The train, moving downhill, covered 160 m in 10 seconds and developed a speed of 17 m / s.

The train, moving downhill, covered 160 m in 10 seconds and developed a speed of 17 m / s. What was the speed of the train at the start of the incline?

t = 10 s.
S = 160 m.
V = 17 m / s.
V0 -?
Since the train moves with constant acceleration, the formula for determining the displacement is valid for it: S = V0 * t + a * t ^ 2/2.
We find the acceleration of the train by the formula: a = (V – V0) / t.
S = V0 * t + (V – V0) * t / 2.
2 * S = 2 * V0 * t + V * t – V0 * t.
2 * S = 2 * V0 * t + V * t – V0 * t.
2 * S = V0 * t + V * t.
V0 = (2 * S – V * t) / t.
V0 = (2 * 160 m – 17 m / s * 10 s) / 10 s = 15 m / s.
Answer: at the beginning of the slope, the train speed was V0 = 15 m / s.