Final answer:
A force of constant magnitude that is always perpendicular to a particle's velocity does no work on the particle, meaning that kinetic energy and speed remain constant while the particle moves in a circle. Therefore, the particle's kinetic energy is constant. Option c is the answer.
Step-by-step explanation:
When a particle is acted upon by a force of constant magnitude that is always perpendicular to the velocity of the particle, with the motion taking place on a plane, the result is circular motion. This type of force is called a centripetal force. The perpendicular nature of the force means that it does no work on the particle, as work is a force exerted along the direction of motion. Because there is no work being done on the particle, its kinetic energy and speed remain constant. The centripetal force continuously changes the direction of the velocity, but not its magnitude. Thus, the particle executes uniform circular motion.
Constant kinetic energy is a result of this scenario because the force is always perpendicular to the velocity implies there is no work being done on the particle to change its kinetic energy. Instead, the force serves as a centripetal force, providing the necessary force to keep the particle moving in a circle without altering its speed. Therefore, the correct answer is C. Its kinetic energy is constant.