A particle is subjected to a force of constant magnitude that is always perpendicular to its velocity. The motion of the particle occurs in a plane. It then follows that

Step-by-step solution

Since the force is always perpendicular to the velocity, the power delivered by the force is zero ( F v = 0 ). Therefore, the work done by the force is zero, which implies that the kinetic energy and the speed v of the particle remain constant. The magnitude of the force is constant, so the magnitude of the acceleration a = F m is also constant. Since the force is perpendicular to the velocity, the acceleration is purely centripetal and is given by a = v^2 R , where R is the radius of curvature. Because both v and