
We use limits to compute instantaneous velocity.

When we compute average velocity, we look at To obtain the (instantaneous) velocity, we want the change in time to “go to” zero. By this point we should know that “go to” is a buzz-word for a limit. The change in time is often given as the length of a time interval, and this length goes to zero.

The average velocity on the (time) interval $[a,b]$ is given by Here $s(t)$ denotes the position, at the time $t$, of an object moving along a line.

Let’s put all of this together by working an example.

In our previous example, we computed average velocity on several different intervals. If we let the size of the interval go to zero, we get instantaneous velocity. Limits will allow us to compute instantaneous velocity. Let’s use the same setting as before.