Yes, it is indeed possible for the average velocity of a particle to be zero in a given time interval, even if the instantaneous velocity is never zero within that interval. This situation can arise due to the symmetrical distribution of velocities.
To understand this concept, let's consider a simple example. Imagine a particle moving along a straight line. Suppose the particle moves in one direction for a certain period of time, then turns around and moves in the opposite direction for an equal amount of time, and repeats this pattern.
During each half of the time interval, the particle will have a non-zero velocity in one direction. However, since the time spent moving in one direction is equal to the time spent moving in the opposite direction, the average velocity over the entire interval will be zero. This is because the positive and negative velocities cancel each other out when calculating the average.
In this case, the instantaneous velocity is never zero within the interval, but the symmetrical distribution of velocities ensures that the average velocity is zero. It's important to note that the concept of average velocity considers the overall displacement of the particle over a given time interval, while the instantaneous velocity refers to the velocity at a particular instant in time.
So, while it may seem counterintuitive that the instantaneous velocity is never zero, yet the average velocity is zero, it is a consequence of the specific distribution of velocities within the interval.