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

Power $P=Fv=m\left(\frac{dv}{dt}\right)v$

Since power is constant, integrating both sides gives:

$m\int vdv=\int Pdt$

$\frac{1}{2}m{v}^2=Pt$

$v={\left(\frac{2P}{m}\right)}^{1/2}{t}^{1/2}$

Since $v=\frac{dx}{dt}$, we have:

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

Integrating both sides with respect to time $t$ from $t=0$ to $t$:

$x=\int {\left(\frac{2P}{m}\right)}^{1/2}{t}^{1/2}dt$

$x={\left(\frac{2P}{m}\right)}^{1/2}\frac{t^{3/2}}{3/2}$

Therefore, $x\propto t^{3/2}$

Answer: $t^{3/2}$