A light-rail train going from one station to the next on a straight section of track accelerates from rest at 1.1m/s^2 for 20s. It then proceeds at constant speed for 1100 m before slowing down at 2.2m/s^2 until it stops at the station. a. What is the distance between the stations? b. How much time does it take the train to go between the stations?

A.) 1430 metres

B.) 80 seconds

Explanation:

Given that the train accelerates from rest at 1.1m/s^2 for 20s. The initial velocity U will be:

U = acceleration × time

U = 1.1 × 20 = 22 m/s

It then proceeds at constant speed for 1100 m

Then, time t will be

Time = distance/ velocity

Time = 1100/22

Time = 50 s

before slowing down at 2.2m/s^2 until it stops at the station.

Deceleration = velocity/time

2.2 = 22/t

t = 22/2.2

t = 10s

Using area under the graph, the distance between the two stations will be :

(1/2 × 22 × 20) + 1100 + (1/2 × 22 × 10)

220 + 1100 + 110

1430 m

The time taken between the two stations will be

20 + 50 + 10 = 80 seconds

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