A 400-m train is moving on a straight track with a speed of 83.4 km/hr. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 16.4 km/hr. Assuming constant acceleration, how long did the train take to pass the crossing?

The train took 28.9 seconds to pass the crossing.

We first convert km/hr to m/s.

83.4 km/hr × (1000 m/km) × (1 hr / 3600 s) = 23.2 m/s

16.4 km/hr × (1000 m/km) × (1 hr / 3600 s) = 4.56 m/s

Given:

Δx = 400 m

v₀ = 23.2 m/s

v = 4.56 m/s

Then we find t:

Δx = ½ (v + v₀) t

400 m = ½ (4.56 m/s + 23.2 m/s) t

t = 28.9 s

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28.9 seconds

Explanation:

Convert km/hr to m/s.

83.4 km/hr × (1000 m/km) × (1 hr / 3600 s) = 23.2 m/s

16.4 km/hr × (1000 m/km) × (1 hr / 3600 s) = 4.56 m/s

Given:

Δx = 400 m

v₀ = 23.2 m/s

v = 4.56 m/s

Find: t

Δx = ½ (v + v₀) t

400 m = ½ (4.56 m/s + 23.2 m/s) t

t = 28.9 s

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