STD 11 - 5. work,energy,power and collision — NEET STD 11 Science — Question

$P=\text { const. }$

$P=F v=\frac{m v^{2} d v}{d x}$

$\int_{0}^{x} \frac{P}{m} d x=\int_{0}^{v} v^{2} d v$

$\frac{P x}{m}=\frac{v^{3}}{3}$

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

$\left(\frac{3 P}{m}\right)^{1 / 3} \int_{0}^{t} d t=\int_{0}^{x} x^{-1 / 3} d x$

$\Rightarrow x=\left(\frac{8 P}{9 m}\right)^{1 / 2} t^{3 / 2}$