(a) Yes. The object is stopped and will remain so. (b) Yes. If the object's acceleration is nonzero, its velocity is changing. That is, the object is stopped at this given instant, but it will not remain so.
Work Step by Step
Acceleration measures the rate of change of velocity with time. So, if the acceleration is zero (the first case), the velocity remains the same. For example: a tree in the yard. In the second case, acceleration is nonzero. So, velocity is changing. For example: you drop a ball from a window. The moment you release the ball, its velocity is zero and its acceleration is the acceleration due to gravity.