Find an expression for velocity?

Question

In a car race, car A takes a time of t sec less than car B at the finish and passed the finishing point with a velocity v m/s more than the car B. Assuming that the cars start from rest and travel with constant acceleration a1 and a2 respectively which of the following is correct?

A) v = t√(a1/a2)

B) v = t√(a1.a2)

C) v = t /√(a1.a2)

D) v = t√(a2/a1)

Answer 1

accelaration of a = a1 and b = a2 and time taken = t1 and t2

distance = ½ a1t1^2 = ½ a2t2^2

so

a1t1^2 = a2t^2 … 1

t2= t1+ t --- 2 (given)

now velocity of a = a1t1 and of b = a2 t2

a1t1 = a2t2 + v(given)

we need to eliminate t1 and t2

or v= a1t1-a2t2

= a2t2^2/t1- a2t2 (sing a1 from 1)

= a2t2(t2 –t1)/t1

= a2 t (t2/t1)

= a2 r (a1/a2)^(1/2) ( from 1)

= t sqrt(a2a1)

Hence ans is B