The car was traveling at a speed of 30 m / s. In front of a dangerous section of the road, he dropped his speed

The car was traveling at a speed of 30 m / s. In front of a dangerous section of the road, he dropped his speed to 10 m / s. In this case, the braking distance of the car was 200 m. What is the braking time of the car and its acceleration during braking?

Path x with uniformly accelerated motion: x = v₀t + at² / 2, where v₀ is the initial speed, t is time, and is acceleration. Acceleration by definition is equal to: a = (v – v₀) / t, where v is the final speed. x = v₀t + ((v – v₀) * t²) / 2t; Reduce by t and multiply both sides by 2: 2x = 2v₀t + ((v – v₀) * t); 2x = 2v₀t + vt – v₀t = v₀t + vt; t = 2x / (v₀ + v) = 400 m / (30 m / s + 10 m / s) = 10 s. a = (10 m / s – 30 m / s) / 10 s = -2 m / s.
Answer: t = 10 s, a = -2 m / s (“minus” because the speed was falling).