Question

can a particle move with the speed whose modulus is constant while accelerated? Justify your answer by an example?

Answer 1

YES.

Such type cases arise when acceleration is perpendicular to the path of motion.

Take the example of a circular motion with constant speed.

For example see the following case:

A particle is moving in a circular path (radius r) with constant speed V.

At different instances as shown in the figure, direction of speed is different and hence the velocity is different but its modulus is constant which is equal to speed of the particle that is V.

In this situation, particle is accelerated towards center at every point during it's motion as it's direction of velocity is changing and hence there is net acceleration at every instant because whenever there is change in velocity (either be magnitude or direction), the motion is accelerated.