A particle of mass m is moving in a circular path of radius R. The centripetal acceleration of the particle varies with time t as a_c = k^2 R t^2. What is the power delivered to the particle by the forces acting on it as a function of time?

Answer and explanation

Correct answer: D. m k^2 R^2 t

  1. Step 1: Centripetal acceleration a_c = v^2 / R = k^2 R t^2 => v^2 = k^2 R^2 t^2 => v = k R t.
  2. Step 2: Kinetic energy K = (1/2) m v^2 = (1/2) m k^2 R^2 t^2.
  3. Step 3: Power delivered P = dK/dt = (1/2) m k^2 R^2 (2t) = m k^2 R^2 t.

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