If an object is moving at a constant velocity and is acted on by a centripetal force, it undergoes uniform acceleration because acceleration is a vector quantity that involves a change in velocity.
Uniform acceleration refers to a situation where the magnitude of acceleration remains constant over time, even if the velocity remains constant. In the case of circular motion, when an object is moving in a circular path at a constant speed, its velocity is changing continuously. Although the object's speed remains the same, its direction of motion is constantly changing due to the centripetal force acting towards the center of the circular path.
The centripetal force is responsible for continuously changing the direction of the object's velocity, even if its speed remains constant. This change in velocity constitutes acceleration, known as centripetal acceleration. The centripetal acceleration is always directed towards the center of the circular path and is perpendicular to the object's velocity vector at any given point. It is this uniform acceleration that keeps the object moving in a circular path.
So, even though the object's speed may be constant, the change in direction of its velocity due to the centripetal force results in a uniform acceleration towards the center of the circular path.