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Work Energy Power

JEE Main level, single correct, medium

157 of 183

Question 157 of 183

An automobile of mass $m$ accelerates starting from the origin and initially at rest, while the engine supplies constant power $P$ . The position is given as a function of time by:

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Answer: (D) ${\left(\dfrac{8P}{9m}\right)}^{\dfrac{1}{2}}{t}^{\dfrac{3}{2}}$

P=const

P={F}_{V}=\dfrac{m{v}^{2}dv}{dx}

{\int }_{0}^{x}\dfrac{P}{m}dx={\int }_{0}^{v}{v}^{2}dv

\dfrac{Px}{m}=\dfrac{{v}^{3}}{3}

{\left(\dfrac{3Px}{m}\right)}^{\dfrac{1}{3}}=v=\dfrac{dx}{dt}

{\left(\dfrac{3P}{m}\right)}^{\dfrac{1}{3}}{\int }_{0}^{t}dt={\int }_{0}^{x}{x}^{-\dfrac{1}{3}}dx

\Rightarrow x={\left(\dfrac{8P}{9m}\right)}^{\dfrac{1}{2}}{t}^{\dfrac{3}{2}}

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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JEE Main Physics practice question on Work Energy Power (Power), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.

An automobile of mass mmm accelerates starting from the origin and initially at rest, while the engine supplies constant power PPP. The position is given as a function of time by:

JEE Main question paper PDF

More Physics practice

An automobile of mass $m$ accelerates starting from the origin and initially at rest, while the engine supplies constant power $P$ . The position is given as a function of time by: