Motion in A Straight Line

Question: Two cars \[A\] and \[B\] are travelling in the same direction with velocities \[{{v}_{1}}\] and \[{{v}_{2}}\]\[({{v}_{1}}>{{v}_{2}})\]. When the car \[A\] is at a distance \[d\] ahead of the car \[B\], the driver of the car \[A\] applied the brake producing a uniform retardation \[a\] There will be no collision when