A body of mass 1 kg begins to move under the action of a time dependent force F = (t i +2 t^2 j ) N , where i and j are unit vectors along x and y axis. The power developed by above force at time t=3 second will be

Step-by-step solution

Given: Mass m = 1 kg and force F = (t i + 2t^2 j ) N . The power developed by the force is P = F v . Applying Newton's second law, acceleration is a = F m = t i + 2t^2 j m/s ^2 . Since the body starts from rest, velocity is found by integrating acceleration: v = (t i + 2t^2 j ) , dt = ( t^2 2 ) i + ( 2t^3 3 ) j m/s . Power is then calculated as P = F v = (t i + 2t^2 j ) ( t^2 2 i + 2t^3 3 j ) = t^3 2 + 4t^5 3 . At t = 3 , P(3) = 27 2 + 4 243 3 = 13.5 + 324 = 337.5 W .