Question

At time t = 0 sec a particle starts moving along the x-axis. If its kinetic energy increases uniformly with time ‘t’, the net force acting on it must be proportional to

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

Answer 1

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

$\frac{dk}{dt}$ = constant or KE $\alpha$ time
$\Rightarrow v\alpha \sqrt{t}$
$Now,P=F.v=constant$
$\Rightarrow F\alpha \frac{1}{v}$
$\Rightarrow F\alpha \frac{1}{\sqrt{t}}$