The train moving at a speed of 72 km / h starts to brake and moving equally

The train moving at a speed of 72 km / h starts to brake and moving equally slows down in 30 seconds. What is the distance the train will take for braking?

V0 = 72 km / h = 20 m / s.

V = 0 m / s.

t = 30 s.

S -?

The movement of a train during braking can be considered uniformly slowed down.

When moving with constant acceleration (braking), the path S traveled by the train is determined by the formula: S = V0 * t – a * t2 / 2, where V0 is the initial speed of the train, t is the time of movement of the train, a is the acceleration of the train.

According to the definition, the acceleration a shows how quickly the speed of the train changes during movement: a = (V0 – V) / t.

Since the train stops, then its final speed V = 0 m / s, the formula will take the form: a = V0 / t.

a = 20 m / s / 30 s = 0.67 m / s2.

S = 20 m / s * 30 s – 0.67 m / s2 * (30 s) 2/2 = 600 m – 301.5 m = 298.5 m.

Answer: to a full stop, the train will travel the path S = 298.5 m.