The document provides a comprehensive guide on calculating speed, emphasizing the relationship between distance, time, and speed, with standard units being meters per second (m/s) and miles per hour (mph). It includes explanations, examples, and practice tasks for measuring speed, using various units and understanding the mathematical concepts behind speed calculations. The summary highlights that greater speeds result in shorter travel times for fixed distances and covers both theoretical and practical applications of speed measurement.

1. Physics
Unit:
Calculating speed
Moving by force

2. Outcome
I can calculate speed.

3. Keywords
distance
time
speed
metres per second (m/s)
miles per hour (mph)

4. Keywords
Distance is a length between two points, usually measured in metres
(m).
Time is a duration, usually measured in seconds (s).
The speed of an object is the distance it travels each second.
The unit metres per second (m/s) is the standard unit used to
measure speed.
The unit miles per hour is often used to measure vehicles’ speeds.

5. Lesson outline
Faster and slower
Speed calculations
Using other units for speed
Calculating speed

6. Explanation
The speed of an object is a measure of how
fast it is moving.
Faster and slower
A fast object travels a large distance
each second.
A slow object travels a smaller
distance each second.
The higher the speed, the faster the object is travelling.
top speed: 1 mm each second top speed: 600 m each second
snail jet plane

7. True False
Justify your answer
True or false?
T F
Check
a
b
The faster car covers a greater distance each second.
A car travelling fast has a greater speed than a car
travelling slow.
The faster car travels for a shorter time.
Faster and slower

8. Explanation
Two cars have different speeds and travel for 1 s.
Faster and slower
The faster car has travelled a greater distance in the same
amount of time.
faster car at start
slower car at start slower car after 1 s
faster car after 1 s
15 m
10 m

9. Check
Faster and slower
Two toy cars have a race:
● a red car travels 4 meters in 2 seconds
● a green car travels 6 meters in 2 seconds
Which car is travelling at the highest speed?
the red car
the green car
both have the same speed
a
b
c

10. Explanation
Two cars have different speeds and travel 15 m.
Faster and slower
The faster car has travelled the same distance in a shorter time.
faster car at start
slower car at start slower takes 3 s
faster car takes 2 s
15 m

11. Check
Faster and slower
Two toy cars, have a race along a 3 m long track:
● the yellow car takes 4 seconds to reach the end of the track
● the blue car takes 6 seconds to reach the end of the track
Which car was travelling at the highest speed?
the yellow car
the blue car
both have the same speed
a
b
c

12. Task A
Practice
1) Table 1 shows the time it took
five swimmers to complete a
race.
Rank the swimmers in order of
average speed starting with the
highest.
Faster and slower
2) Table 2 shows the distance
joggers ran in 50 minutes.
Rank the joggers in order of
average speed starting with the
highest.
swimmer A B C D E
time (s) 25 26 31 27 28
rank
jogger F G H I J
distance (km) 2.5 3.2 1.8 4.1 4.2
rank
table 1
table 2

13. Task A
Feedback
Faster and slower
1) Table 1 shows the time it took
five swimmers to complete a
race.
Rank the swimmers in order of
average speed starting with the
highest.
2) Table 2 shows the distance
joggers ran in 50 minutes.
Rank the joggers in order of
average speed starting with the
highest.
swimmer A B C D E
time (s) 25 26 31 27 28
rank 1st
2nd
5th
3rd
4th
jogger F G H I J
distance (km) 2.5 3.2 1.8 4.1 4.2
rank 4th
3rd
5th
2nd
1st
table 1
table 2

14. Lesson outline
Faster and slower
Speed calculations
Using other units for speed
Calculating speed

15. Explanation
Speed is usually measured in how many metres an
object will travel in each second.
Speed calculations
The word ‘per’ is used instead of ‘each’:
Metres per second is written as m/s:
● The speed of the car is 5 m/s.
● A car travelling 5 metres each second has a speed of
5 metres per second.

16. Check
a
b
c
d
Which of these is the correct way of showing speed in
metres per second?
Speed calculations
8 metres/sec
8 m/sec
8 meters/s
8 m/s
metres is written as m
seconds is written as s
per (each) is written as /

17. Explanation
The greater the speed of an object, the further it
will travel in a given time.
Speed calculations
The distance travelled can be found using the
speed and the time.
These rules describe a mathematical relationship
between distance, speed and time.

18. Explanation
A cyclist travels at a speed of 3 m/s. What distance do they travel in 6 s?
Speed calculations
3 m every second for 6 s
1 s
3 m
1 s
3 m
1 s
3 m
1 s
3 m
1 s
3 m
1 s
3 m
Speed is the distance travelled every second.
3 m every second × 6 seconds = 18 m
speed × time = distance travelled
6 s
18 m

19. Explanation
A faster cyclist travels at a speed of 3.5 m/s. What
distance do they travel in 6 s?
Speed calculations
3.5 m every second for 6 s
1 s
3.5 m
1 s
3.5 m
1 s
3.5 m
1 s
3.5 m
1 s
3.5 m
1 s
3.5 m
3.5 m every second × 6 seconds = 21 m
speed × time = distance travelled
6 s
21 m

20. Check
a
b
c
A boat travels at a speed of 5 m/s.
What distance does it travel in 4 s?
Speed calculations
4 m
5 m
20 m
1 s
5 m
1 s
5 m
1 s
5 m
1 s
5 m
4 s
20 m
5 m every
second
for 4 s
5 m every
second
×
4
seconds
= 20 m

21. Explanation
The distance travelled by an object moving
at constant speed is given by the speed
equation:
Speed calculations
distance travelled = speed × time

22. Explanation Check
A motorcycle is travelling at a
speed of 6.0 m/s.
How far will it travel in 15 s?
A scooter is travelling at a
speed of 3.5 m/s.
How far will it travel in 22 s?
Speed calculations
distance travelled = speed × time
distance travelled = 6.0 × 15
distance travelled = 90 m
distance travelled = speed × time
distance travelled = 3.5 × 22
distance travelled = 77 m

23. Explanation
The greater the speed of an object, the less time it
takes to travel a certain distance.
Speed calculations
A sprinter running at 10 m/s will
finish a 100 m race in less time
than a sprinter running at 8 m/s.
A horse galloping at 15 m/s will
finish a 3000 m race in less time
than a horse galloping at 13 m/s.
The time taken can be found using the speed equation.

24. Explanation Check
How much time will it take for
a car travelling at 30 m/s to
travel a distance of 96 m?
A toy is travelling at 2.5 m/s.
How much time will it take to
travel a distance of 16 m?
Speed calculations
distance travelled = speed × time
96 = 30 × time
96 ÷ 30 = time
time = 3.2 s
distance travelled = speed × time
16 = 2.5 × time
16 ÷ 2.5 = time
time = 6.4 s

25. Explanation
The speed of an object can also be found using the
speed equation if the distance travelled and the time
taken are known.
Speed calculations
distance travelled = speed × time
Swapping sides:
speed = distance ÷ time
speed × time = distance travelled
Dividing both sides by time gives the equation:

26. Explanation Check
Calculate the speed of a car
when it travels 450 m in 25 s.
A ship travels 1000 m in 125 s.
Calculate the speed of the ship.
Speed calculations
speed = distance ÷ time
speed = 450 ÷ 25
speed = 18 m/s
speed = distance ÷ time
speed = 1000 ÷ 125
speed = 8 m/s

27. Practice
Task B
Use the speed equation to complete this table showing
distance, time and speed.
Speed calculations
moving object distance
(m)
time
(s)
speed
(m/s)
camera drone 20 4.0
athlete 400 8.0
skateboard 60 4.0
sailing boat 391 4.6
aeroplane 21 000 87.5

28. Task B
Feedback
Use the speed equation to complete this table showing
distance, time and speed.
Speed calculations
moving object distance
(m)
time
(s)
speed
(m/s)
camera drone 80 20 4.0
athlete 400 50 8.0
skateboard 60 15 4.0
sailing boat 391 4.6 85
aeroplane 21 000 87.5 240

29. Lesson outline
Faster and slower
Speed calculations
Using other units for speed
Calculating speed

30. Explanation
The unit m/s is not the only one that can be used
for speed.
Using other units for speed
centimetres per second
(cm/s)
kilometres per hour
(km/h)
miles per hour
(miles/h or mph)
Speed is always a distance divided by a time, but any unit of distance
and any unit of time can be used.
toy train motorcycle car

31. Check
a
b
c
d
Which three of these units can be used to measure speed?
Using other units for speed
cm/m
km/s
mm/s
cm/hour

32. Explanation
A car travels a distance of 92 km in a time of 4 hours.
Calculate its speed.
distance = 92 km
Speed, distance and time can be calculated in the same
way as before using the different units.
Using other units for speed
speed = distance ÷ time
speed = 92 ÷ 4
speed = 23 km/h
time = 4 hours

33. Explanation Check
A car travels 320 miles along a
motorway in 5 hours.
Calculate the speed of the car.
A wind-up toy travels 80 cm in
16 s.
Calculate the speed of the toy.
speed = distance ÷ time
speed = 320 ÷ 5
speed = 64 miles/hour
speed = distance ÷ time
speed = 80 ÷ 16
speed = 5.0 cm/s
Using other units for speed

34. Explanation
Units of time or distance can also be converted when
calculating speed to give an answer in m/s.
Using other units for speed
speed = distance ÷ time
speed = 4.4 ÷ 20
A toy train travels 440 cm in a
time of 20 s.
Calculate its speed in m/s.
speed = 0.22 m/s
distance: 440 cm = 4.4 m

35. Check
a
b
c
d
Calculate the speed of a cyclist in km/h if they travel 7.5 km in
15 minutes.
Using other units for speed
113 km/h
30 km/h
22.5 km/h
0.5 km/h
speed = distance ÷ time
speed = 7.5 ÷ 0.25
speed = 30 km/h
15 minutes = ¼ hour = 0.25 hours

36. Practice
Task C
1) Calculate the speeds of the following two objects,
using the units given.
a) A snooker ball which travels 140 cm in 2.5 s.
b) A jet which travels 540 km in 45 minutes.
Using other units for speed
2) A car travels a distance of 80 km in a time of 2 hours.
a) Calculate the speed in km/h.
b) Calculate the speed in m/s.

37. Task C
Feedback
Using other units for speed
1) Calculate the speeds of the following two objects,
using the units given.
b) A jet which travels 540 km in
45 minutes.
a) A snooker ball which travels
140 cm in 2.5 s.
speed = distance ÷ time
speed = 140 ÷ 2.5
speed = 56 cm/s
speed = distance ÷ time
speed = 540 ÷ 45
speed = 12 km/min

38. Task C
Feedback
Using other units for speed
2) A car travels a distance of 80 km in a time of 2 hours.
speed = distance ÷ time
speed = 80 ÷ 2
speed = 40 km/h
speed = distance ÷ time
speed = 80 000 ÷ 7200
speed = 11 m/s
b) Calculate the speed in m/s.
a) Calculate the speed in km/h.
distance travelled = 80 000 m
time = 2 h = 2 × 60 × 60 = 7200 s

39. Summary
The greater the speed of an object:
● the less time it takes to travel a fixed distance
● the greater the distance it travels in a fixed time
Calculating speed
The speed equation is:
distance travelled = speed × time
speed = distance travelled ÷ time
Speed is measured in metres per second (m/s).
It can also be measured in other units of distance per time.

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