JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Work, Power & Energy

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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 '

t

' is proportional to:

(A) $t^{1/2}$
(B)t
(C) $t^{3/2}$ ✓ Correct
(D) $t^{2/3}$

Answer: (C)

Solution

Constant power means

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

is fixed. Integrating from rest,

P t = \frac{1}{2} m v^{2} \Rightarrow v \propto t^{1/2}

Since

v = \frac{d x}{d t}

, integrating once more gives

x \propto t^{3/2}

The distance moved by the box is proportional to

t^{3/2}

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Single correct option

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