A particle of mass 0.5 kg moves in a circular path of radius 2 m. Its speed varies with time according to the equation v = 2t^2 m/s, where t is in seconds. The total power delivered by the net force acting on the particle at t = 2 s is :

Step-by-step solution

The net force on a particle in circular motion has two components: tangential force ( F_t ) and centripetal force ( F_c ). Since the centripetal force is always perpendicular to the velocity vector, it does zero work and delivers zero power. The total power is delivered entirely by the tangential force. Power P = F _ net v = F_t v Given v = 2t^2 , the tangential acceleration is: a_t = dv dt = 4t At t = 2 s: v = 2(2)^2 = 8 m/s a_t = 4(2) = 8 m/s ^2 The tangential force is: F_t = m a_t = 0.5 8 = 4 N The total power d