# 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 $L T^{-2}$.

### Units

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

Thus:

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

## 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.