SPEED Primary 6 Mathematics. Speed 2 Chapter Learning Outcomes At the end of this chapter, pupils will be able to: Interpret speed as the distance travelled

SPEEDSPEED

Primary 6 Mathematics

2

SpeedSpeed

Chapter Learning OutcomesChapter Learning Outcomes

At the end of this chapter, pupils will be able to:

Interpret speed as the distance travelled per unit of time

Calculate distance travelled given speed and time taken

Calculate average speed given distance travelled and time taken

Calculate time taken given speed and distance travelled

Solve word problems involving speed

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SpeedSpeed

For example,

Speed is the distance travelled in one unit of time.

Interpret speed as the distance travelled Interpret speed as the distance travelled per unit of timeper unit of time

km/h

m/min

m/s

cm/s

Speed can be expressed in different units.

Speed involves 2 entities: Distance covered : Time taken

Can you name other units that can be used to express speed?

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SpeedSpeed

Mr Ahmad is making a delivery. He is running late. How fast is he travelling?

The speedometer shows that Mr Ahmad is travelling at 60 kilometres an hour.

We say that the speed of the truck is 60 kilometres per hour.

We write 60 kilometres per hour as 60 km/h.


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SpeedSpeed

Example 1


a) Ivy throws a paper aeroplane and it travels 4 m in 1 second.Its speed is 4 m/s.

b) A ball rolls 90 cm in 1 minute. Its speed is .

c) A flock of birds fly a distance of 70 km in 1 hour.Their speed is .

a) A swimmer swims 30 m in 1 min. His speed is .

90 cm/min

70 km/h

30 m/min

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SpeedSpeed

Interpret speed as the distance travelled Interpret speed as the distance travelled

per unit of timeper unit of time

Example 2

The distance between Town X and Town Y is 650 km. A motorist takes 13 hours to travel from Town X to Town Y. What is the speed of the motorist?

Distance = 650 km

Time = 13 h

Speed = Distance ÷ Time

= 650 ÷ 13

= 50 km/h

The speed of the motorist is 50 km/h.

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S T

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SpeedSpeedCalculate distance travelled given speed Calculate distance travelled given speed and time takenand time taken

Distance travelled = Speed × Time taken

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SpeedSpeed

Example 1

A tortoise moves at a speed of 20 cm/h. At this speed, how far does it move in 2 h?

Calculate distance travelled given speed Calculate distance travelled given speed and time takenand time taken

Speed = 20 cm/h

Time = 2 h

Distance = Speed Time = 20 2

= 40 cm/h

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The snail moves 40 cm in 2 h.

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SpeedSpeed

Example 2Shuling walks from her home to the market at a speed of 5 km/h. She takes 15 minutes to reach the market. What is the distance between her home and the market? Give your answer in km and m.

Calculate distance travelled given speed Calculate distance travelled given speed and time takenand time taken

Speed = 5 km/h

Time = 15 min = h4

1

Distance = Speed Time

4

5

4

15

The distance between her home and the market is 1 km 250 m.

= km = 1 km 250 m4

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SpeedSpeedCalculate average speed given distance Calculate average speed given distance travelled and time takentravelled and time taken

We use the concept of average speed as things do not move at a constant/same speed all the time.

What is Average Speed?

Average speed is the average distance travelled per unit of time.

Average speed = Total distance travelled ÷ Total time taken

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SpeedSpeed

Example 1 Sharifa takes 2 min to swim a distance of 50 m. Find her average speed in m/min.

Average speed = Total distance ÷ Total time

= 50 ÷ 2

= 25 m/min

Sharifa’s average speed is 25 m/min.

Calculate average speed given distance Calculate average speed given distance

travelled and time takentravelled and time taken

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SpeedSpeed

Example 2Point W and Point X are 105 m apart. Point X and Point Y are 235 m apart. Gerald runs from Point W to Point X in 18 s. Then he runs from Point X to Point Y in 50 s. Find Gerald’s average speed for the distance from Point W to Point Y.

W X Y

105 m, 18 s 235 m, 50 s

? m/s

Total time taken = 18 + 50 = 68 s

Total distance = 105 + 235 = 340 m

Average speed = 340 ÷68 = 5 m/s

Gerald’s average speed from Point W to Point Y is 5 m/s.

Calculate average speed given distance Calculate average speed given distance

travelled and time takentravelled and time taken

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SpeedSpeedCalculate time taken given speed and Calculate time taken given speed and

distance travelleddistance travelled

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We can calculate the total time taken for a journey, given the speed and

distance travelled.

Total time taken =Total distance travelled ÷ Average speed

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SpeedSpeed

Example 1

= 3901 ÷ 765

≈ 5 h

It takes about 5 h to fly from Singapore to Perth.

Time = Distance travelled ÷ Average speed

The distance from Singapore to Perth is 3901 km. How long does an aeroplane with an average speed of 765 km/h take to fly from Singapore to Perth? Express your answer correct to the nearest hour.

Calculate time taken given speed and Calculate time taken given speed and


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SpeedSpeed

Example 2Car A and Car B are travelling to Town Z which is 252 km away. Car A travels at a speed of 60 km/h while Car B travels at a speed of 78 km/h. How long do Car A and Car B take to reach Town Z?

Time taken by Car A = 252 ÷ 60

h 133

3

h 51

4

Time taken by Car B = 252 ÷ 78

Car A takes to reach Town Z.

Car B takes to reach Town Z.

h 51

4

h 133

3

Car A

Car B

Calculate time taken given speed and Calculate time taken given speed and


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SpeedSpeed

Example 1

Solving word problems involving SpeedSolving word problems involving Speed

Miss Lim drove 240 km from Town A to Town B. She took 1.2 h for the first 100 km. For the remaining journey, she drove at an average speed of 70 km/h. What was her average speed for the whole journey?

Town A X Town B

100 km, 1.2 h 140 km, 70 km/h

? km/h

Time taken for the next 140 km = 140 ÷ 70= 2 h

Time taken for the whole journey = 1.2 + 2= 3.2 h

Average speed for the whole journey = 240 ÷ 3.2

= 75 km/h

Her average speed for the journey was 75 km/h.

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SpeedSpeed

Example 2


41

3

43

21

2

a) Total time taken

Sim Keong travelled of his journey in h. He travelled the remaining 116 km in h.a) Find the total time taken for the whole journey.b) Find the average speed for the whole journey

3

1

43

2

12

Total time taken is h.41

3 41

3

b) 2 units 116 1 unit 116÷2 = 58 km 3 units 58 3

= 174 km Average speed = 174 ÷ =

137

53

Average speed for the whole journey is h.

137

53

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SpeedSpeed


Example 3A scooterist took 5 h to travel from Town A to Town B at an average speed of 48 km/h. A car took 1 h less for the same journey. Find the average speed of the car.

Town A Town B

scooter48 km/h, 5 h

car? km/h, 4 h

Distance from Town A to Town B 548 = 240 km

Average speed of the car = 240÷4= 60 km/h

The average speed of the car is 60 km/h.

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Reference - Reference - TextbooksTextbooks

Learning OutcomesInterpret speed as the distance travelled per unit of time

6B p.2–3 6A p.92

Calculate distance travelled given speed and time taken

6A p.3–6 6A p.93–95

Calculate average speed given distance travelled and time taken

6A p.6–19 6A p.95–96

Calculate time taken given speed and distance travelled

6A p.7–19 6A p.96

Solving word problems involving Speed 6A p.20–27 6A p.97–102

Documents

SPEED Primary 6 Mathematics. Speed 2 Chapter Learning Outcomes At the end of this chapter, pupils will be able to: Interpret speed as the distance travelled