Two vehicles move one after the other with velocities $v_1$ (the one ahead) and $v_2$ (the one behind). The driver of the second vehicle( at a distance d from the first one) slows down so as to avoid reaching it, thus it suffers a deceleration of modulus a. Which ONE of the following statements is correct?

A) If $v_2-v_1= \sqrt{2ad}$ the second car will reach the first one.

B) Only if $v_2-v_1 > \sqrt{2ad}$ will the second car reach the first one.

C) Only if $v_2-v_1 < \sqrt{2ad}$ will the second car reach the first one.

D) If $v_2-v_1 \gt 0$ there is no value of deceleration $a$ which avoids the meeting between vehicles.

This is what I tried:

As the second car slows down so as not to reach the leading car: $v_{2}>v_{1}$

The velocity of the car going behind is (it is not constant as it is decelerating):

$V_{B}= V_{2} - at$

So as you can see I stated that car2 catches car1 when $V_{B} = V_{1}$ but to be honest I did it because I knew I was going to obtain b) if I did so. So if it is like that, could you explain me why?

Thanks