A constant force F = (4 i + 2 j ) N acts on a particle. The position vector of the particle as a function of time t is given by r = (t³ i - 2t² j ) m . The instantaneous power delivered by the force at t = 2 s is:

Step-by-step solution

The position vector of the particle is given by r = (t³ i - 2t² j ) m . The velocity of the particle is the rate of change of its position vector: v = d r dt = d dt (t³ i - 2t² j ) = (3t² i - 4t j ) m/s At t = 2 s , the velocity is: v = 3(2)² i - 4(2) j = (12 i - 8 j ) m/s The force acting on the particle is F = (4 i + 2 j ) N . The instantaneous power delivered by the force is given by the dot product of force and velocity: P = F v = (4 i + 2 j ) (12 i - 8 j ) P = (4)(12) + (2)(-8) = 48 - 16 = 32 W Answer: 32 W