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 accelerations `a_1 and a_2`. Then the ratio `(v_0)/(t_0)` is equal to.

Options

A. `(a_1^2)/(a_2)`
B. `(a_1 + a_2)/(2)`
C. `sqrt(a_1 a_2)`
D. `(a_2^2)/(a_1)`

Answer

C

Explanation

Let `s` be the distance traveled by each car.
Then
`sqrt(2 a_1 s) -sqrt(2 a_2 s) = v_0 and , sqrt((2 s)/(a^2)) - sqrt((2s)/(a_1)) = t_0`
`:. (v_0)/(t_0) = (sqrt(a_1) - sqrt(a_2))/(1/(sqrt(a_2))-(1)/(sqrt(a_1)))= sqrt(a_1 a_2)`.