Can an object have zero velocity and nonzero acceleration at the same time? Give examples.

Yes. For example, a rock thrown straight up in the air has a constant, nonzero acceleration due to gravity for its entire flight. However, at the highest point it momentarily has a zero velocity. A car, at the moment it starts moving from rest, has zero velocity and nonzero acceleration.

If an object is at the instant of reversing direction (like an object thrown upward, at the top of its path), it instantaneously has a zero velocity and a non-zero acceleration at the same time. A person at the exact bottom of a “bungee” cord plunge also has an instantaneous velocity of zero but a nonzero (upward) acceleration at the same time.