Speed and velocity of an MTR train [back]

Key Learning Points

  1. position, distance and displacement
  2. scalar and vector quantities
  3. speed and velocity
Teachers' notes: (Zip 175k)

Maps of MTR routes with scales, typical results, suggested answers, students' worksheet.

Introduction

Using a map and simple apparatus, students will be asked to estimate the average speed and average velocity of an MTR train when it is travelling between two neighbouring stations.

Map of MTR routes

The maps below show Tsuen Wan Line and Tung Chung Line.

Tsuen Wan Line (Courtesy: Highway Department, HKSAR)
Fig. 1(a) MTR Tsuen Wan Line (Courtesy: Highway Department, HKSAR)

Tung Chung Line (Courtesy: Highway Department, HKSAR)
Fig. 1(b) MTR Tung Chung Line (Courtesy: Highway Department, HKSAR)

Suggested questions before activity

  1. What is the fastest way to go to school from, say, a shopping center nearby?
  2. "A taxi travels faster than a bus." What is the meaning of this statement?
  3. How to measure the distance between two MTR stations?
  4. How to estimate the average speed and average velocity of the trains?

Procedures

  1. Decide which two neighbouring stations you are going to study.
  2. Download the map showing the MTR routes (prepared by teacher).
  3. Use a thread to fit over the path. Measure the length of the thread needed.
  4. Measure the length of the straight line joining the two stations on the map.
  5. Calculate the distance and displacement between the two stations from the scale given on the map.
  6. Go to one of the selected stations. Use a stopwatch to record the time taken for the train to move from one station to the other.
  7. Repeat step 6 several times and calculate the average time taken.
  8. Then calculate the average speed and average velocity of the train.

Discussion

  1. Is the measured average speed/velocity of the train the same as the instantaneous speed/velocity? Why?
  2. What is the major source of error? How to minimize the error?

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