Approaching the station, the train starts to slow down with an acceleration of 1m / s ^ 2

Approaching the station, the train starts to slow down with an acceleration of 1m / s ^ 2. Determine the braking distance. Initial speed 72 km / h.

a = 1 m / s2.

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

V = 0 m / s.

S -?

Since the braking of the train occurs with a constant acceleration a, then its braking distance S is expressed by the formula: S = V0 * t – a * t2 / 2, where V0 is the speed of the train at the beginning of braking, t is the braking time.

The braking time t is expressed from the formula for acceleration: a = (V0 – V) / t.

t = (V0 – V) / a.

t = (20 m / s – 0 m / s) / 1 m / s2 = 20 s.

S = 20 m / s * 20 s – 1 m / s2 * (20 s) 2/2 = 200 m.

Answer: the train began to slow down, approaching S = 200 m to the station.