Q: At time t = 0, 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) √t
(b) constant
(c) t
(d) 1/√t
Ans: (d)
Sol: K ∝ t
K = c t , where c = constant
$ \displaystyle \frac{p^2}{2m} = c t$
$\displaystyle p = \sqrt{2mct} = c’ \sqrt{t}$ , c’ = constant
On differentiatimg w.r.t time ;
$ \displaystyle \frac{dp}{dt} = c’ \frac{1}{2\sqrt{t}}$
$ \displaystyle F \propto \frac{1}{\sqrt{t}}$