From ProofWiki
Jump to navigation Jump to search


The velocity $\mathbf v$ of a body $M$ is defined as the first derivative of the displacement $\mathbf s$ of $M$ from a given point of reference with respect to time $t$:

$\mathbf v = \dfrac {\d \mathbf s} {\d t}$

Colloquially, it is described as the rate of change of position.

It is important to note that as displacement is a vector quantity, then it follows by definition of derivative of a vector that so is velocity.


The dimension of measurement of velocity is $\mathsf {L T^{-1} }$.


The SI unit of velocity is the the metre per second: $\mathrm {m \, s^{-1} }$.

The CGS unit of velocity is the centimetre per second: $\mathrm {cm \, s^{-1} }$.

The FPS unit of velocity is the foot per second $\mathrm {ft \, s^{-1} }$.

Also see

  • Results about velocity can be found here.

Historical Note

The first person to treat the velocity as a vector was Leonhard Paul Euler.