Velocity

Velocity is the rate of change of position. One tricky part of the idea of velocity is that velocity requires a comparison of two positions — which means paying attention to the position at two different times. But we talk about a velocity at a single time. How does that work?

To see what's going on — and to provide useful and insightful calculational tools — we will introduce two different kinds of velocity — the average velocity and the instantaneous velocity. The average velocity is what we use when we are paying attention to the time interval explicitly; the instantaneous velocity is what we use when the time interval we use to calculate the velocity from the position is very small compared to any times we want to pay attention to.

In either case, the velocity answers the questions: how fast are you changing your position?

Read the follow-ons for the details of average and instantaneous velocity.

Joe Redish 8/24/11