Velocity Measure

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

where [math][x][/math] symbolizes the conversion of the quantity [math]x[/math] to its units of measurement. Thus, the units of measurement for acceleration can be given in meters per seconds, [math]m/s[/math], (in International System of Units or metric system) or feet per seconds (imperial system).
  • On average the velocity can be estimated to be:
[math]\vec{v}_{average}=\vec{\bar{v}}=\frac{\Delta s}{\Delta t}=\frac{\vec{s_2}-\vec{s_1}}{t_2-t_1}[/math]
[math]\vec{p} =m\vec{v} \quad\iff\quad \vec{v}=\frac{\vec{p}}{m}[/math]
(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).




[math]\vec{v}_{average}=\vec{\bar{v}}=\frac{\Delta x}{\Delta t}=\frac{\vec{x_2}-\vec{x_1}}{t_2-t_1}[/math]
The units for velocity can be implied from the definition to be meters/second or in general any distance unit over any time unit.
[math]\vec{v}_{instantaneous}=\lim_{\Delta\;t\rightarrow\;0}\frac{\Delta \vec{x}}{\Delta t}=\frac{d\vec{x}}{dt}[/math]
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