Velocity

Velocity is a physical quantity that describes the rate at which an object's position changes in a specific direction. It is a vector quantity, meaning it has both magnitude and direction. By contrast, speed is a scalar that only measures how fast an object is moving without regard to direction.

In mathematics, instantaneous velocity is the derivative of position with respect to time, written v(t) = ds/dt. The average velocity over a time interval is the displacement divided by the interval, v_avg = Δs/Δt. In three-dimensional space, velocity is a vector with components v = (dx/dt, dy/dt, dz/dt).

Constant velocity implies straight-line motion at a constant speed. If velocity changes, the object has nonzero acceleration, defined as the time rate of change of velocity. Relative velocity describes the velocity of one object as observed from another, depending on their respective motions. Velocity can be described in one dimension or as a vector field in more complex contexts.

Velocity is central to kinematics and appears in various fields, such as mechanics and fluid dynamics. In fluid dynamics, the velocity at each point in the fluid is described by a velocity field. In relativity, velocities are bounded by the speed of light and transform according to Lorentz transformations. Common units for velocity include meters per second, kilometers per hour, and miles per hour.