Question

At time $t=0s$, 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 $\frac{1}{\sqrt{t}}$

Given K. E = $\frac{1}{2}m{v}^2\propto t$
$\Rightarrow v\propto \sqrt{t}$

Work done = Force $\times$ displacement = $\Delta K.E$

Displacement = $\int vdt\propto t^{3/2}$

Therefore, Force $\propto \frac{t}{t^{3/2}}$
Force $\propto t^{-1/2}$