In a car race, car \( A \) takes a time \( t \) second less than the \( \operatorname{car} B \) ...

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In a car race, car \( A \) takes a time \( t \) second less than the \( \operatorname{car} B \) and passes the finishing point with a velocity \( v \) more than that of the \( \operatorname{car} B \). Assuming that the cars start from rest and travel with constant accelerations \( a_{1} \) and \( a_{2} \) respectively, show that \( v=t \sqrt{a_{1} a_{2}} \)
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