The speed of the train moving downhill increased from 15 m / s to 19 m / s.

The speed of the train moving downhill increased from 15 m / s to 19 m / s. The train covered a distance of 340 m. With what acceleration did the train move and how long did it go downhill.

Data: Vн – speed at the beginning of movement of a given train downhill (Vн = 15 m / s); Vк – final speed (Vк = 19 m / s); S – train path (S = 340 m).

1) Duration of movement: S = (Vn + Vk) * t / 2, whence we express: t = 2S / (Vn + Vk) = 2 * 340 / (15 + 19) = 20 s.

2) Train acceleration: a = (Vк – Vн) / t = (19 – 15) / 20 = 0.2 m / s2.

Check: S = Vн * t + a * t2 / 2 = 15 * 20 + 0.2 * 202/2 = 300 + 40 = 340 m (correct).

Answer: The train was moving for 20 s with an acceleration of 0.2 m / s2.