A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to: - Physics MCQ AIEEE 2003 2026 | ExamTest.live | ExamTest.live

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A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to:

A $t^{3/4}$
B $t^{3/2}$
C $t^{1/4}$
D $t^{1/2}$

Solution & Step-by-step Explanation

Power P = F v = ma \cdot v = m \frac{d v}{d t} v .If P is constant: v d v = \frac{P}{m} d t Integrating: \frac{v ^{2}}{2} = \frac{P}{m} t ⟹ v \propto t^{1/2} .Since v = \frac{d x}{d t} \propto t^{1/2}, integrating again gives: x \propto t^{3/2}

Practice this question

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A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to:

A

t^{3/4}

B

t^{3/2}

C

t^{1/4}

D

t^{1/2}

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