Two cars 1 and 2 move with velocities v1 and v2 respectively on a straight road in the same direction. When the cars are separated by a distance d, the driver of the car 1 applies brakes and the car moves with uniform retardation a1. Simultaneously, the car 2 starts accelerating with a2. If v1>v2, find the minimum initial separation between the cars to avoid collision between them.

Two cars 1 and 2 move with velocities v1 and v2 respectively on a stra

1.	Two cars 1 and 2 move with velocities v1 and v2 respectively on a straight road in the same direction. When the cars are separated by a distance d, the driver of the car 1 applies brakes and the car moves with uniform retardation a1. Simultaneously, the car 2 starts accelerating with a2. If v1>v2, find the minimum initial separation between the cars to avoid collision between them.
Answer» Two cars 1 and 2 move with velocities $v_{1} a n d v_{2}$ respectively on a straight road in the same direction. When the cars are separated by a distance d, the driver of the car 1 applies brakes and the car moves with uniform retardation $a_{1}$ . Simultaneously, the car 2 starts accelerating with $a_{2}$ . If $v_{1} > v_{2}$ , find the minimum initial separation between the cars to avoid collision between them.

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