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

The distance covered by both the cars is the same .Thus ,`s_(1)=s_(2)=s.`
If the cars take time `t_(1)` and `t_(2)` for the race and their velocities at the finish be `v_(1)` and `v_(2)` ,then it is given that
`(v_(1))/(2)t_(1)`=s……….(1)
and `(v_(2))/(2)t_(2)=s`.........(2)
`therefore (v_(1))/(t_(2))=(v_(2))/(t_(1))=(v_(1)-v_(2))/(t_(2)-t_(1))=(v)/(t)` ............(3)
`((v)/(t))^(2)=(v_(1)v_(2))/(t_(2)t_(1))=(v_(1))/(t_(1)).(v_(2))/(t_(2))`..........(4)
`therefore(v)/(t)=sqrt(a_(1)a_(2))impliesv=t sqrt(a_(1)a_(2))`