velocity

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Velocity is defined to be the rate of change of position of an object with respect to time. During an interval of time \Delta t = t_2 - t_1\, in which object undergoes a displacement of \Delta x= x_2 - x_1\,, the average velocity is defined by

v_{avg} \equiv \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{t_2 - t_1}\,.

By considering smaller and smaller intervals \Delta t\,, we define the instantaneous velocity by

v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{x(t+\Delta t) - x(t)}{\Delta t}\,,

which is the derivative of velocity with respect to time:

v \equiv \frac{dx}{dt}\,.

Usually instantaneous velocity is simply called velocity. The dimensions of velocityare length/time and the corresponding units are m/s\,.

3 dimensions

In three dimensions, position is a vector, so velocity must also be a vector:

\mathbf{v} \equiv \frac{d\mathbf{r}}{dt}\,.
back to position
on to acceleration
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