When approaching the metro station, the train speed was 64.8 km / h. When braking to a full stop, it traveled 180 m.

When approaching the metro station, the train speed was 64.8 km / h. When braking to a full stop, it traveled 180 m. Determine the acceleration and deceleration time.

These tasks: V0 (train speed before approaching the metro station) = 64.8 km / h (18 m / s); S (train path to a full stop) = 180 m; V (final speed) = 0 m / s.

1) Determine the acceleration of the train during braking: S = (V ^ 2 – V0 ^ 2) / 2a = -V0 ^ 2 / 2a, whence a = -V0 ^ 2 / (2S) = -18 ^ 2 / (2 * 180 ) = -0.9 m / s2.

2) Determine the braking time: V = V0 + a * t, whence t = (V – V0) / a = V0 / a = 18 / (-0.9) = 20 s.

Answer: Braking of the train with an acceleration of 0.9 m / s2 lasted 20 seconds.