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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 acceleration a_(1) and a_(2),show that (v)/(t)=sqrt(a_(1)a_(2)). |
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Answer» Solution :Let s be the distance covered b y each car.Let the times taken by the two cars to complete the journey be `t_(1)` and `t_(2)` , and their velocity 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_(1)))/(sqrt(1)/(a_(2))-sqrt(1)/(a_(1)))` |
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