In a car race, car A takes time t less than car B and passes the finishing point with a velocity v more than the velocity with which car B passes the point. Assuming that the cars start from rest and travel with constant accelerations `a_1` and `a_2` show that `v/t=sqrt(a_1a_2)` .

Explanation

Let s be the distance covered by each car. Let the times taken by the two cars to complete the journey be `t_1` and `t_2` and their velocities at the finishing point be `v_1` and `v_2` respectively.
According to the given problem,
`v_1-v_2=v` and `t_2-t_1=t`
Now, `v/t=(v_1-v_2)/(t_2-t_1)=(sqrt(2a_1s)-sqrt(2a_2s))/(sqrt((2s)/a_2)-sqrt((2s)/a_1))=(sqrta_1-sqrta_2)/(sqrt(1/a_2)-sqrt(1/a_1))`
`therefore v/t =sqrt(a_1a_2)`