Question

At time t=0 s a particle starts moving along the x- direction. If its kinetic energy increases uniformly with time 't', 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 $\frac{1}{\sqrt{t}}$

Given, $K\propto t⟹\frac{dK}{dt}=constant$

$K\propto t$

$K=\frac{1}{2}m{v}^2⟹v\propto \sqrt{t}$

Also, $P=Fv=\frac{dK}{dt}=constant$

$F\propto \frac{1}{v}⟹F\propto \frac{1}{\sqrt{t}}$