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  4. At time t=0 s 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

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Q. At time $t=0$ s 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

Work, Energy and Power

Solution:

Given, $\frac{d k}{d t}=$ constant
$\Rightarrow k \propto t \Rightarrow v \propto \sqrt{t}$
Also, $P=F v=\frac{d k}{d t}=$ constant
$\Rightarrow F \propto \frac{1}{v} \Rightarrow F \propto \frac{1}{\sqrt{t}}$