In a car race , car A takes a time of t s less than car B at finish and passes the finishing point with a velocity v m//s morn than thecar B . Assuming that the cars start from rest and travel with constant accelerations a_(1) "and " a_(2) respectively, show that v=tsqrt(a_(1)a_(2)).

In a car race , car A takes a time of t s less than car B at finish an

1.	In a car race , car A takes a time of t s less than car B at finish and passes the finishing point with a velocity v m//s morn than thecar B . Assuming that the cars start from rest and travel with constant accelerations a_(1) "and " a_(2) respectively, show that v=tsqrt(a_(1)a_(2)).
Answer» SOLUTION :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)/2t_(1)=s`…….(1) and`v_(2)/2t_(2)=s`.....(2) `:. 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) `:. v/t=sqrt(a_(1)a_(2))rArrv=tsqrt(a_(1)a_(2))`