A particle of mass 2 kg moves along the x-axis. Its position varies with time according to the equation x = t^3 + t , where x is in metres and t is in seconds. The instantaneous power delivered to the particle by the net force at t = 2 s is:

Step-by-step solution

Given, position of the particle is x = t^3 + t Velocity of the particle is: v = dx dt = d dt (t^3 + t) = 3t^2 + 1 Acceleration of the particle is: a = dv dt = d dt (3t^2 + 1) = 6t At t = 2 s : v = 3(2)^2 + 1 = 13 m s ⁻¹ a = 6(2) = 12 m s ⁻² According to Newton's second law, the net force acting on the particle is: F = ma = 2 12 = 24 N The instantaneous power delivered by the net force is: P = Fv = 24 13 = 312 W Answer: 312 W