How long does it take the train to come to a complete stop?

Question

A train is going from Detroit to New York. As the train approaches its final destination at 160 km/h, the conductor hits the brakes, decelerating the train at a rate of 0.5m/s2 . The train slows down and comes to a complete stop exactly in the middle of the railyard.

How long does it take the train to come to a complete stop?

Answer 1

Since the distance is not required, the time to a complete stop can be found from the following formula:

Vf = -at + Vi, where the acceleration a is negative indicating reverse direction to motion. Since a is in m/s², lets convert the initial speed Vi from km/hr to m/s

Vi = 160 km/hr ( 1000 m/km) ( 1 hr / 3600 s) = 44.4 m/s, and a = 0.5 m/s²

The final velocity when the train comes to a complete stop is 0, Vf =0 Substituting all that in the equation above 0 = -(0.5 m/s²)(t) + 44.4 m/s , substract 44.4 m/s from both sides of the equation and you get:

-44.4 m/s = -0.5 m/s² (t), Divide both sides by -0.5 m/s², then t = (-44.4 m/s / -0.5 m/s²) = 88.8 sec or

1 min 28.8 s

Answer 2

v₀ = 160km/h = 160·1000m/3600s = 44.44 m/s; a = - 0.5 m/s²

v = v₀ + at = 0; t = - v0/t = - 44.44/(- 0.5) = 88.88 s