JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Work, Power & Energy

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A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

(A) $t^{2}$
(B) $t^{2/3}$
(C) $t^{3/2}$ ✓ Correct
(D)t

Answer: (C)

Solution

Constant power:

P = F v = m v \frac{d v}{d t}

\int_{0}^{v} v d v = \frac{P}{m} \int_{0}^{t} d t ⟹ \frac{v ^{2}}{2} = \frac{P}{m} t ⟹ v \propto t^{1/2}

Since

v = \frac{d s}{d t} \propto t^{1/2}

\int_{0}^{s} d s \propto \int_{0}^{t} t^{1/2} d t ⟹ s \propto t^{3/2}

JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Single correct option

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