Physics - W.E.P. Question with Solution | TestHub

Power $=$ F. V $\mathrm{F}=\mathrm{m}\left(\frac{\mathrm{dV}}{\mathrm{dt}}\right)\Rightarrow \mathrm{m}\cdot \mathrm{v}\cdot \frac{\mathrm{dV}}{\mathrm{dt}}=$ constant $=\mathrm{C}$ $\Rightarrow \frac{\mathrm{dV}}{\mathrm{dt}}=\frac{\mathrm{C}}{\mathrm{m}}=\mathrm{k}\Rightarrow \mathrm{vdv}=\mathrm{kdt}\Rightarrow \int \mathrm{vdv}=\int \mathrm{kdt}\Rightarrow \frac{{\mathrm{V}}^2}{2}=\mathrm{kt}+\mathrm{c}$ $\Rightarrow \mathrm{v}\propto (\mathrm{t}{)}^{1/2}$ $\frac{\mathrm{ds}}{\mathrm{dt}}=\mathrm{c}\cdot {\mathrm{t}}^{1/2}$ $\Rightarrow \int \mathrm{ds}=\int \left(\mathrm{c}\cdot {\mathrm{t}}^{1/2}\right)\mathrm{dt}\Rightarrow \mathrm{S}=\mathrm{C}\cdot \frac{2}{3}{\mathrm{t}}^{3/2}$ $\Rightarrow \mathrm{S}=\frac{{\mathrm{ct}}^{3/2}}{3/2}\Rightarrow \mathrm{s}\propto {\mathrm{t}}^{3/2}$