Question

A particle located at $x=0$ at time $t=0$, starts moving along the positive x-direction with a velocity 'v' that varies as $v=\alpha \sqrt{x}$. The displacement of the particle varies with time as?

Answer 1

$v=ax$

$\frac{dx}{dt}=ax$

$\frac{dx}{x}=adt$

${\int }_{ln}^x\frac{dx}{x}=a\int dt$

$x=at+c$

$x=e^{at}+c$