The train began to decelerate at a speed of 54 km / h, before reaching the semaphore 200 m.

| May 24, 2021 | education

The train began to decelerate at a speed of 54 km / h, before reaching the semaphore 200 m. The train mass is 2000 tons; when braking, a friction force of 2 MN acts. At what distance from the semaphore was the train 10 s after the start of braking, 30 s?

Task data: V0 = 54 km / h (in SI V0 = 15 m / s); S = 200 m; m = 2000 t (in SI m = 2 * 10 ^ 6 kg); Ftr. = 2 MH (2 * 10 ^ 6 H); t1 = 10 s; t2 = 30 s.

1) Acceleration: m * a = Ftr. and a = Ftr. / m = 2 * 10 ^ 6 / (2 * 10 ^ 6) = 1 m / s2.

2) Deceleration time: t = V0 / a = 15/1 = 15 s.

3) Distance after 10 s: L1 = S – S1 = S – V0 * t1 + 0.5 * a * t1 ^ 2 = 200 – 15 * 10 + 0.5 * 1 * 10 ^ 2 = 100 m.

4) Distance after 30 s (actually 15 s): L1 = S – S2 = S – V0 * t2 + 0.5 * a * t2 ^ 2 = 200 – 15 * 15 + 0.5 * 1 * 15 ^ 2 = 87.5 m.



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