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 problems
`v_(1)-v_(2)=v and t_(2)-t_(1)=t`
Now, `v/t=(v_(1)-v_(2))/(t_(1)-t_(1))=(sqrt(2a_(1)s)-sqrt(2a_(2)s))/(sqrt((2s)/a_(2))-sqrt((2s)/(a_(1))))=(sqrta_(1)-sqrt(a_(2)))/(sqrt((1)/(a_(2))-sqrt((1)/(a_(1)))))`