What is the distance between the stations?

Question

A light-rail train going from one station to the next on a straight section of a track accelerates from rest at 1.0 m/s^2 for 20 s. It then proceeds at constant speed for 2100 m before slowing down at 2.0 m/s^2 until it stops at the station. What is the distance between the stations?

Answer 1

Let's break the problem up into three segments

• segment 1 is distance traveled while the train is accelerating at 1 m/s²
• segment 2 is the distance traveled at constant speed - given as 2100 m
• segment 3 is the distance traveled while decelerating at 2 m/s²

 

In segment 1, the distance that the train moves while accelerating at 1 m/s² for 20 seconds is:

 

     distance₁ = (1/2)*a*t² = (1/2)(1 m/s²)(20 s)² = 200 m

 

     The speed it attains is:

 

     speed = a*t = (1 m/s²)(20 s) = 20 m/s

 

In segment 2, we are given distance₂ = 2100 m. 

 

In segment 3, the train then decelerates at 2 m/s² from a speed of 20 m/s until it stops, speed = 0.  So the train must decelerate by 20 m/s:

 

     a*t = 20 m/s

     (2 m/s²)*t = 20 m/s

     t = 10 sec

 

    So the distance the train traverses while decelerating at 2 m/s² is:

 

    distance₃ = (1/2)*a*t² = (1/2)(2 m/s²)(10 s)² = 100 m

 

The total distance between the stations is the sum of the three distances:

 

     distance between stations = distance₁ + distance₂ + distance₃

         = 200 m + 2100 m + 100 m

         = 2400 m