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.
For constant power
Displacement \(d \propto{t}^{3 / 2}\)
Because \({P}=\frac{\vec{F} \cdot d \vec{s}}{d t}=\vec{F} \cdot \vec{v}=~\text{constant}~~~(\because {P}=\text{constant according to the problem})\)
Now, will use dimensional analysis;
\({[{F}][{V}]=\text { constant }} \)
\(\Rightarrow\left[{MLT}^{-2}\right]\left[{LT}^{-1}\right]=\text { constant } \)
\(\Rightarrow {L}^2 {T}^{-3}=\text { constant }(\because \text { mass is constant }) \)
\(\Rightarrow {L} \propto{T}^{3 / 2}\)
\(\Rightarrow \text{displacemnt}~~d \propto{t}^{3 / 2}\)
Hence, option (2) is the correct answer.
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