# Definition:Velocity

## Definition

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

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

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 $L T^{-1}$.

### Units

The units of measurement of velocity are as follows:

Thus we see:

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

## Historical Note

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