Instruct: Given a question, retrieve relevant passages that can help answer the question.
Query: What is the difference between speed and velocity?
Speed describes only how fast an object is moving, whereas velocity gives both how fast it is and in which direction the object is moving.[1] If a car is said to travel at 60km/h, its speed has been specified. However, if the car is said to move at 60km/h to the north, its velocity has now been specified.
Computing the hypocenters of foreshocks, main shock, and aftershocks of earthquakes allows the three-dimensional plotting of the fault along which movement is occurring. The expanding wavefront from the earthquake's rupture propagates at a speed of several kilometers per second, this seismic wave is what is measured at various surface points in order to geometrically determine an initial guess as to the hypocenter. The wave reaches each station based upon how far away it was from the hypocenter. A number of things need to be taken into account, most importantly variations in the waves speed based upon the materials that it is passing through. With adjustments for velocity changes, the initial estimate of the hypocenter is made, then a series of linear equations is set up, one for each station. The equations express the difference between the observed arrival times and those calculated from the initial estimated hypocenter. These equations are solved by the method of least squares which minimizes the sum of the squares of the differences between the observed and calculated arrival times, and a new estimated hypocenter is computed. The system iterates until the location is pinpointed within the margin of error for the velocity computations.
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 formula_17.
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.
Collision is short-duration interaction between two bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces (there is a change in velocity). The magnitude of the velocity difference just before impact is called the closing speed. All collisions conserve momentum. What distinguishes different types of collisions is whether they also conserve kinetic energy. The Line of impact is the line which is colinear to the common normal of the surfaces that are closest or in contact during impact. This is the line along which internal force of collision acts during impact, and Newton's coefficient of restitution is defined only along this line. Collisions are of three types. They are: 1.perfectly elastic collision 2.inelastic collision 3.perfectly inelastic collision.
In order to obtain a negative result, we should have Δ"L"−Δ"L"=0. However, it can be seen that both formulas only cancel each other as long as the velocities are the same ("v"="v"). But if the velocities are different, then Δ"L" and Δ"L" are no longer equal. (The Michelson–Morley experiment isn't affected by velocity changes since the difference between "L" and "L" is zero. Therefore, the MM experiment only tests whether the speed of light depends on the "orientation" of the apparatus.) But in the Kennedy–Thorndike experiment, the lengths "L" and "L" are different from the outset, so it is also capable of measuring the dependence of the speed of light on the "velocity" of the apparatus.
Explanations based on increased flow speed and Bernoulli's principle first try to establish that there is higher flow speed over the upper surface, but they fail to explain correctly what causes the flow to speed up:Bernoulli-only explanations imply that a speed difference arises from causes other than a pressure difference, and that the speed difference then leads to a pressure difference by Bernoulli’s principle. This implied one-way causation is a misconception. The real cause-and-effect relationship between pressure and velocity is reciprocal. Finally, Bernoulli-only explanations don't explain how the pressure differences in the vertical direction are sustained. That is, they leave out the downward-turning part of the interaction.
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.
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. 
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. 
Because the speed computed by the pitometer is a function of the difference between pressure readings, the pitometer does not produce an accurate result when the ship's velocity is low and the two pressure readings are nearly the same.
The muzzle velocity of an airgun, firearm, or light-gas gun is limited by, but not limited to, the speed of sound in the working fluid—the air, burning gunpowder, or a light gas. Up to the speed of sound, thermodynamics provides a simple, approximate calculation approach: the projectile is accelerated by the pressure difference between its ends, and since such a pressure wave cannot propagate any faster than the speed of sound in the medium, thermodynamic analysis suggests that the muzzle velocity is limited to the speed of sound. However, beyond the speed of sound, the kinetic theory of gases, which determines the speed of sound, provides a more detailed analysis in terms of the gas particles that comprise the working fluid. Kinetic theory indicates that the velocity of the gas particles is Maxwell-Boltzmann distributed, with the velocity of a large fraction of the particles exceeding the speed of sound in the gas. That fraction of the gas can continue to apply pressure to and therefore accelerate the projectile beyond the speed of sound in diminishing amounts as the projectiles speed increases. 
The big difference can be noticed when we consider movement around a circle. When something moves in a circular path (at a constant speed, see above) 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.
If one divides a change in proper distance by the interval of cosmological time where the change was measured (or takes the derivative of proper distance with respect to cosmological time) and calls this a "velocity", then the resulting "velocities" of galaxies or quasars can be above the speed of light, "c". This apparent superluminal expansion is not in conflict with special or general relativity, and is a consequence of the particular definitions used in physical cosmology. Even light itself does not have a "velocity" of "c" in this sense; the total velocity of any object can be expressed as the sum formula_15 where formula_16 is the recession velocity due to the expansion of the universe (the velocity given by Hubble's law) and formula_17 is the "peculiar velocity" measured by local observers (with formula_18 and formula_19, the dots indicating a first derivative), so for light formula_17 is equal to "c" (−"c" if the light is emitted towards our position at the origin and +"c" if emitted away from us) but the total velocity formula_21 is generally different from "c". Even in special relativity the coordinate speed of light is only guaranteed to be "c" in an inertial frame; in a non-inertial frame the coordinate speed may be different from "c". In general relativity no coordinate system on a large region of curved spacetime is "inertial", but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" in which the local speed of light is "c" and in which massive objects such as stars and galaxies always have a local speed smaller than "c". The cosmological definitions used to define the velocities of distant objects are coordinate-dependent – there is no general coordinate-independent definition of velocity between distant objects in general relativity. The issue of how best to describe and popularize the apparent superluminal expansion of the universe has caused a minor amount of controversy. One viewpoint is presented in Davis and Lineweaver, 2004.
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.
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
The refractive index "n" of an optical medium is defined as the ratio of the speed of light in vacuum, "c" = , and the phase velocity "v" of light in the medium,
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.
Variations in local propagation speed of a laminar flame arise due to what is called flame stretch. Flame stretch can happen due to the straining by outer flow velocity field or the curvature of flame; the difference in the propagation speed from the corresponding laminar speed is a function of these effects and may be written as:
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.
The relevant wave speed in the discussion above is the phase velocity of the wave. This is typically close to the group velocity which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction.
Associated with propagation of a disturbance are several different velocities. For definiteness, consider an amplitude modulated electromagnetic carrier wave. The phase velocity is the speed of the underlying carrier wave. The group velocity is the speed of the modulation or envelope. Initially it was thought that the group velocity coincided with the speed at which "information" traveled. However, it turns out that this speed can exceed the speed of light in some circumstances, causing confusion by an apparent conflict with the theory of relativity. That observation led to consideration of what constitutes a "signal".
A fit adult creates a wake. Drag due to a wake is Newtonian drag, increasing with the square of the velocity. For example, if the relative speed between the water and the leg is twice as high on the thrust phase than on the recovery phase, the thrust is four times as high as the drag. Assuming the legs are recovered with a relative speed between leg and body which amounts to the same as the relative speed between water and body, the legs must be kicked back with five times the mean velocity of the swimmer. This limits the top speed. Both effects together, velocity and frontal area, yield a thrust-to-drag ratio of 8 for the legs.
The underlying principles of Buys Ballot's law state that for anyone ashore in the Northern Hemisphere and in the path of a hurricane, the most dangerous place to be is in the right front quadrant of the storm. There, the observed wind speed of the storm is the sum of the speed of wind in the storm circulation plus the velocity of the storm's forward movement. Buys Ballot's law calls this the "Dangerous Quadrant". Likewise, in the left front quadrant of the storm the observed wind is the "difference" between the storm's wind velocity and its forward speed. This is called the "Safe Quadrant" due to the lower observed wind speeds.
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.
The required hyperbolic excess velocity "v" (sometimes called "characteristic velocity") is the difference between the transfer orbit's departure speed and the departure planet's heliocentric orbital speed. Once this is determined, the injection velocity relative to the departure planet at periapsis is:
Relativistic rocket refers to any spacecraft that travels at a velocity close enough to light speed for relativistic effects to become significant. The meaning of "significant" is a matter of context, but often a threshold velocity of 30% to 50% of the speed of light (0.3"c" to 0.5"c") is used. At 30% of c, the difference between relativistic mass and rest mass is only about 5%, while at 50% it is 15%, (at 0.75"c" the difference is over 50%) so that above this range of speeds special relativity is required to accurately describe motion, whereas below this range sufficient accuracy is usually provided by Newtonian physics and the Tsiolkovsky rocket equation.