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A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to
(i) $t^{1 / 2}$
(ii) $t$
(iii) $t^{3 / 2}$
(iv) $t^2$
(i) $t^{1 / 2}$
(ii) $t$
(iii) $t^{3 / 2}$
(iv) $t^2$
Solution:
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Verified Answer
$P=F \times v=\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{LT}^{-1}\right]=\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right]$ $=$ constant
$\therefore \quad \mathrm{L}^2 \mathrm{~T}^{-3}=$ constant $\Rightarrow \frac{\mathrm{L}^2}{\mathrm{~T}^3}=$ constant $\Rightarrow \quad \mathrm{L}^2 \propto T^3 \Rightarrow \mathrm{L} \propto T^{3 / 2}$
$\Rightarrow \mathrm{L}^2 \propto T^3 \Rightarrow \mathrm{L} \propto T^{3 / 2}$ $\therefore \quad$ Displacement is proportional to $t^{3 / 2}$.
$\therefore \quad \mathrm{L}^2 \mathrm{~T}^{-3}=$ constant $\Rightarrow \frac{\mathrm{L}^2}{\mathrm{~T}^3}=$ constant $\Rightarrow \quad \mathrm{L}^2 \propto T^3 \Rightarrow \mathrm{L} \propto T^{3 / 2}$
$\Rightarrow \mathrm{L}^2 \propto T^3 \Rightarrow \mathrm{L} \propto T^{3 / 2}$ $\therefore \quad$ Displacement is proportional to $t^{3 / 2}$.
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