Ncert Exercises & Solutions

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in the figure correctly shows the displacement-time curve for its motion?

1.		2.
3.		4.

Hint: Use dimensional analysis to find the relation between the distance and time.

Step: Identify the correct graph between the displacement-time curve.
As the source supplies constant power i.e., $P = \frac{W}{t}=\text{constant}$
$\Rightarrow \frac{\frac{1}{2}mv^2}{t}= \text{constant}$
$\Rightarrow v^2 \propto t$
$\Rightarrow v = \sqrt{t}$
$\Rightarrow \frac{dx}{dt} = t^\frac{1}{2}$
$\Rightarrow \int{dx}= \int t^\frac{1}{2}{dt}$
$\Rightarrow x = t^{3/2}+ c$
Therefore, the correct graph between the displacement-time curve is shown in the figure below;

Hence, option (2) is the correct answer.

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