Question

At time $t=0s$ a particle starts moving along the $x-$axis. If its kinetic energy increases uniformly with time ${}^{\prime }{t}^{\prime }$, the net force acting on it must be proportional to :

• A. $constant$
• B. $t$
• C. $\frac{1}{\sqrt{t}}$
• D. $\sqrt{t}$

Answer 1

The correct option is C $\frac{1}{\sqrt{t}}$

$KE=kt$

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

$\Rightarrow v=\sqrt{\frac{2k}{m}}\sqrt{t}$

differentiate above equation w.r.t. time

$\frac{dv}{dt}=\sqrt{\frac{2k}{m}}\frac{1}{2\sqrt{t}}$

$a=\sqrt{\frac{k}{2mt}}$

$F_{net}=ma=\sqrt{\frac{mk}{2t}}$