Definition:Acceleration

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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 $\mathbf a$.


Acceleration in a Straight Line

Let $P$ be a particle in motion along a straight line $\LL$ with acceleration $\map {\mathbf a} t$ as a function of time $t$.

It is conventional to align $\LL$ along the $x$-axis of a Cartesian coordinate system such that the $\mathbf a$ can be expressed as $a \mathbf i$.

Then the unit vector of the component vector $a \mathbf i$ is suppressed, and $\map {\mathbf a} t$ is treated as a scalar quantity $\map a t$.


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.


Sources

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