Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. 60 km/h northbound).

(“Velocity” 2022)

Instantaneous velocity

If we consider \(v\) as velocity and \(x\) as the displacement (change in position) vector, then we can express the (instantaneous) velocity of a particle or object, at any particular time \(t\), as the derivative of the position with respect to time:

\(\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {x}}}{\Delta t}}={\frac {d{\boldsymbol {x}}}{dt}}\)

(“Velocity” 2022)

See Derivative (math).