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

$P=\mathit{F}v=\left(\mathit{\text{ma}}\right)v=m\left(\frac{d^{2}x}{d{t}^2}\right)\left(\frac{dx}{dt}\right)$

Since, power is constant

$\left(\frac{d^{2}x}{d{t}^2}\right)\left(\frac{dx}{dt}\right)=k$

or$\frac{d}{dt}{\left(\frac{dx}{dt}\right)}^2=k$

${\left(\frac{dx}{dt}\right)}^2=k_{1}t$

$\frac{dx}{dt}=\sqrt{k_{1}t}$

$\frac{dx}{dt}=k_2{\left(t\right)}^{1/2}$$\left(\because k_1^{1/2}=k_2\right)$

$x=k_3{t}^{3/2}$$\left(\because k_3=\frac{2}{3}{k}_2\right)$

Hence$\frac{dx}{dt}\propto t^{1/2}\propto x^{1/3}$