The train stopped 20 s after the start of braking, having passed this time 120 m.

The train stopped 20 s after the start of braking, having passed this time 120 m. Determine the initial speed of the train and the acceleration of the train.

V = 0 m / s.

t = 20 s.

S = 120 m.

V0 -?

a -?

We will assume that when braking, the train moved with constant acceleration, that is, uniformly accelerated.

Acceleration during deceleration and we express the formula: a = (V0 – V) / t. So the train stopped V = 0 m / s, then a = V0 / t.

We express the braking distance of the train S by the formula: S = V0 * t – a * t2 / 2.

Substitute the first expression into the second.

S = V0 * t – V0 * t2 / 2 * t = V0 * t – V0 * t / 2 = V0 * t / 2.

The train speed at the beginning of braking V0 will be determined by the formula: V0 = 2 * S / t.

V0 = 2 * 120 m / 20 s = 12 m / s.

a = 12 m / s / 20 s = 0.6 m / s2.

Answer: at the beginning of deceleration, the speed of the train was V0 = 12 m / s, it was moving with acceleration a = 0.6 m / s2.