Average velocity and average speed
Average velocity
The average velocity \(\overline{v_x}\) of a particle is defined as the particle's displacement \(\Delta x\) divided by the time interval \(\Delta t\) during which that displacement occurs:
\[\overline{v_x} := \frac{\Delta x}{\Delta t}.\]
Average velocity is a vector quantity.
The SI unit of average velocity is the metre per second: \[\left[v\right] = 1\,\frac{\mathrm{m}}{\mathrm{s}}.\]
In one dimension, average velocity is a single coordinate. Its directionality is in its sign: when it is positive, the object is moving in the positive direction, and a negative sign indicates motion in the negative direction.
Consider a marathon runner who runs more than 40 km, yet ends up at her starting point. Her displacement, and thus her average velocity, is zero, yet it does not mean she was not moving. To be able to describe situations like these, we shall define the average speed, which is the scalar counterpart of average velocity.
Average speed
The average speed \(\overline{v_x^*}\) of a particle is defined as the distance \(\Delta s\) travelled by the particle divided by the time interval \(\Delta t\) travelling this distance takes:
\[\overline{v_x^*} := \frac{\Delta s}{\Delta t}.\]
Average speed is a scalar quantity.
The SI unit of average speed is the metre per second:
\[\left[v\right] = 1\,\frac{\textrm{m}}{\textrm{s}}.\]