Show that the average velocity of a particle over an interval over an interval of time is is either is either smaller than and the average speed of the particle over same interval

Answer 1

Huh? <<is either smaller than and the average >>

I think you want to show that the average velocity is smaller or the same as the average speed.

Remember, velocity is a vector, with direction. Average velociyt is the displacement (Final-initial)/time . Average speed does not include intermediate changes in direction.

For instance, consider going from A to B then Back to A.
average veloctiy would be zero (no change in position). Average speed would not be figured that way