In which case is the average velocity equal to the instantaneous velocity? Why?

The instantaneous velocity would equal the average velocity if the instantaneous velocity were to equal the average of all the velocities of the measured data.

I'm thinking that the Mean Value Theorem implies that for any given velocity curve, there will be at least one point where the instantaneous velocity equals the average velocity. But the actual time where this occurs (and how many times, etc.) depends on the acceleration.

For example, if acceleration is zero, then the velocity is constant, so v_{avg} = v at any point.