Question

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?

Answer 1

A.) 1430 metres

B.) 80 seconds

Step-by-step 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