Question

Figure shows the acceleration-time graph of a particle moving along a straight line. After what time the particle acquires its initial velocity?

Answer 1

The area under the a-t curve gives the change in velocity.
So, positive area = negative area
$\Rightarrow \frac{1}{2}(2+1)\times 2=\frac{1}{2}\times t_o\times 2t_o$
$\Rightarrow 3={t_o}^2\Rightarrow t_o=\sqrt{3}s$
So, total time $=2+\sqrt{3}s$