A body of mass 2 kg starts from rest and moves in a straight line. The power delivered by the net force acting on the body is given as a function of time by P(t) = 4t³ W . The magnitude of the net force acting on the body as a function of time t is:

Step-by-step solution

Given power P = 4t³ W and mass m = 2 kg . We know that power is the product of force and velocity: P = Fv = (ma)v = m v dv dt Substituting the given values: 4t³ = (2) v dv dt 2t³ dt = v dv Integrating both sides from t = 0 to t (since the body starts from rest, v = 0 at t = 0 ): ₀^ t 2t³ dt = ₀^ v v dv 2t⁴ 4 = v² 2 t⁴ 2 = v² 2 v² = t⁴ Since the body starts from rest and moves in the direction of the force, v = t² . Now, the acceleration is: a = dv dt = d dt (t²) = 2t The magnitude of the net force is: F = ma = 2(2t