Final answer:
The minimum distance D to prevent a collision, when the rear car with initial speed V2 starts to brake with acceleration a, can be calculated using the equation D = V2² / (2a).
Step-by-step explanation:
To determine the minimum distance D required for the rear car not to collide with the car in front, given that the rear car has an initial speed V₂ greater than the front car's speed V₁ and starts to brake with acceleration a, we can use kinematic equations. As the rear car brakes, we must find the point at which it will come to a stop without hitting the car in front.
The stopping distance D can be calculated using the kinematic equation D = V₂² / (2a). This equation assumes the worst-case scenario in which the front car will come to an immediate halt (V₁ = 0) and the rear car will have to brake to a complete stop to avoid a collision.
In a scenario where the second car does not come to a complete stop but maintains a reduced constant velocity, the problem becomes more complex and requires simultaneous equations to solve for both the time and distance before a potential collision occurs.