A particle moves in the x - y plane such that its position vector at any time t is given by r = (2t^2 i + 5t j ) m. If it is acted upon by a constant force F = (3 i + 4 j ) N, the instantaneous power delivered by the force at t = 1 s is:

Step-by-step solution

The position vector of the particle is r = (2t^2 i + 5t j ) m. The velocity vector v is the rate of change of the position vector: v = d r dt = d dt (2t^2 i + 5t j ) = (4t i + 5 j ) m/s At t = 1 s, the velocity is: v = (4(1) i + 5 j ) = (4 i + 5 j ) m/s The instantaneous power P is the dot product of force and velocity: P = F v = (3 i + 4 j ) (4 i + 5 j ) P = (3 4) + (4 5) = 12 + 20 = 32 W. Taking the dot product with the position vector instead of velocity would incorrectly give 26 W, and multiplying the magnitude