# Definition:Acceleration

## Contents

## Definition

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

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

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:

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

## Also see

## Linguistic Note

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

## 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.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 1966: Isaac Asimov:
*Understanding Physics*: $\text{I}$: Chapter $2$ - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $8$: The System of the World