Final answer:
The statement is False. Velocity being at zero does not necessitate that acceleration be zero; an object can have zero velocity while still accelerating, as with an object at the peak of its motion under gravity. option B is correct.
Step-by-step explanation:
The statement that if the velocity of an object is zero at some point, then its acceleration must also be zero at that point is False. Velocity being zero only indicates that the object is not moving at that particular point in time. However, acceleration can be non-zero if the object is changing its velocity; that is, if it is starting to move (speeding up) or coming to a stop (slowing down). For example, a ball thrown vertically upwards has a velocity of zero at the highest point, but it still has a downward acceleration due to gravity.
Acceleration is the rate of change of velocity, and this can be non-zero even when velocity is zero. A position vs time graph of an object that is speeding up is not a straight line; rather, it curves, indicating changing velocity. A straight line on a position vs time graph indicates constant velocity, not accelerating motion. Conversely, a displacement versus time squared graph for an object moving with constant acceleration is a straight line because the relationship between displacement and time squared is linear in such cases.