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The velocity $\mathbf v$ of a body $M$ is defined as the first derivative of the displacement $\mathbf s$ of $M$ from a given point of reference with respect to time $t$:

$\mathbf v = \dfrac {\d \mathbf s} {\d t}$

Colloquially, it is described as the rate of change of position.

It is important to note that as displacement is a vector quantity, then it follows by definition of derivative of a vector that so is velocity.


The dimension of measurement of velocity is $L T^{-1}$.


The units of measurement of velocity are as follows:

Thus we see:

$1 \ \mathrm m \ \mathrm s^{-1} = 10^2 \ \mathrm {cm} \ \mathrm s^{-1} = 100 \ \mathrm {cm} \ \mathrm s^{-1}$

Also see

Historical Note

The first person to treat the velocity as a vector was Leonhard Paul Euler.