Final answer:
The formula 'd = v²/2a' is used to calculate the distance needed to stop a vehicle or the distance traveled while accelerating, which is essential for vehicle safety.
Step-by-step explanation:
The formula for figuring out the impact and braking distance from a speed increase is d = v²/2a, where d is the distance, v is the velocity, and a is the acceleration (or deceleration if braking). This formula derives from the basic equations of motion under constant acceleration, specifically the kinematic equation v² = v0² + 2a(x - x0), which relates the square of the velocity to the acceleration and the displacement covered.
For a vehicle starting from rest (v0 = 0), the distance traveled after accelerating to a certain velocity can be determined using this formula, and the braking distance when decelerating to a stop (final velocity v = 0) can likewise be calculated. This understanding is crucial for safety reasons, which is evidenced by reduced speed zones near schools to ensure that vehicles can stop safely within a shorter distance.