The statement that the velocity of a body is increasing at the maximum rate when its acceleration is zero is incorrect. In fact, when the acceleration of a body is zero, it means that there is no change in its velocity.
Acceleration is the rate of change of velocity with respect to time. When the acceleration is zero, it means that the velocity of the body remains constant, neither increasing nor decreasing. If the velocity is not changing, there is no acceleration acting on the body.
However, it is important to note that if the acceleration is not zero and its sign is positive, the velocity of the body will be increasing. The rate of increase in velocity depends on the magnitude of the acceleration. If the acceleration is constant, the velocity will increase linearly over time. If the acceleration is changing, the velocity may increase at a varying rate.
So, to summarize, when the acceleration is zero, the velocity remains constant. When the acceleration is nonzero and positive, the velocity will increase, but the maximum rate of increase in velocity occurs when the acceleration is at its maximum value, not when the acceleration is zero.