Can an object have zero velocity but still have an acceleration?

Answer 1

A simple example is a ball tossed into the air. When the ball reaches its apex -- its highest point -- its instantaneous velocity is zero. If we assume that up is the positive direction, the ball's velocity is positive when it is initially tossed into the air, but it slows immediately. That is, its velocity becomes less positive until it reaches zero velocity. After that point, the velocity becomes increasingly negative (because down is the negative direction). Until the ball returns to earth and reaches the height at which it was initially thrown, its average velocity is non-zero. If the ball is allowed to hit the ground, its average velocity will be slightly negative, which is still non-zero. But it still had an instant -- at its apex -- when its velocity was zero.

Answer 2

Yes, an object having zero average velocity over a given time may still be accelerating during that interval, relative to another object which is accelerating away from it (i.e., an observer on that other object would see the "zero average velocity" object moving away from him/her).

Answer 3

Yes. It won't have zero velocity for long, but it's possible for the instantaneous velocity to be zero when the acceleration is non-zero.

For example, if you throw a ball straight up, at the very top of its path it's not moving upward or downward, but it still has an acceleration, and will fall from that point starting immediately.