The acceleration – time graph of a particle moving along a straight line is shown. After what time in seconds the particle attains its initial velocity?

For  $0\le \mathrm{t}\le 1\mathrm{a}=2\text{ For }\mathrm{t}\ge 1\mathrm{a}=-2\mathrm{t}+4$
Let ‘t’ be the time taken by the particle to attain its initial velocity
$\begin{array}{l}\mathrm{a}=\frac{\mathrm{du}}{\mathrm{dt}}\\ \mathrm{du}=\mathrm{adt}\\ 0={\int }_0^1 2\mathrm{dt}+{\int }_1^{\mathrm{t}} (-2\mathrm{t}+4)\mathrm{dt}\\ {\mathrm{t}}^2-4\mathrm{t}+1=0\Rightarrow \mathrm{t}=2+\sqrt{3}=3.732\sec \end{array}$