In a car race, car A takes less time to finish than car B and passes finishing point with a velocity $v_0$ more than velocity of car B and $t_0$ time earlier than car B. The cars starts from rest and travel with acceleration $a_1$ and $a_2$ respectively. Then ratio of $\large\frac{v_0}{t_0}$ is

Question

\[(a)\;\frac{a_1^2}{a_2}\quad (b)\;\frac{a_1+a_2}{2} \quad (c)\;\frac{{a_2}^2}{a_1} \quad (d)\sqrt {a_1a_2}\]