Starting from rest a particle is first accelerated for time t_1...

Starting from rest a particle is first accelerated for time $t_1$ with constant acceleration $a_1$ and then stops in time $t_2$ with constant retardation $a_2$. Let $v_1$ be the average velocity in this case and $s_1$ the total displacement. In the second case, it is accelerating for the same time $t_1$ with constant acceleration $2 a_1$ and come to rest with constant retardation $a_2$ in time $t_3$. If $v_2$ is the average velocity in this case and $s_2$ the total displacement, then