Yes, it is possible for a body to have constant acceleration while its velocity and/or speed vary.
Acceleration is the rate of change of velocity with respect to time. If the acceleration of a body is constant, it means that its velocity is changing at a constant rate. However, this does not mean that the velocity itself is constant. The velocity can still vary if the acceleration is in a different direction than the initial velocity or if the acceleration changes over time.
When the acceleration is constant and in the same direction as the initial velocity, the body's velocity will increase or decrease linearly over time. This results in a uniformly changing velocity. In this case, the speed (magnitude of velocity) will also change at a constant rate.
On the other hand, if the acceleration is not in the same direction as the initial velocity, the body's velocity will change both in magnitude and direction. This leads to a curvilinear path or a change in the body's trajectory. In such cases, the speed may vary as well since it depends on the magnitude of velocity.
In summary, a body can have constant acceleration while its velocity and/or speed vary. The specific behavior of velocity and speed will depend on the direction of acceleration and how it changes over time.