Work Energy Power

JEE Main level, single correct, medium

158 of 183

Question 158 of 183

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time tt is proportional to :-

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Answer: (B) t32{t}^{\dfrac{3}{2}}

P=CP=C⇒FV=C\Rightarrow FV=C⇒MdVdtV=C\Rightarrow M\dfrac{dV}{dt}V=C
⇒V22∝t\Rightarrow \dfrac{{V}^{2}}{2}\propto t
⇒V∝t1/2\Rightarrow V\propto {t}^{1/2}
⇒dxdt∝t1/2\Rightarrow \dfrac{dx}{dt}\propto {t}^{1/2}
⇒x∝t3/2\Rightarrow x\propto {t}^{3/2}

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