A particle of mass 2 ~kg initially at rest is acted upon by a constant force F = (4 i + 2 j ) ~N . The instantaneous power delivered by the force at t = 3 ~s is:

Step-by-step solution

From Newton's second law, the acceleration of the particle is: a = F m = 4 i + 2 j 2 = (2 i + j ) ~m~s ⁻² Since the particle starts from rest ( u = 0 ), its velocity at time t = 3 ~s is: v = u + a t = 0 + (2 i + j )(3) = (6 i + 3 j ) ~m~s ⁻¹ The instantaneous power delivered by the force is the dot product of force and velocity: P = F v P = (4 i + 2 j ) (6 i + 3 j ) P = (4)(6) + (2)(3) = 24 + 6 = 30 ~W Answer: 30 ~W