Fig. 3-2

 Example

A bus travels 2 km to the North in 2 minutes, it turns East and travels at a constant velocity for 5 km in 4 minutes, then it stops for 30 s before a traffic lamp, and finally it travels to the South for 2 km in 2 minutes (Fig. 3-2).

  1. What are the distance and displacement travelled by the bus?
  2. What are the average speed and average velocity for the whole trip?
  3. What is the instantaneous velocity of the bus when it is travelling to the East?

Solution

  1. Total distance = 2 + 5 + 2 = 9 km
    Total displacement = 5 km (to the East)
  2. Average speed =
    Average velocity = (to the East)
  3. Since the bus travels at a constant velocity to the East, its instantaneous velocity =
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Fig. 3-3

 Exercise

Peter travels from Tsim Sha Tsui to Wan Chai by MTR (Fig. 3-3). The MTR train takes 4 minutes to travel a distance of 2.46 km from Tsim Sha Tsui to Admiralty. Peter uses 1 minute to change to the Island line. The train travels 1 km and arrives at Wan Chai in 2 minutes. Then Peter takes 10 minutes to walk a distance of 800 m form Wan Chai MTR station to the Hong Kong Convention and Exhibition Centre.

  1. What are the distance and displacement travelled by Peter?
  2. What are the average speed and average velocity of his whole trip?
  3. What is the average walking speed of Peter?

Answer:

  1. distance: 4.26 km, displacement: 1.57 km to the South.
  2. average speed: 4.17, average velocity: 1.54 to the South.
  3. walking speed of Peter: 1.33 .


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Fig. 3-4

 Exercise

Mary practices running along a track. The track is made up of two semi-circular paths and two straight paths as shown in Fig. 3-4. She runs at a constant speed and completes the track once in 1.5 minutes.

  1. What are the distance and displacement travelled by Mary when she
    1. runs from A to B?
    2. completes the track once?
  1. What are the average speed and average velocity when Mary
    1. runs from A to B?
    2. completes the track once?

Answer:

    1. distance: 200 m, displacement: 114 m in direction of NE
    2. distance: 400 m, displacement: 0
    1. average speed: ; average velocity: in direction of NE,
    2. average speed: , average velocity: 0

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Activity: 1. Speed and velocity of an MTR train    2. Toy train
Flash animation: Toy train showing the difference between speed and velocity
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