Position tells where an object is. To describe how quickly that position changes, we compare a change in position with the time taken.

Average velocity

Over a time interval $\Delta t$, the average velocity is

$$\bar v=\frac{\Delta x}{\Delta t}.$$

Because displacement can be positive or negative, average velocity carries direction in one dimension.

For example, if an object moves from $x=2,\mathrm m$ to $x=8,\mathrm m$ in $3,\mathrm s$,

$$\bar v=\frac{6,\mathrm m}{3,\mathrm s}=2,\mathrm{m/s}.$$

Average speed

Average speed uses total distance travelled rather than displacement:

$$\text{average speed}=\frac{\text{distance travelled}}{\Delta t}.$$

Speed is nonnegative and does not contain direction.

A round trip

If an object travels $10,\mathrm m$ away from its starting point and $10,\mathrm m$ back in $5,\mathrm s$, its displacement is zero, so its average velocity is zero. Its distance travelled is $20,\mathrm m$, so its average speed is

$$4,\mathrm{m/s}.$$

Velocity describes net change of position; speed describes how quickly path length accumulates.