Is it possible that the average velocity for some interval may be zero although the average velocity for a shorter interval included in the first interval is not zero?

Explanation

Yes.If a particle moves along a straight line with constant acceleration 1 st in on direction say in +x direction for some interval of time `Deltat_(1)` then it everses its direction and moves for another time interval .`Deltat_(2)` and reaches the same point then for total time interval `Deltat_(1)+Deltat_(2)` the average velocity is zero
`(because(Deltax)/(Deltat)=(0)/(Deltat)=0)`.The average velocity of the particle during a time interval `barDeltat` is equal to the slope of the straight line joining initial and final points on the position -time graph.