A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a_c is varying with time t as, a_c = k^2 r t^2 . The power delivered to the particle by the forces acting on it is ( K = constant)

Step-by-step solution

Given centripetal acceleration a_c = k^2 r t^2 Using the formula a_c = v^2 r : v^2 r = k^2 r t^2 v^2 = k^2 r^2 t^2 v = k r t The kinetic energy of the particle is given by: E = 1 2 m v^2 E = 1 2 m (k r t)^2 = 1 2 m k^2 r^2 t^2 The total power delivered by all forces acting on the particle is equal to the rate of change of its kinetic energy: P = dE dt P = d dt ( 1 2 m k^2 r^2 t^2 ) P = 1 2 m k^2 r^2 (2t) P = m k^2 r^2 t