JEE Main 2024 — 5 April, Shift 2 — Question 42

$P=$ costant $\Rightarrow F V=$ constant

$\Rightarrow \mathrm{m} \frac{\mathrm{dV}}{\mathrm{dt}} \mathrm{V}=$

constant $\int_{0}^{\mathrm{V}} \mathrm{VdV}=(C) \int_{0}^{\mathrm{t}} \mathrm{dt}$ $\left(\frac{\mathrm{V}^{2}}{2}\right)=\mathrm{Ct}$

$\mathrm{V} \propto \mathrm{t}^{1 / 2}$

$\frac{\mathrm{ds}}{\mathrm{dt}} \propto \mathrm{t}^{1 / 2}$

$\int_{0}^{\mathrm{s}} \mathrm{ds}=\mathrm{K} \int_{0}^{\mathrm{t}} \mathrm{t}^{1 / 2} \mathrm{dt}$ $S=K \times \frac{2}{3} \mathrm{t}^{3 / 2}$

$S \propto \mathrm{t}^{3 / 2}$

$\therefore$ displacement is proportional to $(t)^{3 / 2}$