Two cars A and B are travelling in the same direction with velocities v1 and v2(v1>v2) 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
Initial relative velocity =v1−v2, final relative velocity=0
From v2=u2−2as⇒0=(v1−v2)2−2×a×s
⇒s=(v1−v2)22a
If the distance between two cars 's' then collision will take place.To avoid collision d>s
∴d>(v1−v2)22a
where d=actual initial distance between two cars.