Two particles start moving from the same point in a straight line. The first moves with constant velocity v and second moves with constant acceleration a. During the time that elapses before the second catches the first, the greatest distance between the particle is

Question

$$(a)\;\frac{v^2}{a}\quad (b)\;\frac{v^2}{2a} \quad (c)\;\frac{2v^2}{a} \quad (d)\frac{v^2}{4a}$$