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An automobile of mass m accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by
Asked in JEE Main 27th July 2nd Shift 2021 · Motion under constant power
- (1) ((8P)/(9m))^1/2t^3/2
- (2) ((9P)/(8m))^1/2t^3/2
- (3) ((8P)/(9m))^1/2t^2/3
- (4) ((9m)/(8P))^1/2t^3/2
Answer: (1) ((8P)/(9m))^1/2t^3/2
Step-by-step solution
1/2mv²=Pt⇒ v=((2P)/m)^1/2t^1/2.
x=∫₀^tv dt=2/3((2P)/m)^1/2t^3/2=((8P)/(9m))^1/2t^3/2.
Why the other options are wrong
- (2) No single slip gives 9P/8m; it merely swaps the 8 and 9 of the correct prefactor.
- (3) Comes from inverting the exponent of t.
- (4) Comes from inverting the whole prefactor; the distance must grow with P.
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