Answer to Question #23497 in Mechanics | Relativity for toriane graal

Question

A train is traveling down a straight track at 26 m/s when the engineer applies the brakes, resulting in an acceleration of −1.0 m/s2 as long as the train is in motion. How far does the train move during a 52-s time interval starting at the instant the brakes are applied?

Answer 1

The train will stop at time t:
v - a*t = 0
a - an acceleration
v - initial speed
t = v/a = 26/1 = 26 seconds
During this time it will cover the distance d:
d = v*t - a*t^2/2 = 26*26 - 1*26*26/2 = 26*13 = 338 m
For the next 26 seconds it will stand still.
Answer: 338 m.