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In a car race, car A takes time t less t...

In a car race, car A takes time t less than car B and passes thre 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 a1 and a2, show that `v/t=sqrt(a_(1)a_(2))`.

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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))`
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