A particle of mass 2 kg moves along a straight line starting from rest. The power delivered to it by the net force is given by P = 4t^3 W, where t is the time in seconds. The magnitude of the net force acting on the particle as a function of time is :

Step-by-step solution

Power P = F v = m a v = m v dv dt Given m = 2 kg and P = 4t^3 W, we have: 2 v dv dt = 4t^3 v dv = 2t^3 dt Integrating both sides from t = 0 (where v = 0 ) to t : ₀^v v' dv' = ₀^t 2t'^3 dt' v^2 2 = 2t^4 4 v^2 = t^4 v = t^2 The acceleration of the particle is: a = dv dt = 2t The magnitude of the net force is: F = ma = 2(2t) = 4t N Answer: 4t N