A body of mass 2 kg begins to move under the influence of time dependent force F = (2t i + 6t^2 j ) N, where i and j are unit vectors along x and y -axis respectively. The power produced by the force at t = 2 s is _____ W.

Step-by-step solution

Given F = (2t i + 6t^2 j ) N and m = 2 kg. Acceleration of the body is a = F m = 2t i + 6t^2 j 2 = t i + 3t^2 j m/s ^2 . Since the body begins to move from rest, its velocity at time t is given by v = a dt = (t i + 3t^2 j ) dt = t^2 2 i + t^3 j m/s. At t = 2 s, the force is F = 2(2) i + 6(2)^2 j = 4 i + 24 j N. At t = 2 s, the velocity is v = (2)^2 2 i + (2)^3 j = 2 i + 8 j m/s. Power produced by the force is P = F v = (4 i + 24 j ) (2 i + 8 j ) . P = (4 2) + (24 8) = 8 + 192 = 200 W. Answer: 200