A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, the power delivered to the particle is:
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Question

A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, the power delivered to the particle is:

G1 Physics · Accepted Answer

Step 1 — Principle: Average power is the total work divided by elapsed time; instantaneous power is F·v. Step 2 — Working: The speed increases uniformly from zero to v in time T. Step 3 — Working: The gain in kinetic energy is ΔK = ½Mv². Step 4 — Working: Average power over the interval is ΔK/T = Mv²/(2T), corresponding to option D. Step 5 — Working: If 'power' means instantaneous power at the final moment, then P(T) = Fv = M(v/T)v = Mv²/T, which is a different option. Step 6 — Working: The pri…