# The train, traveling at a speed of 54 km / h, stops 2 minutes after braking.

The train, traveling at a speed of 54 km / h, stops 2 minutes after braking. Determine the braking distance if the acceleration is 0.5 m / s2

Given: V0 (speed before braking) = 54 km / h (in SI V0 = 15 m / s); t (time to complete stop) = 2 minutes (in SI t = 120 s); a (acceleration) = 0.5 m / s2.

1) Let’s specify the acceleration: V = 0 = V0 – a * t = 15 – 120 * 0.5 = 15 – 60 = -45 m / s (incorrect). Let us assume that a = V0 / t = 15/120 = 0.125 m / s2.

2) Calculate the braking distance:

a) S = V0 * t – 0.5 * a * t ^ 2 = 15 * 120 – 0.5 * 0.125 * 1202 = 900 m.

b) S = (V + V0) * t / 2 = (0 + 15) * 120/2 = 900 m.

c) S = (V ^ 2 + V0 ^ 2) / 2a = (0 + 15 ^ 2) / (2 * 0.125) = 900 m.

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