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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) . |
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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))/(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))` |
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