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Question
A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shows the displacement-time curve for its motion?
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Solution
Explanation:
For constant power
Displacement ∝ t3/2
Because P = `(vecF * dvecs)/(dt) = vecF * vecv` = constant .....(∵ P = constant according to the problem)
Now, will by dimensional analysis
[F][v] = constant
⇒ [MLT–2][LT–1] = constant
⇒ L2T–3 = constant .....(∵ mass is constant)
⇒ L ∝ T3/2
⇒ Displacement (d) ∝ t3/2
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