# 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 $\mathsf {L T}^{-2}$.

### Units

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

The CGS unit of acceleration is the gal: $\mathrm {Gal}$.

The FPS unit of acceleration is the foot per second squared $\mathrm {ft \, s^{-2} }$.

### Symbol

The usual symbol used to denote the acceleration of a body is $\mathbf a$.

## 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.