An object of mass 1000 g experiences a time-dependent force F = (2t, 3t²) N. Assuming zero initial velocity, the instantaneous power generated by the force at time t is:
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An object of mass 1000 g experiences a time-dependent force F = (2t, 3t²) N. Assuming zero initial velocity, the instantaneous power generated by the force at time t is:

G1 Physics · Accepted Answer

Mass is m = 1000 g = 1 kg. Hence acceleration is a = F/m = (2t, 3t²) m/s². With zero initial velocity, integrate each component: v x v_x v x ​ = ∫2t dt = t², v y v_y v y ​ = ∫3t² dt = t³. Thus, v = (t², t³) m/s. Instantaneous power is P = F·v. Therefore, P = (2t)(t²) + (3t²)(t³) = 2t³ + 3t⁵ W. Correct option: D.