Definition:Acceleration

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 from Derivative of 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

 * Definition:Displacement
 * Definition:Position


 * Definition:Velocity
 * Definition:Speed

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