Question

If you divide the total distance traveled on a car trip (as determined by the odometer) by the elapsed time of the trip, are you calculating average speed or magnitude of average velocity? Under what circumstances are these two quantities the same?

Answer 1

In general, you're calculating the magnitude of average velocity. In fact, speed is a vector, and as such it also has a direction and orientation.

So, if you compute the average speed, you're assuming that you went directly from point A to point B, which is basically never the case.

If, instead, you actually moved on a straight line from point A to point B, then the two quantities are the same.