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

Step-by-step solution

Given F = t i + 3t^2 j and m = 1 kg . Acceleration a = F m = t i + 3t^2 j Velocity v = a dt = t^2 2 i + t^3 j (since the body begins to move from rest, v (0) = 0 ). At t = 2 s : F = 2 i + 3(2)^2 j = 2 i + 12 j v = 2^2 2 i + (2)^3 j = 2 i + 8 j Power P = F v = (2 i + 12 j ) (2 i + 8 j ) P = (2 2) + (12 8) = 4 + 96 = 100 W Answer: 100