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In a car race, car A takes $t_{0} time less to finish than car B and passes the finishing point with a velocity v_{0}$ more than car B. The cars start from rest and travel with constant acceleration $a_{1} and a_{2} . Then the ratio \frac{v_{o}}{t_{o}} is equal to$

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$\frac{{a_{1}}^{2}}{a_{2}}$

$\frac{a_{1} + a_{2}}{2}$

$\sqrt{a_{1} a_{2}}$

$\frac{{a_{2}}^{2}}{a_{1}}$

answer is C.

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Detailed Solution

Let s be the distance traveled by each car.

Then

$\sqrt{2 a_{1} s} - \sqrt{2 a_{2} s} = v_{0} and; \sqrt{\frac{2 s}{a_{2}}} - \sqrt{\frac{2 s}{a_{1}}} = t_{0}$

$∴ \frac{v_{o}}{t_{o}} = \frac{\sqrt{a_{1}} - \sqrt{a_{2}}}{\frac{1}{\sqrt{a_{2}}} - \frac{1}{\sqrt{a_{1}}}} = \sqrt{a_{1} a_{2}}$

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