A body can have zero velocity while experiencing non-zero acceleration, as illustrated by a ball thrown upwards that momentarily stops at its peak before descending. This scenario demonstrates that acceleration can exist even when velocity is zero. Conversely, a body with constant velocity cannot have variable acceleration, as acceleration implies a change in velocity. Both scenarios discussed are possible, with the first being a common occurrence in motion under gravity. Understanding these concepts clarifies the relationship between velocity and acceleration in physics.