A body starts from rest and is accelerated by a force F=kt(N). Options given below show the variation of power with time. Find the correct option related to the above case.
A
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B
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C
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D
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Solution
The correct option is C Given F=kt Let mass of car be m Then, F=ma=kt ⟹a=kt/m ⟹dvdt=ktm
Integrating both sides: ∫v0dv=∫t0ktmdt (since body starts from rest, v=0 at t=0 ⟹v=kt22m
Instantaneous power at time t, P=F.v=kt.kt22m=k2t32m ∴P∝t3 This implies that the graph starts from origin and has a cubic curve, hence option (c) is correct.