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)anda_(2), show that (v)/(t)=sqrt(a_(1)a_(2)).

In a car race, car A takes time t less than car B and passes the finis

1.	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)anda_(2), show that (v)/(t)=sqrt(a_(1)a_(2)).
Answer» Solution :Let s be the distance covered by each car. Let the times taken by the two CARS to COMPLETE the journey be `t_(1)andt_(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_(1)s)-sqrt(2a_(2)s))/(sqrt((2s)/(a_(2)))-sqrt((2s)/(a_(1))))=(sqrt(a_(1))-sqrt(a_(2)))/(sqrt((1)/(a_(2)))-sqrt((1)/(a_(1))))` `therefore (V)/(t)=sqrt(a_(1)a_(2))`