# Velocity Measure

(Redirected from Velocity)

A Velocity Measure is a physical object measure of the rate of change of physical distance traveled with respect to time.

$\displaystyle{ [velocity]=\frac{[distance]}{[time]}=\frac{[length]}{[time]} }$
where $\displaystyle{ [x] }$ symbolizes the conversion of the quantity $\displaystyle{ x }$ to its units of measurement. Thus, the units of measurement for acceleration can be given in meters per seconds, $\displaystyle{ m/s }$, (in International System of Units or metric system) or feet per seconds (imperial system).
• On average the velocity can be estimated to be:
$\displaystyle{ \vec{v}_{average}=\vec{\bar{v}}=\frac{\Delta s}{\Delta t}=\frac{\vec{s_2}-\vec{s_1}}{t_2-t_1} }$
• It can also be defined as the integral of the acceleration $\displaystyle{ \vec{v}=\int\vec{a}\;dt }$.
• There is direct proportionality of velocity to momentum and the inverse proportionality of velocity to mass
$\displaystyle{ \vec{p} =m\vec{v} \quad\iff\quad \vec{v}=\frac{\vec{p}}{m} }$
(Note: this is assuming object's mass is a constant, relativistic effects have to be taken into account when the object approches the speed of light).

## References

### 2005

$\displaystyle{ \vec{v}_{average}=\vec{\bar{v}}=\frac{\Delta x}{\Delta t}=\frac{\vec{x_2}-\vec{x_1}}{t_2-t_1} }$
The units for velocity can be implied from the definition to be meters/second or in general any distance unit over any time unit.
$\displaystyle{ \vec{v}_{instantaneous}=\lim_{\Delta\;t\rightarrow\;0}\frac{\Delta \vec{x}}{\Delta t}=\frac{d\vec{x}}{dt} }$
You can approach an expression for the instantaneous velocity at any point on the path by taking the limit as the time interval gets smaller and smaller. Such a limiting process is called a derivative and the instantaneous velocity can be defined as