No, it's not possible for a body to have an acceleration when moving with constant velocity. Here's why:

* Acceleration is the rate of change of velocity. This means acceleration occurs when the velocity of an object is either increasing (speeding up) or decreasing (slowing down), or changing direction.

* Constant velocity means that both the speed and direction of motion are unchanging.

Since constant velocity implies no change in speed or direction, there is no change in velocity, and therefore no acceleration.