour, which suggests that the prescription for calculating relative velocity in this fashion is to add the two velocities.

text: Though the Sprint GT Veloce's replacement—the 1750 GT Veloce—was introduced in 1967, production continued throughout the year and thirty final cars were completed in 1968. By then total Giulia Sprint GT Veloce production amounted to

text: Though the Sprint GT Veloce's replacement—the

text: 1750 GT Veloce

text: —was introduced in 1967, production continued throughout the year and thirty final cars were completed in 1968. By then total Giulia Sprint GT Veloce production amounted to

text: where  is the relative velocity between frames in the -direction,  is the speed of light, and

text: where  is the relative velocity between frames in the -direction,  is the

text: speed of light

text: , and

text: However, integrating this is often unnecessary if the burn duration is short. For example, as a vehicle falls towards periapsis in any orbit (closed or escape orbits) the velocity relative to the central body increases. Briefly burning the engine (an "impulsive burn") prograde at periapsis increases the velocity by the same increment as at any other time (). However, since the vehicle's kinetic energy is related to the square of its velocity, this increase in velocity has a non-linear effect on the vehicle's kinetic energy; leaving it with higher energy than if the burn were achieved at any other time.

text: However, integrating this is often unnecessary if the burn duration is short. For example, as a vehicle falls towards

text: periapsis

text: in any orbit (closed or escape orbits) the velocity relative to the central body increases. Briefly burning the engine (an "impulsive burn")

text: prograde

text: at periapsis increases the velocity by the same increment as at any other time (

text: ). However, since the vehicle's kinetic energy is related to the square of its velocity, this increase in velocity has a non-linear effect on the vehicle's kinetic energy; leaving it with higher energy than if the burn were achieved at any other time.

text: The reason for this is that the velocity for P-waves and S-waves is governed by both the different properties in the material which they travel through and the different mathematical relationships they share in each case. The three properties are: incompressibility (

text: The reason for this is that the velocity for P-waves and S-waves is governed by both the different properties in the material which they travel through and the different mathematical relationships they share in each case. The three properties are:

text: incompressibility

text: where v is the velocity of the source in the observer's rest frame, θ is the angle between the velocity vector and the observer-source direction measured in the reference frame of the source, and c is the speed of light. This can be simplified for the special cases of objects moving directly towards (θ = π) or away (θ = 0) from the observer, and for speeds much less than c.

text: where v is the velocity of the source in the observer's rest frame, θ is the angle between the velocity vector and the observer-source direction measured in the reference frame of the source, and c is the

text: speed of light

text: . This can be simplified for the special cases of objects moving directly towards (θ = π) or away (θ = 0) from the observer, and for speeds much less than c.

text: The set of all null vectors at an event of Minkowski space constitutes the light cone of that event. Given a timelike vector , there is a worldline of constant velocity associated with it, represented by a straight line in a Minkowski diagram.

text: The set of all null vectors at an event of Minkowski space constitutes the

text: light cone

text: of that event. Given a timelike vector , there is a

text: worldline

text: of constant velocity associated with it, represented by a straight line in a Minkowski diagram.

text: A velocity filter removes interfering signals by exploiting the difference between the travelling velocities of desired seismic waveform and undesired interfering signals.

text: A velocity filter removes

text: interfering

text: signals by exploiting the difference between the travelling velocities of desired

text: seismic wave

text: form and undesired interfering signals.

text: If each round represents 1 second and each square represents 1 metre, the vector representing each move is a velocity vector in metres per second. The four neighbour rule allows accelerations up to 1 metre per second squared, and the eight neighbours rule allows accelerations up to √2 metres per second squared. (If each square represents 10 metres instead, the size of the track and the maximum acceleration will be more realistic.)

text: If each round represents 1 second and each square represents 1 metre, the vector representing each move is a

text: velocity vector

text: in metres per second. The four neighbour rule allows

text: acceleration

text: s up to 1 metre per second squared, and the eight neighbours rule allows accelerations up to √2 metres per second squared. (If each square represents 10 metres instead, the size of the track and the maximum acceleration will be more realistic.)

text: For any object moving through space, the velocity vector is tangent to the trajectory. If

text: For any object moving through space, the velocity vector is

text: tangent

text: to the trajectory. If

text: Since the thermal velocity is only a "typical" velocity, a number of different definitions can be and are used.

text: Fully legitimate expressions for "the velocity of A relative to B" include "the velocity of A with respect to B" and "the velocity of A in the coordinate system where B is always at rest".  The violation of special relativity occurs because this equation for relative velocity falsely predicts that different observers will measure different speeds when observing the motion of light.

text: Fully legitimate expressions for "the velocity of A relative to B" include "the velocity of A with respect to B" and "the velocity of A in the coordinate system where B is always at rest".  The

text: violation of special relativity

text: occurs because this equation for relative velocity falsely predicts that different observers will measure different speeds when observing the motion of light.

text: The modern method consists of numerical integration in 3-dimensional space. One starts with a high accuracy value for the position (x, y, z) and the velocity (v, v, v) for each of the bodies involved. When also the mass of each body is known, the acceleration (a, a, a) can be calculated from Newton's Law of Gravitation. Each body attracts each other body, the total acceleration being the sum of all these attractions. Next one chooses a small time-step Δt and applies Newton's Second Law of Motion. The acceleration multiplied with Δt gives a correction to the velocity. The velocity multiplied with Δt gives a correction to the position. This procedure is repeated for all other bodies.

text: The modern method consists of numerical integration in 3-dimensional space. One starts with a high accuracy value for the position (x, y, z) and the velocity (v, v, v) for each of the bodies involved. When also the mass of each body is known, the acceleration (a, a, a) can be calculated from

text: Newton's Law of Gravitation

text: . Each body attracts each other body, the total acceleration being the sum of all these attractions. Next one chooses a small time-step Δt and applies

text: Newton's Second Law of Motion

text: . The acceleration multiplied with Δt gives a correction to the velocity. The velocity multiplied with Δt gives a correction to the position. This procedure is repeated for all other bodies.

text: Barycentric Coordinate Time (TCB) is the analog of TCG, used for calculations relating to the solar system beyond Earth orbit.  TCG is defined by a different reference frame from TCB, such that they are not linearly related.  Over the long term, TCG ticks more slowly than TCB by about 1.6 × 10 (about 0.5 seconds per year).  In addition there are periodic variations, as Earth moves within the Solar system.  When the Earth is at perihelion in January, TCG ticks even more slowly than it does on average, due to gravitational time dilation from being deeper in the Sun's gravity well and also velocity time dilation from moving faster relative to the Sun.  At aphelion in July the opposite holds, with TCG ticking faster than it does on average.

text: Barycentric Coordinate Time

text: (TCB) is the analog of TCG, used for calculations relating to the solar system beyond Earth orbit.  TCG is defined by a different

text: reference frame

text: from TCB, such that they are not linearly related.  Over the long term, TCG ticks more slowly than TCB by about 1.6 × 10 (about 0.5 seconds per year).  In addition there are periodic variations, as Earth moves within the Solar system.  When the Earth is at

text: perihelion

text: in January, TCG ticks even more slowly than it does on average, due to gravitational time dilation from being deeper in the

text: Sun

text: 's gravity well and also

text: velocity time dilation

text: from moving faster relative to the Sun.  At

text: aphelion

text: in July the opposite holds, with TCG ticking faster than it does on average.

text: One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the index finger "V", the middle finger "B", and the thumb "F" with your right hand. When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also right hand rule.

text: One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the

text: index finger

text: "V", the

text: middle finger

text: "B", and the

text: thumb

text: "F" with your right hand. When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also

text: right hand rule

text: In many cases, the discharge and normal depth for a mild slope will not initially be known.  The discharge can be calculated through an iterative process.  First, a discharge must be assumed so that the normal depth can be calculated. The following equation solves for discharge in terms of velocity and area.  Normal depth is a function of both velocity and area and can therefore be solved using this equation.

text: Often expressed in cm/s. This value is inversely related to the total cross-sectional area of the blood vessel and also differs per cross-section, because in normal condition the blood flow has laminar characteristics. For this reason the blood flow velocity is the fastest in the middle of the vessel and slowest at the vessel wall. In most cases the mean velocity is used. There are many ways to measure blood flow velocity, like videocapillary microscoping with frame-to-frame analysis, or laser Doppler anemometry.Blood velocities in arteries are higher during systole than during diastole. One parameter to quantify this difference is the pulsatility index (PI), which is equal to the difference between the peak systolic velocity and the minimum diastolic velocity divided by the mean velocity during the cardiac cycle. This value decreases with distance from the heart.

text: Often expressed in cm/s. This value is inversely related to the total cross-sectional area of the blood vessel and also differs per cross-section, because in normal condition the blood flow has

text: laminar characteristics

text: . For this reason the blood flow velocity is the fastest in the middle of the vessel and slowest at the vessel wall. In most cases the mean velocity is used. There are many ways to measure blood flow velocity, like videocapillary microscoping with frame-to-frame analysis, or

text: laser Doppler anemometry

text: .Blood velocities in

text: arteries

text: are higher during

text: systole

text: than during

text: diastole

text: . One parameter to quantify this difference is the pulsatility index (PI), which is equal to the difference between the peak systolic velocity and the minimum diastolic velocity divided by the mean velocity during the

text: cardiac cycle

text: . This value decreases with distance from the heart.

text: , and the velocity difference, or approaching rate,

text: With this form for the displacement, the velocity now is found. The time derivative of the displacement vector is the velocity vector. In general, the derivative of a vector is a vector made up of components each of which is the derivative of the corresponding component of the original vector. Thus, in this case, the velocity vector is:

text: As required by the experimentally proven equivalence between Einstein synchronization and slow clock-transport synchronization, which requires knowledge of time dilation of moving clocks, the same non-standard synchronisations must also affect time dilation. It was indeed pointed out that time dilation of moving clocks depends on the convention for the one-way velocities used in its formula. That is, time dilation can be measured by synchronizing two stationary clocks A and B, and then the readings of a moving clock C are compared with them. Changing the convention of synchronization for A and B makes the value for time dilation (like the one-way speed of light) directional dependent. The same conventionality also applies to the influence of time dilation on the Doppler effect. Only when time dilation is measured on closed paths, it is not conventional and can unequivocally be measured like the two-way speed of light. Time dilation on closed paths was measured in the Hafele–Keating experiment and in experiments on the Time dilation of moving particles such as Bailey et al. (1977).Thus the so-called twin paradox occurs in all transformations preserving the constancy of the two-way speed of light.

text: As required by the experimentally proven equivalence between Einstein synchronization and slow clock-transport synchronization, which requires knowledge of

text: time dilation

text: of moving clocks, the same non-standard synchronisations must also affect time dilation. It was indeed pointed out that time dilation of moving clocks depends on the convention for the one-way velocities used in its formula. That is, time dilation can be measured by synchronizing two stationary clocks A and B, and then the readings of a moving clock C are compared with them. Changing the convention of synchronization for A and B makes the value for time dilation (like the one-way speed of light) directional dependent. The same conventionality also applies to the influence of time dilation on the

text: Doppler effect

text: . Only when time dilation is measured on closed paths, it is not conventional and can unequivocally be measured like the two-way speed of light. Time dilation on closed paths was measured in the

text: Hafele–Keating experiment

text: and in experiments on the

text: Time dilation of moving particles

text: such as Bailey et al. (1977).Thus the so-called

text: twin paradox

text: occurs in all transformations preserving the constancy of the two-way speed of light.

text: be a Frenet–Serret orthonormal basis which consists of a tangential unit vector, a normal unit vector, and a binormal unit vector to the streamline, respectively.Since a streamline is a curve that is tangent to the velocity vector of the flow, the left-handed side of the above equation, the convective derivative of velocity, can be described as follows:

text: be a Frenet–Serret

text: orthonormal basis

text: which consists of a tangential unit vector, a normal unit vector, and a binormal unit vector to the streamline, respectively.Since a streamline is a curve that is tangent to the velocity vector of the flow, the left-handed side of the above equation, the

text: convective derivative

text: of velocity, can be described as follows:

text: are then calculated from the positions and predicted velocities.

text: The company was founded by John Goodman  (born Johannes Gütgemann and later known as John Taylor before formally changing his name to Goodman) and William Gue, as "Taylor, Gue Ltd." in 1905. Its first motorcycle was the Veloce. Later that year, John Taylor set up Veloce Limited, to produce cycles and related products and services. Veloce Ltd initially produced four-stroke motorcycles, first with Belgian 'Kelecom' engines, then an F-head design of their own, with an integral two-speed gearbox.

text: The company was founded by

text: John Goodman

text: (born Johannes Gütgemann and later known as John Taylor before formally changing his name to Goodman) and William Gue, as "Taylor, Gue Ltd." in 1905. Its first motorcycle was the Veloce. Later that year, John Taylor set up Veloce Limited, to produce cycles and related products and services. Veloce Ltd initially produced four-stroke motorcycles, first with

text: Belgian

text: Kelecom

text: ' engines, then an

text: F-head

text: design of their own, with an integral two-speed gearbox.

text: The drift velocity then determines the electric current density and its relationship to E and is independent of the collisions.  Drude calculated the average drift velocity from p = −eEτ where p is the average momentum, −e is the charge of the electron and τ is the average time between the collisions.   Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field; this leads to Ohm's law.

text: The

text: drift velocity

text: then determines the electric

text: current density

text: and its relationship to E and is independent of the collisions.  Drude calculated the average drift velocity from p = −eEτ where p is the average

text: momentum

text: , −e is the charge of the electron and τ is the average time between the collisions.   Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field; this leads to Ohm's law.

text: For two gases, the difference between velocities,

text: After the Cartesian velocity moment is calculated, it can be normalised by

text: The above equation illustrates that the Lorentz force is the sum of two vectors.  One is the cross product of the velocity and magnetic field vectors.  Based on the properties of the cross product, this produces a vector that is perpendicular to both the velocity and magnetic field vectors.  The other vector is in the same direction as the electric field.  The sum of these two vectors is the Lorentz force.

text: The above equation illustrates that the Lorentz force is the sum of two vectors.  One is the

text: cross product

text: of the velocity and magnetic field vectors.  Based on the properties of the cross product, this produces a vector that is perpendicular to both the velocity and magnetic field vectors.  The other vector is in the same direction as the electric field.  The sum of these two vectors is the Lorentz force.

text: where the velocity,  is the velocity of the body relative to the observer,

text: A signal on a transmission line can become distorted even if the line constants, and the resulting transmission function, are all perfectly linear.  This happens in two ways: firstly, the attenuation of the line can vary with frequency which results in a change to the shape of a pulse transmitted down the line.  Secondly, and usually more problematically, distortion is caused by a frequency dependence on phase velocity of the transmitted signal frequency components.  If different frequency components of the signal are transmitted at different velocities the signal becomes "smeared out" in space and time, a form of distortion called dispersion.

text: A signal on a transmission line can become distorted even if the line constants, and the resulting

text: transmission function

text: , are all perfectly linear.  This happens in two ways: firstly, the attenuation of the line can vary with frequency which results in a change to the shape of a pulse transmitted down the line.  Secondly, and usually more problematically, distortion is caused by a frequency dependence on

text: phase velocity

text: of the transmitted signal frequency components.  If different frequency components of the signal are transmitted at different velocities the signal becomes "smeared out" in space and time, a form of distortion called

text: dispersion

text: 4,557 of 1300 Junior were made and 4,848 of 1600 Junior. 16,320 of 2000 Spider Veloce were made and 22,059 of 2000 Spider Veloce US version. 4,027 1750 Spider Veloce were made.

text: Evidence of rupture propagation at velocities greater than S-wave velocities expected for the surrounding crust have been observed for several large earthquakes associated with strike-slip faults. During strike-slip, the main component of rupture propagation will be horizontal, in the direction of displacement, as a Mode II (in-plane) shear crack. This contrasts with a dip-slip rupture where the main direction of rupture propagation will be perpendicular to the displacement, like a Mode III (anti-plane) shear crack. Theoretical studies have shown that Mode III cracks are limited to the shear wave velocity but that Mode II cracks can propagate between the S and P-wave velocities  and this may explain why supershear earthquakes have not been observed on dip-slip faults.

text: Evidence of rupture propagation at velocities greater than S-wave velocities expected for the surrounding crust have been observed for several large earthquakes associated with

text: strike-slip faults

text: . During strike-slip, the main component of rupture propagation will be horizontal, in the direction of displacement, as a

text: Mode II

text: (in-plane) shear crack. This contrasts with a dip-slip rupture where the main direction of rupture propagation will be perpendicular to the displacement, like a

text: Mode III

text: (anti-plane) shear crack. Theoretical studies have shown that Mode III cracks are limited to the shear wave velocity but that Mode II cracks can propagate between the S and P-wave velocities  and this may explain why supershear earthquakes have not been observed on dip-slip faults.

text: An alternative characterization of Euclidean vectors, especially in physics, describes them as lists of quantities which behave in a certain way under a coordinate transformation. A contravariant vector is required to have components that "transform opposite to the basis" under changes of basis. The vector itself does not change when the basis is transformed; instead, the components of the vector make a change that cancels the change in the basis. In other words, if the reference axes (and the basis derived from it) were rotated in one direction, the component representation of the vector would rotate in the opposite way to generate the same final vector. Similarly, if the reference axes were stretched in one direction, the components of the vector would reduce in an exactly compensating way. Mathematically, if the basis undergoes a transformation described by an invertible matrix M, so that a coordinate vector x is transformed to , then a contravariant vector v must be similarly transformed via . This important requirement is what distinguishes a contravariant vector from any other triple of physically meaningful quantities. For example, if v consists of the x, y, and z-components of velocity, then v is a contravariant vector: if the coordinates of space are stretched, rotated, or twisted, then the components of the velocity transform in the same way. On the other hand, for instance, a triple consisting of the length, width, and height of a rectangular box could make up the three components of an abstract vector, but this vector would not be contravariant, since rotating the box does not change the box's length, width, and height. Examples of contravariant vectors include displacement, velocity, electric field, momentum, force, and acceleration.

text: An alternative characterization of Euclidean vectors, especially in physics, describes them as lists of quantities which behave in a certain way under a

text: coordinate transformation

text: . A contravariant vector is required to have components that "transform opposite to the basis" under changes of

text: basis

text: . The vector itself does not change when the basis is transformed; instead, the components of the vector make a change that cancels the change in the basis. In other words, if the reference axes (and the basis derived from it) were rotated in one direction, the component representation of the vector would rotate in the opposite way to generate the same final vector. Similarly, if the reference axes were stretched in one direction, the components of the vector would reduce in an exactly compensating way. Mathematically, if the basis undergoes a transformation described by an

text: invertible matrix

text: M, so that a coordinate vector x is transformed to , then a contravariant vector v must be similarly transformed via . This important requirement is what distinguishes a contravariant vector from any other triple of physically meaningful quantities. For example, if v consists of the x, y, and z-components of

text: velocity

text: , then v is a contravariant vector: if the coordinates of space are stretched, rotated, or twisted, then the components of the velocity transform in the same way. On the other hand, for instance, a triple consisting of the length, width, and height of a rectangular box could make up the three components of an abstract

text: vector

text: , but this vector would not be contravariant, since rotating the box does not change the box's length, width, and height. Examples of contravariant vectors include

text: displacement

text: velocity

text: electric field

text: momentum

text: force

text: , and

text: acceleration

text: Its existence was predicted in 1902 independently and almost simultaneously by the American electrical engineer Arthur Edwin Kennelly (1861–1939) and the British physicist Oliver Heaviside (1850–1925). However, it was not until 1924 that its existence was shown by British scientist Edward V. Appleton, for which he received the 1947 Nobel Prize in Physics. Physicists resisted the idea of the reflecting layer for one very good reason; it would require total internal reflection, which in turn would require that the speed of light ("c") in the ionosphere would be greater than in the atmosphere below it. Since the latter speed is essentially the same as the speed of light in vacuum, scientists were unwilling to believe the speed in the ionosphere could be higher. Nevertheless, Marconi had received signals in Newfoundland that were broadcast in England, so clearly there must be some mechanism allowing the transmission to reach that far. The paradox was resolved by the discovery that there were two velocities of light, the phase velocity and the group velocity. The phase velocity can in fact be greater than c, but the group velocity, being capable of transmitting information, cannot, by special relativity, be greater than c. The phase velocity for radio waves in the ionosphere is indeed greater than c, and that makes total internal reflection possible, and so the ionosphere can reflect radio waves. The geometric mean of the phase velocity and the group velocity cannot exceed c, so when the phase velocity goes above c, the group velocity must go below it. In 1925, Americans Gregory Breit and Merle A. Tuve first mapped its variations in altitude. The ITU standard model of absorption and reflection of radio waves by the Heaviside Layer was developed by the British Ionospheric physicist Louis Muggleton in the 1970s.

text: Its existence was predicted in 1902 independently and almost simultaneously by the American electrical engineer

text: Arthur Edwin Kennelly

text: (1861–1939) and the British physicist

text: Oliver Heaviside

text: (1850–1925). However, it was not until 1924 that its existence was shown by British scientist

text: Edward V. Appleton

text: , for which he received the 1947

text: Nobel Prize in Physics

text: . Physicists resisted the idea of the reflecting layer for one very good reason; it would require

text: total internal reflection

text: , which in turn would require that the speed of light (

text: "c"

text: ) in the ionosphere would be greater than in the atmosphere below it. Since the latter speed is essentially the same as the speed of light in vacuum, scientists were unwilling to believe the speed in the ionosphere could be higher. Nevertheless,

text: Marconi

text: had received signals in Newfoundland that were broadcast in England, so clearly there must be some mechanism allowing the transmission to reach that far. The paradox was resolved by the discovery that there were two velocities of light, the

text: phase velocity

text: and the

text: group velocity

text: . The phase velocity can in fact be greater than c, but the group velocity, being capable of transmitting information, cannot, by

text: special relativity

text: , be greater than c. The phase velocity for radio waves in the ionosphere is indeed greater than c, and that makes total internal reflection possible, and so the ionosphere can reflect radio waves. The geometric mean of the phase velocity and the group velocity cannot exceed c, so when the phase velocity goes above c, the group velocity must go below it. In 1925, Americans

text: Gregory Breit

text: and

text: Merle A. Tuve

text: first mapped its variations in altitude. The

text: ITU

text: standard model of absorption and reflection of radio waves by the Heaviside Layer was developed by the British Ionospheric physicist

text: Louis Muggleton

text: in the 1970s.

text: The objective of the approach is to gradually accelerate to a maximum controlled speed at takeoff. The most important factor for the distance traveled by an object is its velocity at takeoff – both the speed and angle. Elite jumpers usually leave the ground at an angle of twenty degrees or less; therefore, it is more beneficial for a jumper to focus on the speed component of the jump. The greater the speed at takeoff, the longer the trajectory of the center of mass will be. The importance of a takeoff speed is a factor in the success of sprinters in this event.

text: The objective of the approach is to gradually accelerate to a maximum controlled speed at takeoff. The most important factor for the distance traveled by an object is its

text: velocity

text: at takeoff – both the speed and angle. Elite jumpers usually leave the ground at an angle of twenty degrees or less; therefore, it is more beneficial for a jumper to focus on the speed component of the jump. The greater the speed at takeoff, the longer the trajectory of the

text: center of mass

text: will be. The importance of a takeoff speed is a factor in the success of sprinters in this event.

text: In Germany, the Autobahn-Richtgeschwindigkeits-Verordnung (Directive on Reference Speed on Motorways), introduced in 1974, recommends a speed of no more than  for autobahns and similar roads, whose lanes are separated by a median or which have at least two lanes per direction, provided there are no traffic signs posting a lower speed limit.

text: In Germany, the Autobahn-Richtgeschwindigkeits-Verordnung (Directive on Reference Speed on Motorways), introduced in 1974, recommends a speed of no more than  for autobahns and similar roads, whose lanes are separated by a median or which have at least two lanes per direction, provided there are no

text: traffic signs

text: posting a lower speed limit.

text: Except for low-power applications, turbine blades are arranged in multiple stages in series, called compounding, which greatly improves efficiency at low speeds. A reaction stage is a row of fixed nozzles followed by a row of moving nozzles. Multiple reaction stages divide the pressure drop between the steam inlet and exhaust into numerous small drops, resulting in a pressure-compounded turbine. Impulse stages may be either pressure-compounded, velocity-compounded, or pressure-velocity compounded. A pressure-compounded impulse stage is a row of fixed nozzles followed by a row of moving blades, with multiple stages for compounding. This is also known as a Rateau turbine, after its inventor. A velocity-compounded impulse stage (invented by Curtis and also called a "Curtis wheel") is a row of fixed nozzles followed by two or more rows of moving blades alternating with rows of fixed blades. This divides the velocity drop across the stage into several smaller drops. A series of velocity-compounded impulse stages is called a pressure-velocity compounded turbine.

text: Except for low-power applications, turbine blades are arranged in multiple stages in series, called

text: compounding

text: , which greatly improves

text: efficiency

text: at low speeds. A reaction stage is a row of fixed nozzles followed by a row of moving nozzles. Multiple reaction stages divide the pressure drop between the steam inlet and exhaust into numerous small drops, resulting in a pressure-compounded turbine. Impulse stages may be either pressure-compounded, velocity-compounded, or pressure-velocity compounded. A pressure-compounded impulse stage is a row of fixed nozzles followed by a row of moving blades, with multiple stages for compounding. This is also known as a Rateau turbine, after its inventor. A velocity-compounded impulse stage (invented by Curtis and also called a "Curtis wheel") is a row of fixed nozzles followed by two or more rows of moving blades alternating with rows of fixed blades. This divides the velocity drop across the stage into several smaller drops. A series of velocity-compounded impulse stages is called a pressure-velocity compounded turbine.

text: Its operation relies on the different properties of gases flowing at subsonic and supersonic speeds. The speed of a subsonic flow of gas will increase if the pipe carrying it narrows because the mass flow rate is constant. The gas flow through a de Laval nozzle is isentropic (gas entropy is nearly constant). In a subsonic flow the gas is compressible, and sound will propagate through it. At the "throat", where the cross-sectional area is at its minimum, the gas velocity locally becomes sonic (Mach number = 1.0), a condition called choked flow. As the nozzle cross-sectional area increases, the gas begins to expand, and the gas flow increases to supersonic velocities, where a sound wave will not propagate backwards through the gas as viewed in the frame of reference of the nozzle (Mach number > 1.0).

text: Its operation relies on the different properties of gases flowing at

text: subsonic

text: and

text: supersonic

text: speeds. The speed of a subsonic flow of gas will increase if the pipe carrying it narrows because the

text: mass flow rate

text: is constant. The gas flow through a de Laval nozzle is

text: isentropic

text: (gas

text: entropy

text: is nearly constant). In a subsonic flow the gas is compressible, and

text: sound

text: will propagate through it. At the "throat", where the cross-sectional area is at its minimum, the gas velocity locally becomes sonic (Mach number = 1.0), a condition called

text: choked flow

text: . As the nozzle cross-sectional area increases, the gas begins to expand, and the gas flow increases to supersonic velocities, where a sound wave will not propagate backwards through the gas as viewed in the frame of reference of the nozzle (

text: Mach number

text: > 1.0).

text: While drives are burning DVD+R, DVD+RW and all Blu-ray formats, they do not require any such error correcting recovery as the recorder is able to place the new data exactly on the end of the suspended write effectively producing a continuous track (this is what the DVD+ technology achieved).  Although later interfaces were able to stream data at the required speed, many drives now write in a 'zoned constant linear velocity'.  This means that the drive has to temporarily suspend the write operation while it changes speed and then recommence it once the new speed is attained.  This is handled in the same manner as a buffer underrun.

text: While drives are burning DVD+R, DVD+RW and all Blu-ray formats, they do not require any such error correcting recovery as the recorder is able to place the new data exactly on the end of the suspended write effectively producing a continuous track (this is what the DVD+ technology achieved).  Although later interfaces were able to stream data at the required speed, many drives now write in a '

text: zoned constant linear velocity

text: '.  This means that the drive has to temporarily suspend the write operation while it changes speed and then recommence it once the new speed is attained.  This is handled in the same manner as a buffer underrun.

text: V0 is difficult to measure, so a second concept has been developed in ballistic testing called V50. This is the velocity at which 50 percent of the shots go through and 50 percent are stopped by the armor. US military standards define a commonly used procedure for this test. The goal is to get three shots that penetrate and a second group of three shots that are stopped by the armor all within a specified velocity range. It is possible, and desirable to have a penetration velocity lower than a stop velocity.  These three stops and three penetrations can then be used to calculate a V50 velocity.

text: The definition of angular momentum for a point particle is a pseudovector r×p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector p = mv. This definition can be applied to each point in continua like solids or fluids, or physical fields. Unlike momentum, angular momentum does depend on where the origin is chosen, since the particle's position is measured from it. The angular momentum of an object can also be connected to the angular velocity ω of the object (how fast it rotates about an axis) via the moment of inertia I (which depends on the shape and distribution of mass about the axis of rotation). However, while ω always points in the direction of the rotation axis, the angular momentum L may point in a different direction depending on how the mass is distributed.

text: The definition of angular momentum for a

text: point particle

text: is a

text: pseudovector

text: r×p, the

text: cross product

text: of the particle's

text: position vector

text: r (relative to some origin) and its

text: momentum vector

text: p = mv. This definition can be applied to each point in

text: continua

text: like solids or fluids, or

text: physical fields

text: . Unlike momentum, angular momentum does depend on where the origin is chosen, since the particle's position is measured from it. The angular momentum of an object can also be connected to the

text: angular velocity

text: ω of the object (how fast it rotates about an axis) via the

text: moment of inertia

text: I (which depends on the shape and distribution of mass about the axis of rotation). However, while ω always points in the direction of the rotation axis, the angular momentum L may point in a different direction depending on how the mass is distributed.

text: The gust angular velocity components (p,q,r) are defined as the variations of the linear velocity components along the different vehicle axes,

text: Wally's primary superpower is his ability to control the speed with which his body vibrates and to move at super speed, which he uses primarily to run at super-human velocities. This super speed is derived from his connection to the Speed Force: a vaguely defined extra-dimensional energy force from which most speedster heroes draw their powers. Wally is faster than Barry Allen.

text: Wally's primary

text: superpower

text: is his ability to control the speed with which his body vibrates and to move at super speed, which he uses primarily to run at super-human velocities. This super speed is derived from his connection to the

text: Speed Force

text: : a vaguely defined extra-dimensional energy force from which most speedster heroes draw their powers. Wally is faster than

text: Barry Allen

text: is the average fluid velocity.

text: is the average fluid velocity.

text: Mass-averaged velocity is widely used concept in chemical kinetics.

text: Mass-averaged velocity is widely used concept in

text: chemical kinetics

text: When velocity is constant, the total distance traveled over the given time interval can be computed by multiplying velocity and time.  For example, travelling a steady 50 mph for 3 hours results in a total distance of 150 miles.  In the diagram on the left, when constant velocity and time are graphed, these two values form a rectangle with height equal to the velocity and width equal to the time elapsed.  Therefore, the product of velocity and time also calculates the rectangular area under the (constant) velocity curve.  This connection between the area under a curve and distance traveled can be extended to any irregularly shaped region exhibiting a fluctuating velocity over a given time period. If  in the diagram on the right represents speed as it varies over time, the distance traveled (between the times represented by  and ) is the area of the shaded region .

text: The drift velocity is the average velocity that a particle, such as an electron, attains in a material due to an electric field. It can also be referred to as axial drift velocity. In general, an electron will propagate randomly in a conductor at the Fermi velocity. An applied electric field will give this random motion a small net flow velocity in one direction.

text: The drift velocity is the

text: average velocity

text: that a particle, such as an

text: electron

text: , attains in a material due to an

text: electric field

text: . It can also be referred to as axial drift velocity. In general, an electron will propagate randomly in a

text: conductor

text: at the

text: Fermi velocity

text: . An applied electric field will give this random motion a small net flow velocity in one direction.

text: are predicted and the forces calculated, before producing a corrected form of the velocities.

text: Projections into the future can differ radically for different models of dark energy. For a cosmological constant, or any other model that predicts that the acceleration will continue indefinitely, the ultimate result will be that galaxies outside the Local Group will have a line-of-sight velocity that continually increases with time, eventually far exceeding the speed of light. This is not a violation of special relativity because the notion of "velocity" used here is different from that of velocity in a local  inertial frame of reference, which is still constrained to be less than the speed of light for any massive object (see Uses of the proper distance for a discussion of the subtleties of defining any notion of relative velocity in cosmology). Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually. However, because of the accelerating expansion, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future because the light never reaches a point where its "peculiar velocity" toward us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in  Uses of the proper distance). Assuming the dark energy is constant (a cosmological constant), the current distance to this cosmological event horizon is about 16 billion light years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event were less than 16 billion light years away, but the signal would never reach us if the event were more than 16 billion light years away.

text: Projections into the future can differ radically for different models of dark energy. For a cosmological constant, or any other model that predicts that the acceleration will continue indefinitely, the ultimate result will be that galaxies outside the

text: Local Group

text: will have a

text: line-of-sight velocity

text: that continually increases with time, eventually far exceeding the speed of light. This is not a violation of

text: special relativity

text: because the notion of "velocity" used here is different from that of velocity in a local

text: inertial frame of reference

text: , which is still constrained to be less than the speed of light for any massive object (see

text: Uses of the proper distance

text: for a discussion of the subtleties of defining any notion of relative velocity in cosmology). Because the

text: Hubble parameter

text: is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually. However, because of the accelerating expansion, it is projected that most galaxies will eventually cross a type of cosmological

text: event horizon

text: where any light they emit past that point will never be able to reach us at any time in the infinite future because the light never reaches a point where its "peculiar velocity" toward us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in

text: Uses of the proper distance

text: ). Assuming the dark energy is constant (a

text: cosmological constant

text: ), the current distance to this cosmological event horizon is about 16 billion light years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event were less than 16 billion light years away, but the signal would never reach us if the event were more than 16 billion light years away.

text: The relationship between the density of a material and the velocity of a P wave moving through the material was noted when research was conducted on waves in different materials. In the experiment, a pulse of voltage is applied to a circular plate of polarized barium titanate ceramic (the transducer) which is attached to the end of the material sample. The added voltage creates vibrations in the sample. Those vibrations travel through the sample to a second transducer on the other end. The vibrations are then converted into an electrical wave which is viewed on an oscilloscope to determine the travel time. The velocity is the lender of the damper decided by the wave's travel time. The resulting relationship between the density of the material and the discovered velocity is known as Birch's law.

text: The relationship between the density of a material and the velocity of a

text: P wave

text: moving through the material was noted when research was conducted on waves in different materials. In the experiment, a pulse of voltage is applied to a circular plate of polarized barium titanate ceramic (the transducer) which is attached to the end of the material sample. The added voltage creates vibrations in the sample. Those vibrations travel through the sample to a second transducer on the other end. The vibrations are then converted into an electrical wave which is viewed on an oscilloscope to determine the travel time. The velocity is the lender of the damper decided by the wave's travel time. The resulting relationship between the density of the material and the discovered velocity is known as Birch's law.

text: (delta v) is the integration over time of the magnitude of the acceleration produced by using the rocket engine (what would be the actual acceleration if external forces were absent). In free space, for the case of acceleration in the direction of the velocity, this is the increase of the speed. In the case of an acceleration in opposite direction (deceleration) it is the decrease of the speed. Of course gravity and drag also accelerate the vehicle, and they can add or subtract to the change in velocity experienced by the vehicle. Hence delta-v is not usually the actual change in speed or velocity of the vehicle.

text: delta v

text: ) is the integration over time of the magnitude of the acceleration produced by using the rocket engine (what would be the actual acceleration if external forces were absent). In free space, for the case of acceleration in the direction of the velocity, this is the increase of the speed. In the case of an acceleration in opposite direction (deceleration) it is the decrease of the speed. Of course gravity and drag also accelerate the vehicle, and they can add or subtract to the change in velocity experienced by the vehicle. Hence delta-v is not usually the actual change in speed or velocity of the vehicle.

text: , and with respect to the velocity

text: , and with respect to the velocity

text: The tropical cyclones are internationally classified with these depending on their maximum wind speed or peak wind velocities (V) as follows:

text: Each negative logic selector bail that is displaced by the interposer in turn pulls a latch interposer and link which causes a selector latch near the cycle shaft to be pulled away from the latch bail. The latches pulled away in this manner are disengaged for the rest of the cycle, while the remaining latches take part in character selection, hence the term "negative logic". The minus five selector bail pulls an interposer and link which causes a latch to disengage from a cam, allowing it to move an additional input into the whiffletree that subtracts five units of rotation from any negative logic inputs. An additional "low velocity" selector latch is also engaged by certain keys, such as '.' and '_', which require a reduced striking force so as not to cut the paper; this selector latch engages the low velocity control cam follower, which pulls the low velocity cable connected to the cam in the carrier, causing the low velocity lobe to be used instead of the usual high velocity lobe. Additionally, punctuation marks are deliberately placed about the ball so the maximum amount of energy is used to position the element prior to striking, further reducing the impact.

text: By adjusting the window where the Doppler shift is calculated, it is possible to measure the relative velocity between the instrument and the bottom. This feature is referred to as bottom-track. The process has two parts; first identify the position of the bottom from the acoustic echo, then calculating the velocity from a window centered around the bottom position.  When an ADCP is mounted on a moving ship, the bottom track velocity may be subtracted from the measured water velocity.  The result is the net current profile. Bottom track provides the foundation for surveys of the water currents in coastal areas.  In deep water where the acoustic signals cannot reach the bottom, the ship velocity is estimated from a more complex combination of velocity and heading information from GPS, gyro, etc.

text: By adjusting the window where the Doppler shift is calculated, it is possible to measure the relative velocity between the instrument and the bottom. This feature is referred to as bottom-track. The process has two parts; first identify the position of the bottom from the acoustic echo, then calculating the velocity from a window centered around the bottom position.  When an ADCP is mounted on a moving ship, the bottom track velocity may be subtracted from the measured water velocity.  The result is the net current profile. Bottom track provides the foundation for surveys of the water currents in coastal areas.  In deep water where the acoustic signals cannot reach the bottom, the ship velocity is estimated from a more complex combination of velocity and heading information from

text: GPS

text: gyro

text: , etc.

text: In elastodynamics, Love waves, named after Augustus Edward Hough Love, are horizontally polarized surface waves. The Love wave is a result of the interference of many shear waves (S–waves) guided by an elastic layer, which is welded to an elastic half space on one side while bordering a vacuum on the other side. In seismology, Love waves (also known as Q waves (Quer: German for lateral)) are surface seismic waves that cause horizontal shifting of the Earth during an earthquake. Augustus Edward Hough Love predicted the existence of Love waves mathematically in 1911.  They form a distinct class, different from other types of seismic waves, such as P-waves and S-waves (both body waves), or Rayleigh waves (another type of surface wave).  Love waves travel with a lower velocity than P- or S- waves, but faster than Rayleigh waves. These waves are observed only when there is a low velocity layer overlying a high velocity layer/ sub–layers.

text: In

text: elastodynamics

text: , Love waves, named after

text: Augustus Edward Hough Love

text: , are horizontally

text: polarized

text: surface wave

text: s. The Love wave is a result of the

text: interference

text: of many

text: shear wave

text: s (S–waves) guided by an elastic layer, which is welded to an elastic half space on one side while bordering a vacuum on the other side. In

text: seismology

text: , Love waves (also known as Q waves (Quer: German for lateral)) are

text: surface

text: seismic wave

text: s that cause horizontal shifting of the Earth during an

text: earthquake

text: . Augustus Edward Hough Love predicted the existence of Love waves mathematically in 1911.  They form a distinct class, different from other types of

text: seismic wave

text: s, such as

text: P-wave

text: s and

text: S-wave

text: s (both

text: body wave

text: s), or

text: Rayleigh waves

text: (another type of surface wave).  Love waves travel with a lower velocity than P- or S- waves, but faster than Rayleigh waves. These waves are observed only when there is a low velocity layer overlying a high velocity layer/ sub–layers.

text: A Cherenkov (Черенко́в) detector is a particle detector using the speed threshold for light production, the speed-dependent light output or the velocity-dependent light direction of Cherenkov radiation.

text: A Cherenkov (Черенко́в) detector is a

text: particle detector

text: using the speed threshold for light production, the speed-dependent light output or the velocity-dependent light direction of

text: Cherenkov radiation

text: Once calculated the radial velocity of currents, distance to target, and the angular direction to target it is possible to determine the current vector and to construct current vector maps.  In fact, for the area in which vector data from two CODAR sites overlap, it is possible to calculate the velocity and direction of the current and comparisons with surface drifters and error analysis made in 1979 indicate that CODAR measures surface currents with at least 10 cm/s accuracy.In 2010, retailers of modern CODAR equipments guarantee an accuracy typically < 7 cm/s of the total current velocity and 1–2 cm of the tidal component, in normal environment condition.However, the accuracy of the system depends on several factors, such as signal-to-noise ratios, geometry and pointing errors.

text: One possible unreal solution for the stream thrust averaged velocity yields a negative entropy.  Another method of determining the proper solution is to take a simple average of the velocity and determining which value is closer to the stream thrust averaged velocity.

text: Wind direction is the opposite of the direction in which the windsock is pointing (note that wind directions are conventionally specified as being the compass point from which the wind originates; so a windsock pointing due north indicates a southerly wind). Wind speed is indicated by the windsock's angle relative to the mounting pole; in low winds, the windsock droops; in high winds it flies horizontally.

text: Wind direction

text: is the opposite of the direction in which the windsock is pointing (note that wind directions are conventionally specified as being the

text: compass point

text: from which the wind originates; so a windsock pointing due

text: north

text: indicates a

text: south

text: erly wind). Wind speed is indicated by the windsock's

text: angle

text: relative to the mounting

text: pole

text: ; in low winds, the windsock droops; in high winds it flies

text: horizontal

text: ly.

text: A velocity receiver (velocity sensor) is a sensor that responds to velocity rather than absolute position. For example, dynamic microphones are velocity receivers. Likewise, many electronic keyboards used for music are velocity sensitive, and may be said to possess a velocity receiver in each key.  Most of these function by measuring the time difference between switch closures at two different positions along the travel of each key.

text: A velocity receiver (velocity sensor) is a sensor that responds to velocity rather than absolute position. For example,

text: dynamic microphones

text: are velocity receivers. Likewise, many

text: electronic keyboard

text: s used for music are velocity sensitive, and may be said to possess a velocity receiver in each key.  Most of these function by measuring the time difference between switch closures at two different positions along the travel of each key.

text: The first law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant. Velocity is a vector quantity which expresses both the object's speed and the direction of its motion; therefore, the statement that the object's velocity is constant is a statement that both its speed and the direction of its motion are constant.

text: The first law states that if the

text: net force

text: (the

text: vector sum

text: of all forces acting on an object) is zero, then the

text: velocity

text: of the object is constant. Velocity is a

text: vector

text: quantity which expresses both the object's

text: speed

text: and the direction of its motion; therefore, the statement that the object's velocity is constant is a statement that both its speed and the direction of its motion are constant.

text: The Ge-detector determines the pulse-shape of the γ-ray which contains the information about the three-dimensional position of each individual interaction within the detector with the released energy in the interactions. The efficiency of the tracking array depends on these data. We must be able to compare the pulse-shapes to the respective shapes produced by charges each point to extract the position of the interaction. This is done experimentally using tightly collimated γ-ray sources with an external collimated detector for the Compton scattered coincidence. The conductivity of the Ge-detector influences the magnitude of the drift velocities and the angle between the electric field vector and the drift velocity. As a result the shape of the signal is directly influence because the Ge crystal is anisotropic with respect to the crystallographic axis direction. To determine the position of the interaction of the γ-ray one needs to consider the shapes of the induced real and mirror signals. The electrodes of the segment in which an interaction takes place are used to measure the real signals while mirror signals are measured on the neighboring segments where no interaction takes place.

text: Gear trains are usually formed by the meshing engagement of two or more gears on a frame to form a transmission. This can provide translation (linear motion) or rotation as well as mechanically alter displacement, speed, velocity, acceleration, direction and torque depending on the type of gears employed, transmission configuration and gearing ratio.

text: Gear trains are usually formed by the meshing engagement of two or more

text: gear

text: s on a frame to form a

text: transmission

text: . This can provide

text: translation

text: (linear motion) or

text: rotation

text: as well as mechanically alter

text: displacement

text: speed

text: velocity

text: acceleration

text: , direction and

text: torque

text: depending on the type of gears employed, transmission configuration and

text: gearing ratio

text: The substance is a basic yellow oil, while the form used in tablets, solifenacin succinate, consists of white to slightly yellowish crystals.

text: The substance is a

text: basic

text: yellow oil, while the form used in tablets, solifenacin

text: succinate

text: , consists of white to slightly yellowish crystals.

text: Irrespective of a fuzzball’s mass and resultant density, the determining factor establishing where its surface lies is the threshold at which the fuzzball’s escape velocity precisely equals the speed of light. Escape velocity, as its name suggests, is the velocity a body must achieve to escape from a massive object. For earth, this is 11.2 km/s. In the other direction, a massive object’s escape velocity is equal to the impact velocity achieved by a falling body that has fallen from the edge of a massive object’s sphere of gravitational influence. Thus, event horizons—for both classic black holes and fuzzballs—lie precisely at the point where spacetime has warped to such an extent that falling bodies just achieve the speed of light. According to Albert Einstein, via his special theory of relativity, the speed of light is the maximum permissible velocity in spacetime. At this velocity, infalling matter and energy impacts the surface of the fuzzball and its now-liberated, individual strings contribute to the fuzzball’s makeup.

text: Irrespective of a fuzzball’s mass and resultant density, the determining factor establishing where its surface lies is the threshold at which the fuzzball’s escape velocity precisely equals the speed of light. Escape velocity, as its name suggests, is the velocity a body must achieve to escape from a massive object. For earth, this is 11.2 km/s. In the other direction, a massive object’s escape velocity is equal to the impact velocity achieved by a falling body that has fallen from the edge of a massive object’s sphere of gravitational influence. Thus, event horizons—for both classic black holes and fuzzballs—lie precisely at the point where spacetime has warped to such an extent that falling bodies just achieve the speed of light. According to

text: Albert Einstein

text: , via his

text: special theory of relativity

text: , the speed of light is the maximum permissible velocity in spacetime. At this velocity, infalling matter and energy impacts the surface of the fuzzball and its now-liberated, individual strings contribute to the fuzzball’s makeup.

text: , the velocities,

text: , the velocities,

text: Three candidates were nominated. The list below is set out in descending order of the number of votes received at the by-election.

text: where ‘fs’ stands for free surface. This implies that the normal component of the velocity of the fluid at the surface is equal to the normal component of the velocity of the free surface.

text: The cross-sectional area of the flow is calculated from a depth measurement and the average velocity of the flow is measured directly (Doppler and propeller methods are common). Velocity times the cross-sectional area yields a flow rate which can be integrated into volumetric flow.There are two types of area velocity flow meter: (1) wetted; and (2) non contact. Wetted area velocity sensors have to be typically mounted on the bottom of a channel or river and use doppler to measure the velocity of the entrained particles. With depth and a programmed cross-section this can then provide discharge flow measurement. Non contact devices that use laser or radar are mounted above the channel and measure the velocity from above and then use ultrasound to measure the depth of the water from above. Radar devices can only measure surface velocites whereas laser based devices can measure velocities sub-surface.

text: Elements of vector calculus: divergence and curl; Gauss' and Stokes' theorems, Maxwell's equations: differential and integral forms. Wave equation, Poynting vector. Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth. Transmission lines: characteristic impedance; impedance transformation; Smith chart; impedance matching; pulse excitation. Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Antennas: Dipole antennas; antenna arrays; radiation pattern; reciprocity theorem, antenna gain.

text: Elements of

text: vector calculus

text: divergence

text: and

text: curl

text: Gauss'

text: and

text: Stokes' theorem

text: s,

text: Maxwell's equations

text: : differential and integral forms.

text: Wave equation

text: Poynting vector

text: Plane waves

text: : propagation through various media;

text: reflection

text: and

text: refraction

text: phase

text: and

text: group velocity

text: skin depth

text: Transmission lines

text: characteristic impedance

text: ; impedance transformation;

text: Smith chart

text: impedance matching

text: ; pulse excitation.

text: Waveguides

text: : modes in rectangular waveguides;

text: boundary conditions

text: cut-off frequencies

text: dispersion relation

text: s. Antennas:

text: Dipole antenna

text: s;

text: antenna array

text: s; radiation pattern; reciprocity theorem,

text: antenna gain

text: One can identify a terrestrial Rossby wave as its phase velocity, marked by its wave crest, always has a westward component. However, the collected set of Rossby waves may appear to move in either direction with what is known as its group velocity. In general, shorter waves have an eastward group velocity and long waves a westward group velocity.

text: One can identify a terrestrial Rossby wave as its

text: phase velocity

text: , marked by its wave crest, always has a westward component. However, the collected set of Rossby waves may appear to move in either direction with what is known as its

text: group velocity

text: . In general, shorter waves have an eastward group velocity and long waves a westward group velocity.

text: Particle velocity should not be confused with the speed of the wave as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity. Particle velocity should also not be confused with the velocity of individual molecules.

text: Particle velocity should not be confused with the speed of the

text: wave

text: as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the

text: speed of sound

text: . The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity. Particle velocity should also not be confused with the velocity of individual molecules.

text: However, the last two are a different coordinate condition when you go to the second order in h.

text: dependence on flow velocity, meaning that fluid drag increases with the square of flow velocity. When flow velocity is doubled, for example, not only does the fluid strike with twice the flow velocity, but twice the mass of fluid strikes per second. Therefore the change of momentum per second is multiplied by four. Force is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid friction, which generally has very little flow velocity dependence.

text: dependence on flow velocity, meaning that fluid drag increases with the square of flow velocity. When flow velocity is doubled, for example, not only does the fluid strike with twice the flow velocity, but twice the

text: mass

text: of fluid strikes per second. Therefore the change of

text: momentum

text: per second is multiplied by four.

text: Force

text: is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid

text: friction

text: , which generally has very little flow velocity dependence.