# Definition:Velocity

## Definition

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.

### Dimension

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

### SI

The SI unit of velocity is the metre per second $\mathrm m \ \mathrm s^{-1}$, or, less formally, $\mathrm m / \mathrm s$.

### CGS

The CGS unit of velocity is the centimetre per second $\mathrm {cm} \ \mathrm s^{-1}$, or, less formally, $\mathrm {cm} / \mathrm s$.

### FPS

The FPS unit of velocity is the foot per second $\mathrm f \ \mathrm s^{-1}$, or, less formally, $\mathrm f / \mathrm s$.

## Historical Note

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