A block is resting over a rough horizontal floor. At t = 0, time-varying force starts acting on it, the force is described by equation F = kt, where k is constant and t is in seconds. Mark the correct statement(s) for this situation.

For some time, the block would not move due to friction force. 

When F> f_L, the motion of block starts.

$\begin{array}{l}\mathrm{a}=\frac{\mathrm{F}-{\mathrm{f}}_{\mathrm{k}}}{\mathrm{m}}=\frac{\mathrm{kt}-{\mathrm{f}}_{\mathrm{k}}}{\mathrm{m}}\\ \Rightarrow \frac{\mathrm{dv}}{\mathrm{dt}}=\mathrm{a}=\frac{\mathrm{kt}-{\mathrm{f}}_{\mathrm{k}}}{\mathrm{m}}\end{array}$

It is equation of straight line, hence acceleration-time graph is a straight line. It means (2) is correct.

$\mathrm{v}=\frac{\frac{{\mathrm{kt}}^2}{2}-{\mathrm{f}}_{\mathrm{k}}\mathrm{t}}{\mathrm{m}}.$

This is the equation of parabola. Hence (3) is correct.

$\Rightarrow \frac{\mathrm{ds}}{\mathrm{dt}}=\frac{\frac{{\mathrm{kt}}^2}{2}-{\mathrm{f}}_{\mathrm{k}}\mathrm{t}}{\mathrm{m}}\Rightarrow \mathrm{s}=\frac{\frac{{\mathrm{kt}}^3}{6}-\frac{{\mathrm{f}}_{\mathrm{k}}{\mathrm{t}}^2}{2}}{\mathrm{m}}$

The displacement-time relation is cubic. The curve should be more steep, hence (4) is correct.