Uniform Circular Motion

A particle moving with uniform speed in a circular path has varying velocity and varying acceleration. To understand why this is true, consider the following:

1. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. For a particle moving in a circular path at constant speed, while the speed remains the same, the direction continually changes.
2. Since velocity involves direction, and the direction is constantly changing in circular motion, the velocity is therefore varying.
3. Acceleration is the rate of change of velocity. In circular motion, acceleration is present even if the object is moving at a constant speed because the velocity's direction is changing.
4. This type of acceleration in circular motion is known as centripetal acceleration, directed towards the center of the circle.
5. Thus, although the speed is constant, both the velocity and its rate of change (acceleration) vary continuously.

Hence, the correct answer is: Varying velocity and varying acceleration.