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}}$