Definition:Velocity

From ProofWiki
Jump to navigation Jump to search

Definition

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 $t$:

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


Informally, 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.


Symbol

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


Dimension

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


Units

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 $\mathrm {ft \, s^{-1} }$.


Velocity in a Straight Line

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

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

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


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.


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Definition:Velocity&oldid=741155"