# Definition:Acceleration

## Definition

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

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

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

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

### Dimension

Acceleration has dimension $\mathsf {L T}^{-2}$.

### SI

The SI unit of acceleration is the the metre per second squared $\mathrm m \ \mathrm s^{-2}$, or, less formally, $\mathrm m / \mathrm s^2$.

### CGS

The CGS unit of acceleration is the centimetre per second $\mathrm {cm} \ \mathrm s^{-2}$, or, less formally, $\mathrm {cm} / \mathrm s^2$..

### FPS

The FPS unit of acceleration is the foot per second $\mathrm f \ \mathrm s^{-2}$, or, less formally, $\mathrm f / \mathrm s^2$.

## Also see

• Results about acceleration can be found here.

## Historical Note

The first person to study the acceleration of a particle moving along a general curve was first studied by Leonhard Paul Euler.

He was also the first to treat acceleration as a vector.

## Linguistic Note

The word acceleration comes from the Latin for to add speed.