Calculating speed
Physics
Unit: Moving by force
Outcome
I can calculate speed.
Keywords
distance
time
speed
metres per second (m/s)
miles per hour (mph)
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.
Lesson outline
Calculating speed
Faster and slower
Speed calculations
Using other units for speed
Faster and slower
Explanation
The speed of an object is a measure of how
fast it is moving.
The higher the speed, the faster the object is travelling.
A slow object travels a smaller distance
each second.
snail
top speed: 1 mm each second
A fast object travels a large distance
each second.
jet plane
top speed: 600 m each second
Faster and slower
Check
True or false?
A car travelling fast has a greater speed than a car
travelling slow.
T True
F False
Justify your answer
a
The faster car covers a greater distance each second.
b
The faster car travels for a shorter time.
Faster and slower
Explanation
Two cars have different speeds and travel for 1 s.
15 m
faster car at start
faster car after 1 s
10 m
slower car at start
slower car after 1 s
The faster car has travelled a greater distance in the same
amount of time.
Faster and slower
Check
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?
a
the red car
b
the green car
c
both have the same speed
Faster and slower
Explanation
Two cars have different speeds and travel 15 m.
faster car at start
slower car at start
15 m
faster car takes 2 s
slower takes 3 s
The faster car has travelled the same distance in a shorter time.
Faster and slower
Check
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?
a
the yellow car
b
the blue car
c
both have the same speed
Lesson outline
Calculating speed
Faster and slower
Speed calculations
Using other units for speed
Speed calculations
Explanation
Speed is usually measured in how many metres an
object will travel in each second.
The word ‘per’ is used instead of ‘each’:
● A car travelling 5 metres each second has a speed of
5 metres per second.
Metres per second is written as m/s:
● The speed of the car is 5 m/s.
Speed calculations
Check
Which of these is the correct way of showing speed in
metres per second?
a
8 metres/sec
metres is written as m
b
8 m/sec
c
8 meters/s
d
8 m/s
seconds is written as s
per (each) is written as /
Speed calculations
Explanation
The greater the speed of an object, the further it will
travel in a given time.
The distance travelled can be found using the speed
and the time.
These rules describe a mathematical relationship
between distance, speed and time.
Speed calculations
Explanation
Speed is the distance travelled every second.
A cyclist travels at a speed of 3 m/s. What distance do they travel in 6 s?
1s
1s
1s
1s
1s
1s
6s
3m
3m
3m
3m
3m
3m
18 m
3 m every second
for 6 s
3 m every second
×
6 seconds
=
18 m
speed
×
time
=
distance travelled
Speed calculations
Explanation
A faster cyclist travels at a speed of 3.5 m/s. What
distance do they travel in 6 s?
1s
1s
1s
1s
1s
1s
6s
3.5 m
3.5 m
3.5 m
3.5 m
3.5 m
3.5 m
21 m
3.5 m every second
for 6 s
3.5 m every second
×
6 seconds
=
21 m
speed
×
time
=
distance travelled
Speed calculations
Check
A boat travels at a speed of 5 m/s.
What distance does it travel in 4 s?
a
b
c
4m
5m
20 m
1s
1s
1s
1s
4s
5m
5m
5m
5m
20 m
5 m every
second
for 4 s
5 m every
second
4
seconds
×
= 20 m
Speed calculations
Explanation
The distance travelled by an object moving at
constant speed is given by the speed equation:
distance travelled = speed × time
Speed calculations
Explanation
A motorcycle is travelling at a
A scooter is travelling at a
speed of 6.0 m/s.
speed of 3.5 m/s.
How far will it travel in 15 s?
How far will it travel in 22 s?
distance travelled = speed × time
distance travelled = speed × time
distance travelled = 6.0 × 15
distance travelled = 3.5 × 22
distance travelled = 90 m
distance travelled = 77 m
Check
Speed calculations
Explanation
The greater the speed of an object, the less time it takes
to travel a certain distance.
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.
Speed calculations
Explanation
How much time will it take for a
A toy is travelling at 2.5 m/s.
car travelling at 30 m/s to travel
How much time will it take to
a distance of 96 m?
travel a distance of 16 m?
distance travelled = speed × time
distance travelled = speed × time
96 = 30 × time
16 = 2.5 × time
96 ÷ 30 = time
16 ÷ 2.5 = time
time = 3.2 s
time = 6.4 s
Check
Speed calculations
Explanation
The speed of an object can also be found using the
speed equation if the distance travelled and the time
taken are known.
distance travelled = speed × time
Swapping sides:
speed × time = distance travelled
Dividing both sides by time gives the equation:
speed = distance ÷ time
Speed calculations
Explanation
Calculate the speed of a car
A ship travels 1000 m in 125 s.
when it travels 450 m in 25 s.
Calculate the speed of the ship.
speed = distance ÷ time
speed = distance ÷ time
speed = 450 ÷ 25
speed = 1000 ÷ 125
speed = 18 m/s
speed = 8 m/s
Check
Lesson outline
Calculating speed
Faster and slower
Speed calculations
Using other units for speed
Using other units for speed
Explanation
The unit m/s is not the only one that can be used for
speed.
Speed is always a distance divided by a time, but any unit of distance and
any unit of time can be used.
toy train
centimetres per second
(cm/s)
motorcycle
car
kilometres per hour
(km/h)
miles per hour
(miles/h or mph)
Using other units for speed
Check
Which three of these units can be used to measure speed?
a
cm/m
b
km/s
c
mm/s
d
cm/hour
Using other units for speed
Explanation
Speed, distance and time can be calculated in the same
way as before using the different units.
A car travels a distance of 92 km in a time of 4 hours.
Calculate its speed.
distance = 92 km
speed = distance ÷ time
time = 4 hours
speed = 92 ÷ 4
speed = 23 km/h
Using other units for speed
Explanation
Check
A car travels 320 miles along a
A wind-up toy travels 80 cm in 16
motorway in 5 hours.
s.
Calculate the speed of the car.
Calculate the speed of the toy.
speed = distance ÷ time
speed = distance ÷ time
speed = 320 ÷ 5
speed = 80 ÷ 16
speed = 64 miles/hour
speed = 5.0 cm/s
Using other units for speed
Explanation
Units of time or distance can also be converted when
calculating speed to give an answer in m/s.
A toy train travels 440 cm in a
time of 20 s.
Calculate its speed in m/s.
distance: 440 cm = 4.4 m
speed = distance ÷ time
speed = 4.4 ÷ 20
speed = 0.22 m/s
Using other units for speed
Check
Calculate the speed of a cyclist in km/h if they travel 7.5 km in 15
minutes.
a
113 km/h
15 minutes = ¼ hour = 0.25 hours
b
30 km/h
speed = distance ÷ time
speed = 7.5 ÷ 0.25
c
d
22.5 km/h
0.5 km/h
speed = 30 km/h
Summary Calculating speed
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
Speed is measured in metres per second (m/s).
It can also be measured in other units of distance per time.
The speed equation is:
distance travelled = speed × time
speed = distance travelled ÷ time