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Newtonian Mechanics

Speed and velocity

Thursday, 19 November 2009 19:14 Bruno Lebon

We define the average velocity $<\vec{v}>$ of a particle during the time interval $\Delta t$ as the displacement $\Delta \vec{r}$ of the particle divided by that time interval. The SI unit for velocity is the metre per second (m s^–1).

$<\vec{v}>=\frac{\Delta \vec{r}}{\Delta t}$

The instantaneous velocity $\vec{v}$ is defined as the limit of the average velocity $<\vec{v}>=\frac{\Delta \vec{r}}{\Delta t}$ as $\Delta t$ approaches zero:

$\vec{v}=\lim_{\Delta t\to 0}\frac{\Delta \vec{r}}{\Delta t}={\operatorname{d}r\over\operatorname{d}t}$

The magnitude of the instantaneous velocity vector, $v=|\vec{v}|$ is called speed. The unit of speed is the metre per second (m s^–1). Speed is a scalar quantity, while velocity is a vector quantity.

The difference between an average value and an instantaneous value is that an average value is calculated over a period of time, while an instantaneous value is calculated at an instant in time.