JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Work, Power & Energy

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A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :

(A) $t^{\frac{3}{4}}$
(B) $t^{\frac{3}{2}}$ ✓ Correct
(C) $t^{\frac{1}{2}}$
(D) $t^{\frac{1}{4}}$

Answer: (B)

Solution

Constant power delivered to a body starting from rest makes its kinetic energy grow linearly with time,

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

, so

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

Since

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

, integrating

d s \propto t^{1/2} d t

gives

s \propto t^{\frac{3}{2}}

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Single correct option

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