Question

A particle moving with uniform speed in a circular path maintains :

• A. Constant velocity
• B. Constant acceleration
• C. Constant velocity but varying acceleration
• D. Varying velocity and varying acceleration

Answer 1

The Correct Option is D

A particle maintaining a constant speed in a circular trajectory experiences both a changing velocity and a changing acceleration. The rationale is as follows:

1. Velocity is a vector, possessing both magnitude (speed) and direction. In uniform circular motion, despite constant speed, the direction of motion is perpetually in flux.
2. Because velocity is direction-dependent, and circular motion inherently involves a shifting direction, the velocity itself is consequently variable.
3. Acceleration quantifies the rate at which velocity changes. In circular motion, acceleration exists even with constant speed due to the continuous alteration of velocity's direction.
4. This specific form of acceleration in circular motion is termed centripetal acceleration and is directed inward, toward the circle's center.
5. Consequently, even with a stable speed, both the velocity and its rate of change (acceleration) exhibit continuous variation.

Therefore, the accurate conclusion is: Velocity and acceleration are both varying.