QJEEM23Ph611b: JEE Main 2023 Physics - Class 11 JEEM23Ph611b Solution: A body of mass is initially at rest. It starts moving…

$P = Fv$

$m{{vdv} \over {dt}} = P$

$m\int_0^v {vdv = \int_0^t {Pdt} }$

${{m{v^2}} \over 2} = Pt$

$v = \sqrt {{{2P} \over m}} {t^{1/2}}$

$\int_0^s {dx = \sqrt {{{2P} \over m}} \int_0^t {{t^{1/2}}dt} }$

$s = {2 \over 3}\sqrt {{{2P} \over m}} {t^{3/2}}$

or $s = {2 \over 3}\sqrt {{{2P} \over 2}} \times {4^{3/2}}$

$= {{16} \over 3}\sqrt P ~m$

So, $\alpha = 4$