Time, Distance and Speed - Complete Notes

TIME

Time is the measure of duration in which an event happens.

Conversions:
1 minute = 60 seconds
1 hour = 60 minutes = 3600 seconds
1 day = 24 hours

DISTANCE

Distance is the length between two points.

1 kilometre = 1000 metres

SPEED

Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed

1 km/h = 5/18 m/s
To convert m/s to km/h multiply by 18/5
To convert km/h to m/s multiply by 5/18

WORKED EXAMPLES

Example 3.26

Question: Convert 2700 seconds to hours.

1 hour = 3600 seconds 2700 ÷ 3600 = 0.75 hours 0.75 = 3/4 hour

Watch Video Explanation

Example 3.27

Question: Convert 2.5 hours to seconds.

1 hour = 3600 seconds 2.5 × 3600 = 9000 seconds

Watch Video Explanation

Example 3.28

Question: Convert 1050 metres to kilometres.

1 km = 1000 m 1050 ÷ 1000 = 1.05 km

Watch Video Explanation

Example 3.29

Question: Convert 10 m/s to km/h.

To convert m/s to km/h multiply by 18/5 10 × 18/5 = 36 km/h

Watch Video Explanation

Example 3.30

Question: Convert 30 m/s to km/h.

30 × 18/5 = 108 km/h

Watch Video Explanation

Example 3.31

Question: Convert 540 km/h to m/s.

To convert km/h to m/s multiply by 5/18 540 × 5/18 = 150 m/s

Watch Video Explanation

Example 3.32

Question: A bus travels 345 km in 6 hours. Find its speed.

Solution: 57.5 km/h

Speed = Distance ÷ Time Speed = 345 ÷ 6 Speed = 57.5 km/h

Watch Video Explanation

Example 3.33

Question: An athlete runs 100 metres in 12.5 seconds. Find speed in m/s and km/h.

Solution: 8 m/s and 28.8 km/h

Speed = Distance ÷ Time Speed = 100 ÷ 12.5 Speed = 8 m/s Convert to km/h: 8 × 18/5 = 28.8 km/h

Watch Video Explanation

Example 3.34

Question: A cyclist travels at 20 km/h for 50 minutes. Find the distance travelled.

Convert 50 minutes to hours: 50 ÷ 60 = 50/60 hours Distance = Speed × Time Distance = 20 × 50/60 Distance = 16.67 km

Watch Video Explanation

Exercise 3.5 Interactive

Exercise 3.5 – Complete Interactive Questions

1(a) Convert 30 minutes to seconds.

1 minute = 60 seconds 30 × 60 = 1800 seconds

1(b) Convert 2 hours to seconds.

1 hour = 3600 seconds 2 × 3600 = 7200 seconds

1(c) Convert 1 hour 30 minutes to seconds.

1 hour = 3600 seconds 30 minutes = 30 × 60 = 1800 seconds Total = 3600 + 1800 = 5400 seconds

1(d) Convert 3.5 hours to seconds.

3.5 × 3600 = 12600 seconds

2(a) Convert 1.6 kilometres to metres.

1 km = 1000 m 1.6 × 1000 = 1600 metres

2(b) Convert 4 kilometres 50 metres to metres.

4 km = 4000 m 4000 + 50 = 4050 metres

3(a) Convert 700 metres to kilometres.

700 ÷ 1000 = 0.7 km

3(b) Convert 3050 metres to kilometres.

3050 ÷ 1000 = 3.05 km

4(a) Convert 5 metres per second to kilometres per hour.

5 × ¹⁸₅ = 18 km/h

4(b) Convert 25 metres per second to kilometres per hour.

25 × ¹⁸₅ = 90 km/h

5(a) Convert 54 kilometres per hour to metres per second.

54 × ⁵₁₈ = 15 m/s

5(b) Convert 126 kilometres per hour to metres per second.

126 × ⁵₁₈ = 35 m/s

6. A car covers 142 kilometres in 2 hours. Calculate its speed in km/h.

Speed = Distance ÷ Time 142 ÷ 2 = 71 km/h

7. A plane is moving at 960 km/h. What distance does it cover in 1 hour 50 minutes?

50 minutes = ⁵⁰₆₀ hours Total time = 1 + 50/60 Distance = 960 × 1.83 = 1760 km

8(a) A cyclist covers 950 metres in 5 minutes. Calculate his speed in metres per second.

5 minutes = 300 seconds Speed = 950 ÷ 300 = 3.17 m/s

8(b) Convert the above speed to kilometres per hour.

3.17 × ¹⁸₅ = 11.4 km/h

9. The speed of a train is 72 km/h. Find its speed in metres per second.

72 × ⁵₁₈ = 20 m/s