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. |  |
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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