Velocities

Velocity is a vector quantity that describes the rate at which an object's position changes in time, including both speed and direction. It contrasts with speed, which is the magnitude of velocity and does not specify direction.

Instantaneous velocity is the limit of average velocity as the time interval approaches zero; for a particle with position r(t), the instantaneous velocity is v(t) = dr/dt. In one dimension, velocity is often described by a signed quantity; in three dimensions, it is a vector.

Average velocity over a time interval is displacement divided by the interval length: (r(t2) − r(t1)) / (t2 − t1).

Velocity depends on the frame of reference; different observers may measure different velocities for the same motion. Relative velocity is obtained by subtracting the velocity of one frame from another (u = v_A − v_B).

Velocity is related to acceleration, which is the rate of change of velocity: a = dv/dt. If velocity is constant, the motion has zero acceleration. Velocity can be described as a function of time, v(t), or as a velocity field v(x,t) in continua such as fluids and gases.

Common units are meters per second (m/s) in SI, though kilometers per hour (km/h) are common for everyday speeds. Measurements rely on position-tracking methods, such as timers, radar, or motion sensors. Velocity is fundamental in kinematics, navigation, astronomy, and fluid dynamics.