Question

In which case average velocity becomes zero?

Answer 1

a circular motion in which after travelling for a distance of 2πr u reach again the starting position In this case your net displacement is zero and hence the velocity is also zero regardless of the time taken to complete this journey but instaneous velocity may or may not be zero through out the trip.

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Answer 2

When the displacement of the body is zero then the average velocity becomes zero.
as velocity = displacement/time.