Igcse Physics 3ed TR Chapter 2

CAMBRIDGE IGCSE™ PHYSICS: TEACHER’S RESOURCE
2 Describing motion
Teaching plan
Topic Approximate Learning content Resources
number of
learning
hours
2.1 2 hours Core: Coursebook: Section 2.1
Understanding Define speed as distance travelled per unit Understanding speed
speed s Workbook: Chapter 2,
time; recall and use the equation v = __
   
t Understanding speed,
Define velocity as speed in a given direction. Exercise 2.1, Exercise 2.2,
Recall and use the equation Exercise 2.3
total distance
_____________ Practical Workbook:
average speed =        
total time Practical investigation
2.1: Average speed
2.2 2 hours Core: Coursebook: Section 2.2
Distance–time Sketch, plot and interpret distance–time Distance–time graphs
graphs and speed–time graphs (covered here and Workbook: Chapter 2,
in Section 2.3). Distance–time graphs,
Determine from given data or the shape of Exercise 2.4
a distance–time graph or speed–time graph Practical Workbook:
when an object is: Practical investigation
a at rest 2.2: Speed–time graphs
using ticker tape
b moving with constant speed
c accelerating
d decelerating.
(Covered here and in Section 2.3.)
Calculate speed from the gradient of
a straight-line section of a distance–
time graph.
1

number of
learning
hours
2.3 2 hours Core: Coursebook: Section
Understanding Sketch, plot and interpret distance–time 2.3 Understanding
acceleration and speed–time graphs (covered here and acceleration
in Section 2.2). Workbook: Chapter 2,
Determine from given data or the shape of Calculating speed and
a distance–time graph or speed–time graph acceleration, Exercise 2.5
when an object is: and Exercise 2.6
a at rest Practical Workbook:
Practical Investigation
2.2: Speed–time graphs
c accelerating using ticker tape
d decelerating.
Calculate the area under a speed–time
graph to determine the distance travelled
for motion with constant speed or constant
acceleration.
Understand that acceleration and
deceleration are related to changing
speed including qualitative analysis of the
gradient of a speed–time graph.
State that the acceleration of free fall, g,
for an object near to the surface of the
Earth is approximately constant and is
approximately 9.8 m/s2.
Supplement:
Determine from given data or the shape
of a speed–time graph when an object is
moving with:
a constant acceleration
b changing acceleration.
Calculate acceleration from the gradient of
a speed–time graph (covered here and in
Section 2.2).
Know that a deceleration is a negative
acceleration and use this in calculations.
Describe the motion of objects falling in a
uniform gravitational field with and without
air / liquid resistance (including reference to
terminal velocity).
2

number of
learning
hours
2.4 Calculating 2 hours Core: Coursebook: Section 2.4
speed and Calculate speed from the gradient of a Calculating speed and
acceleration straight-line section of a distance–time graph. acceleration
Calculate the area under a speed–time Workbook: Chapter 2,
graph to determine the distance travelled Understanding
for motion with constant speed or acceleration, Exercise 2.5
constant acceleration. Chapter 2, Calculating
speed and acceleration,
Supplement:
Exercise 2.6, Exercise 2.7
Define acceleration as change in velocity
per unit time; recall and use the equation
  ∆v 
a = ___
∆t
Determine from given data or the shape
of a speed–time graph when an object is
moving with:
Calculate acceleration from the gradient of
a speed–time graph.
BACKGROUND LEARNING
• Learners should recall the concept of speed are at rest; they should know that a steeper
from previous courses. line means higher speed.
• Learners should know how to calculate speed • Learners should recall the difference between
from distance travelled and time taken from scalar and vector quantities from Chapter 1.
previous courses. • Learners should know how to measure
• Learners should know that speed is usually distances and times from Chapter 1.
measured in metres per second, but can also • Learners should be familiar with the
be expressed in other units of distance per concept of acceleration from their
unit time, e.g. km/h. everyday experiences.
• Learners should know how to sketch and • Learners should recall from previous courses
interpret distance–time graphs for objects that air resistance acts on objects falling or
travelling at constant speed and objects that moving in the air.
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TEACHING SKILLS FOCUS
Area of focus: Metacognition • Are there any key positions on the line where
Specific focus: Understanding graphs it changes in any way?
The Organization for Economic and Commercial Learners can use the mnemonic device DATA for
Development (OECD), in a report in the year this: Describe, Address, Tell, Analyse.
2000, recognised that the ability to sketch, plot Strategy involves learners thinking about
and interpret graphs is a central part of literacy how to solve a problem, for example by
in reading, science and mathematics. Yet many asking themselves:
learners struggle with the concept of graphs and • What strategy will I use to solve this problem?
graphs involving distance–time and speed–time
can be especially confusing for some. • How will I approach this?
Educational researchers refer to ‘graph sense’ For example, a learner may decide to imagine
as a particular way of thinking. Research in the that they are riding on the object to which the
late 20th century showed that developing graph graph relates. Their journey starts at the origin
sense was much more cognitively demanding and proceeds with time as they go along the
than previously recognised. Learners struggle horizontal axis. The property that changes is
to make the cognitive leap from the basic level shown on the vertical axis. If this is a distance–
of reading the value of a particular point to the time graph, then are they travelling further? Are
higher level of interpreting trends. they showing no change in distance? etc. If this
is a speed–time graph, are they getting faster?
In addition, many learners view graphs in a slower? or maybe showing no change in speed.
very different manner to what we intend. For
example, a graph can be seen as a simple icon Connection means forming links between the
where the line itself has no significance, or current problem and any similar problem that
learners may confuse the height of a line with was solved in the past. This is an example of
the gradient of a line. insight learning, where previously developed
skills are used to solve new problems,
Also in this topic, the distance–time graph and possibly in different contexts. Learners can ask
the speed–time graph look superficially very of themselves:
similar to learners, yet are supposed to convey
very different information. • What graphs have I interpreted before?
Benefits of metacognition: The use of • How did I approach that task?
metacognitive methods can greatly help your • Was I successful?
learners. Research has shown that learners • Can I do the same here?
that receive metacognitive instruction towards
developing graph sense out-perform those who Reflection is the last stage of the process where
do not. learners look at their results or their conclusion
and ask:
Developing your skills using metacognition:
Metacognitive instruction can be divided into • Does my interpretation seem reasonable?
four parts: • Does this make sense in the context of what I
1 comprehension was asked?
2 strategy Try using these methods with your learners. Get
them to work in groups and go through these
3 connection stages, helping each other and discussing their
4 reflection. individual answers to the questions.
Comprehension involves asking questions such as: If used properly, your learners should
• What does the horizontal axis show? develop graph sense more quickly with the
metacognitive approach than without.
• What does the vertical axis show?
Reflection: Once this metacognitive method is
• what does the line show? established, think: where else can you apply it?
• Why does the line show this?
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LANGUAGE SUPPORT
For meanings of key words, please see that velocity is only a more scientific word for
the glossary. speed and actually means the same thing. It is
Learners often use the terms ‘speed’ and worth drawing attention to this, and pointing
‘velocity’ incorrectly. This is because they think out that the two are actually different quantities.
2.1: Understanding speed

LEARNING PLAN
Syllabus learning objectives Learning intentions Success criteria
Core: • Define speed and calculate Learners can state what is

Define speed as distance average speed. meant by the word speed
travelled per unit time; recall and recall and use the
and use the equation equations for speed and
s average speed.
v = __
   
t
Define velocity as speed in a
given direction.
Recall and use the equation
total distance
_____________
average speed =          
total time
Common misconceptions
Misconception How to identify How to overcome
Many learners think that speed n/a Learners may have heard the
and velocity are the same thing. words speed and velocity used
interchangeably in everyday
speech. Hence, before velocity
is explained in physics lessons,
learners may already have the
misconception that velocity
is only a more scientific word
for speed.
Take care when first using the
word velocity in order not to
reinforce this misconception. It
must be introduced as a different
term with a different meaning
from the start. Teachers should
think of this issue in the same
way as they would think of using
the words weight and mass.
5
Starter ideas
1 Coursebook ‘Getting started’ activity (5 minutes)
Resources: ‘Getting started’ activity in Chapter 2 of the Coursebook.
Description and purpose: See Coursebook. Learners who followed the Cambridge Lower Secondary Science
course should recall how to draw a distance–time graph, while others may need to be told what this is.
Remind learners that a sketch graph does not need numbers or units. The common error here is for learners
to think that the distance is all covered uniformly. Point out to them that even if they walk at a constant
speed, they may need to stop, for example, before crossing a road. How will this look on the graph?
What to do next: Learners may not have met speed–time graphs before, but they can be asked to think how
the speed of, for example, a 100 m sprinter changes over the time of the run.
What to do next: Use the activity to check for misconceptions or incomplete prior understanding which may
need to be addressed.
2 Coursebook ‘Science in context’ discussion activity (5–10 minutes)

Resources: ‘Science in context’ discussion activity in Chapter 2 of the Coursebook.
Description and purpose: See Coursebook. The purpose of the activity is to allow learners to think about
average speed rather than the speed of an object at any one instant. All of the examples given will have
speeds that varied. For example, Magellan’s voyage in the 1500s made many stops, so the ship was not
moving constantly for three years. The answer to question 2 is based on both distance and maximum speed.
The boat that is capable of the highest maximum speed could actually have a lower average speed than a
boat that is not capable of such a high maximum speed. Learners could be reminded of, or told, the ancient
story (Aesop fable) of the tortoise and the hare to illustrate this.
What to do next: Use the context as a ‘hook’ to engage learners to the topic.
Main teaching ideas

1 Describing speed (10–15 minutes)
Learning intention: to help learners to understand the concept of speed.
Description and purpose: Begin by asking learners to describe what they understand by the term speed
without using words such as fast or slow. Speed cannot be directly measured. It is one of those quantities
where other things need to be measured and then speed derived from those. Even the speedometer in a
vehicle uses electrical pulses and converts these to a speed display. The speedometer in an aeroplane works
by converting air pressure in an open tube to speed. Measuring the distance travelled and the time taken
is the most common way to determine speed in physics. Explain that the methods for this will be shown in
another activity.
The equation for speed uses distance divided by time. The units always include the word ‘per’, which means
‘in each’. So a speed of 20 kilometres per hour means 20 kilometres are travelled in each hour. The unit of
speed can also be worked out from the unit of distance and the unit of time. For example, an distance in
centimetres and a time in minutes would give a speed unit of centimetres per minute. In science, we almost
always use m/s as the metre and the second are SI units.
The highest possible speed is the speed of light which is 3.0 × 108 m/s. If light could circumnavigate the
Earth, it could do so 7.5 times in 1 second! Einstein famously predicted that it would never be possible for
any object to reach this speed.
Differentiation ideas:
Support – learners can be asked to estimate a typical walking speed in m/s.
Challenge – learners can be asked whether the instantaneous speed of any object can ever be measured
completely accurately (no, as even timing over a very short distance could include speed changes).
Assessment ideas: Learners can understand where the units of speed come from and what the word ‘per’
means in the unit. This can be assessed by giving the class some distance and some time measurements in
different units and asking for them to orally volunteer the unit of speed that each would give. Exercise 2.1 in
the Workbook provides questions which test learners’ understanding of the concept of speed.
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Practical investigation 2.1 in the Practical Workbook provides instructions and structured questions for
learners to carry out and analyse the results from measuring how long learners in a group take to run a set
distance, including drawing a distance–time graph.
2 Determining speed in the laboratory (15–30 minutes)

Learning intention: To allow learners to use different methods to determine the speed of objects in
the laboratory.
Resources: Metre rulers, trolleys, stopwatches, ticker–timer and ticker tape, light gates and timers with
interrupt card, strobe light and long exposure camera (all optional).
Description and purpose: Explain to learners that speed cannot be directly measured. Then ask what
quantities we need to measure to be able to calculate speed (distance and time). Show the trolley and ask
how we might measure these quantities. A suggestion of timing the trolley over a fixed distance is sufficient.
Remind learners about human reaction time and how this might affect the accuracy of the results. Ask how
sporting events such as Formula 1 or athletic track events are timed accurately (light gates). These can be
demonstrated as shown in the Coursebook. This method removes any human reaction time error.
Ticker tape and a ticker timer can be demonstrated, or the concept explained.
The use of a strobe light and long exposure camera can also be demonstrated, or the concept explained.
Safety: If a strobe light is used, this can cause seizures in people with photosensitive epilepsy so the teacher
needs to be aware of any such medical conditions in the learners in advance of the lesson. This information
should be obtained from the school’s medical records and not from learners themselves.
Support – learners should be able to explain why light gates will give a more accurate time than a
stopwatch controlled by hand.
Challenge – learners can be asked whether the ticker timer method will give the true speed that the
object would travel without any measurement (no because the tape causes extra drag and the timer that
makes the mark needs to make contact with the tape, so slowing the trolley).
Assessment idea: Learners can describe how each method works using labelled diagrams. This can be peer-
assessed if criteria have been provided.
3 Running with the wind behind you (15–20 minutes)

Learning intention: To consider the effect of wind, and air resistance, on speed.
Resources: Coursebook Chapter 2, activity 2.1.
Description and purpose: The activity could be introduced by using the example of the world land speed
records. For a record to be valid, a vehicle needs to travel in one direction and then again in the opposite
direction within a certain time period. The average of the two speeds is taken. Why is this done?
When any object is moving in air, it experiences air resistance which causes drag and provides a force that
opposes the motion (although air resistance is not the same as friction). The concept of relative speed needs
to be introduced. If a runner travels at 6 m/s on a day with no wind, their speed relative to the air, which
is not moving, is 6 m/s. However, if the wind is blowing at 5 m/s in the opposite direction to running, their
speed relative to the air is now 6 + 5 = 11 m/s. This gives greater air resistance. Now consider running with
a 5 m/s wind in the same direction. The running speed relative to the air is now 6 − 5 = 1 m/s which greatly
reduces the effect of air resistance.
Prevailing wind direction at high altitude on Earth in many places is westerly. That means the time taken for
east and west-bound flights between the same cities can differ considerably.
Support – learners can understand how wind direction and speed affect air resistance.
Challenge – learners can be told that in motor racing, a faster car will travel progressively closer directly
behind a slower car before pulling out sideways to overtake. What is the purpose of the faster car
travelling directly behind the slower one?
Assessment idea: Learners can discuss the answers to the questions in the Coursebook in groups or as a
whole class.
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Plenary ideas
1 Two stars and a wish (2–3 minutes)
Description and purpose: Learners work individually to give themselves two stars and a wish. The two stars
are areas of the lesson where they felt they did really well or understood easily. The wish is one area where
they would like to do better.
Assessment idea: Volunteers can be asked to share their ideas or this can be done as an anonymous
exit-slip activity. (Learners are given small pieces of paper, or slips, about 5 cm square. They can write or
draw on these, then hand them to the teacher as they leave, or exit, the class.)
2 What I would like to know (2–3 minutes)

Resources: Small pieces of paper.
Description and purpose: Learners work individually to think what they would like to find out more
about from the context of the lesson or topic. This can be written as one or two points and done as an
exit-slip activity.
Homework ideas
1 Coursebook questions
Learners can answer questions 1–8.
2 Workbook questions
Learners can work through Exercise 2.1 to consolidate their knowledge on the concept of speed,
Exercise 2.2 to practise using the equation for speed and Exercise 2.3 on rearranging the equation for speed.
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2.2 Distance–time graphs

LEARNING PLAN
Core: • Plot and interpret distance– Learners can sketch, plot and
Sketch, plot and interpret time graphs. explain the motion shown in
distance–time and speed–time • Use the gradient of a distance–time graphs.
graphs (covered here and in distance–time graph to Learners can use a distance–
Section 2.3). calculate speed. time graph to calculate
Determine from given data or speed.
the shape of a distance–time
graph or speed–time graph
when an object is:
a at rest
c accelerating
d decelerating.
Calculate speed from the
gradient of a straight-line
section of a distance–
time graph.
Many learners have difficulty Ask learners to describe the See the Teaching Skills Focus
with interpreting or motion of an object from a section in this chapter of the
sketching graphs. distance–time graph. Teacher's Resource.
Starter ideas
1 Why do we use graphs? (2 minutes)
Description and purpose: Learners work in groups of two or three to brainstorm ideas about why graphs
are used.
What to do next: Use the activity to pick up on any misconceptions, gaps in understanding or potential areas
of difficulty.
2 Meanings of words (2 minutes)

Resources: List of words associated with graphs on the board or screen, such as axis, scale, gradient, point,
coordinate etc.
Description and purpose: Learners work in pairs to develop meanings for each of the words and volunteers
can share some of these with the class.
What to do next: Use as a starter activity for assessing prior understanding and address any issue before
starting the topic of distance–time graphs.
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Main teaching ideas

1 Explaining the distance–time graph (20 minutes)
Learning intention: To help learners understand what a distance–time graph shows.
Resources: Toy car, metre ruler, stopwatch, board and pens, flipchart or graph plotting software.
Description and purpose: Use the activity for learners who struggle to understand how to sketch or interpret
distance–time graphs.
Start by placing the toy car with the front level with the zero end of a metre ruler. Sketch the axes for
a distance–time graph on the board with times going up in 10 s intervals and distance going up in 5 cm
intervals (these are deliberately different to minimise confusion between the two). Explain that the graph will
follow the movement of the car. Tell one learner to move the car at a slow constant speed and another to
start the stopwatch when you call ‘start’ and then both to stop when you say ‘stop’. Do this after the car has
moved through about 15 cm. Ask for the distance and the time at this point. Leave the car at that position.
Now go to the graph and ask learners to recall what the distance was when the time was zero. Plot this as the
first point. Now ask for the distance and time when you said ‘stop’ and plot this. Join the two with a straight
line. Next, when you say ‘start’ the stopwatch is started but the car does not move, for example at a road
junction. Say ‘stop’ again and plot this as a horizontal line. Keep the car at the same point, then start and
stop again after pushing at a slightly greater speed. Continue until the graph is understood.
Only then can the car be moved back along the metre ruler so the line slopes down again.
Support – learners can be asked why we always measure the distance from the same point on the car.
Challenge – learners can be asked to predict how the graph would look if the car was (a) getting faster,
(b) getting slower.
Assessment idea: Learners should be able to sketch and interpret distance–time graphs. This can be
done orally as a whole class together.
Practical investigation 2.2 in the Practical Workbook provides instructions for learners to carry out and
analyse the results from an investigation into speed using ticker-tape and a trolley, including plotting a
speed–time graph and using the graph to calculate the gradient (acceleration) and the distance travelled.
2 Understanding the gradient (15 minutes)

Learning intention: To help learners understand the meaning of the gradient in a distance–time graph.
Description and purpose: Start by asking learners to recall (a) the equation for average speed and (b) how to
work out the gradient of the line on a graph. Make the link between the two – so the gradient of a distance
time graph is change in distance divided by change in time, which is also speed. Ask learners some questions
about gradients, such as ‘What does a line look like if the gradient is (a) greater, (b) smaller, (c) zero,
(d) negative?’ to assess their understanding. Once this is understood, introduce acceleration and
deceleration. What will happen to the line on a distance–time graph in each case? Ask learners to think how
the speed changes in each case, then how this will affect the gradient. For example, when decelerating, the
line will start with a positive gradient. The gradient will decrease, possibly to zero if the object is coming to
a stop. For acceleration, the line curves upward and becomes steeper.
What about a straight line with a negative gradient? This may have been covered in the previous activity. If
not, it can be covered here and used to make the link between speed and velocity. The negative sign shows
that the speed is in the opposite direction to when the gradient was positive.
Support – learners can calculate the gradient of a straight line.
Challenge – learners can draw a tangent to a curve and determine the instantaneous speed of an
accelerating or decelerating object.
Assessment idea: Learners should be given scenarios from which to sketch distance–time graphs that
involve changes in speed. Exercise 2.4 in the Workbook provides data for learners to sketch distance–time
graphs and use these in calculations.
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3 Real life distance–time analysis (10 minutes)

Learning intention: To show an application of distance–time analysis.
Resources: Internet access (optional).
Description and purpose: Motorsport, such as F1 and Moto-GP, sees manufacturers invest large sums of money
into competition that ultimately benefits their sales of road vehicles and pushes technological development
forward. Races and tests are carried out on circuits that are split into three (F1) or four (Moto-GP) sectors.
A sector is a specific distance of track, although they are not each of equal distance. Sectors are chosen to be
approximately equal in terms of time take to cover that distance. For example, one sector may be long and
straight while another may be shorter but twisty. Sector times are the times taken for competitors to cover each
of these distances. Comparing performance in different sectors is an application of distance–time analysis.
Support – learners can understand that it takes a longer time to cover a distance when going
more slowly.
Challenge – learners can use the internet to find motor racing circuits in their part of the world and
identify where the sectors are on those.
Assessment idea: Ask questions during the activity to make it as interactive as possible.
Plenary ideas
1 Tips for distance–time graphs (5 minutes)
Description and purpose: Learners work in pairs to devise a set of tips to help others learn what distance–
time graphs show.
Assessment idea: Tips can be swapped with other pairs for comparison and discussion. Some of them can
be shared with the class.
2 What my partner knows (2–3 minutes)
Description and purpose: Learners work in pairs and each has 20 seconds to tell the other what they learned.
The teacher coordinates the time to ensure the whole class is at the same point at the same time. At the end,
any learner can volunteer to tell the class any two things that their partner told them. The teacher should
confirm with the partner that the information was relayed correctly.
Homework ideas
Learners can answer questions 9 and 10.
Learners can work through Exercise 2.4 to practise sketching and using distance–time graphs in calculations.
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2.3: Understanding acceleration

LEARNING PLAN
Core: • Plot and interpret speed– Learners can sketch and

Sketch, plot and interpret distance– time graphs. interpret speed–time
time and speed–time graphs • Work out the distance graphs to work out distance
(covered here and in Section 2.2). travelled from the travelled and acceleration.
Determine from given data or the area under a speed– Learners can describe
shape of a distance–time graph or time graph. what acceleration and
speed–time graph when an object is: deceleration mean.
• Understand that
a at rest acceleration is a change Learners can calculate the
in speed and the gradient gradient of a straight line
of a speed–time graph. graph.
c accelerating
d decelerating.
Calculate the area under a
speed–time graph to determine
the distance travelled for
motion with constant speed or
constant acceleration.
Understand that acceleration and
deceleration are related to changing
speed including qualitative analysis of
the gradient of a speed–time graph.
State that the acceleration of free fall,
g, for an object near to the surface of
the Earth is approximately constant
and is approximately 9.8 m/s2.
Supplement: Distinguish between Learners can describe

Determine from given data or speed and velocity. the difference between
the shape of a speed–time graph Define and calculate speed and velocity.
when an object is moving with: acceleration; understand Learners can calculate
a constant acceleration deceleration as a acceleration from
b changing acceleration. negative acceleration. change in speed and
Use the gradient of a time taken.
speed–time graph to Learners can calculate
Calculate acceleration from
calculate acceleration. the gradient of a graph
the gradient of a speed–time
at a particular point on
graph (covered here and in
a curve
Section 2.2).
Know that a deceleration is a
negative acceleration and use
this in calculations.
Describe the motion of objects
falling in a uniform gravitational
field with and without air / liquid
resistance (including reference
to terminal velocity).
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Many learners confuse n/a Distance–time and speed–time
speed–time and distance–time graphs convey very different
graphs because they look information, but many learners
superficially similar. see them as being almost the
same. See the Teaching Skills
Focus section in this chapter
of the Teacher's Resource for
guidance on this.
Starter ideas
1 Distance–time brainstorm (5 minutes)
Description and purpose: Learners need to thoroughly understand distance–time graphs before progressing
onto speed–time graphs. Allow learners to work in groups of three or four to brainstorm all their ideas
about distance–time graphs and get the groups to share their ideas with the class.
What to do next: Use the activity to pick up on misconceptions or gaps in understanding and address these
before progressing.
2 What is acceleration? (2–3 minutes)
Description and purpose: Learners will have heard the word acceleration in everyday life, but what does it
mean to them? Allow learners to discuss this in pairs, then volunteer their thoughts to share with the class.
Any ideas that relate to change in speed such as getting faster are acceptable. Some may say things like ‘how
fast something can go’. Deal with this by explaining that we will define acceleration later.
What to do next: Use the activity to pick up on pre-existing misconception.
Main teaching ideas

1 Explaining the speed–time graph (10–15 minutes)
Learning intention: To help learners to understand what a speed–time graph shows.
Resources: Internet access (optional).
Description and purpose: Show, or ask learners to imagine, the start of a motor race, such as F1 or Moto-GP where
competitors accelerate from the start and visibly slow towards turn 1. This could be done from an on-board camera
view. Pause the video there and ask how speed has changed over the time that they watched. How would this appear
if plotted on a graph?
Sketch axes on the board and explain that speed is on the vertical axis and time on the horizontal. Label
these but do not add numbers. Ask learners where the line will start on the graph for the clip they have just
seen (at the origin). What happens next? (the line stays at zero until the start is signalled). What happens
next? How, if at all, does speed change? (it increases and this can be drawn as a straight line with positive
gradient). Ask learners to suggest what happens to the line as competitors approach turn 1.
If possible, use a search engine to do an image search for ‘F1 telemetry speed’ and show a real speed time
graph. Point out the various parts and ask learners to describe what is happening.
Support – learners should be able to recognise when speed is increasing, decreasing or staying the same
from a speed–time graph.
Challenge – ask learners why analysis of speed–time graphs in motorsport is so important.
Assessment idea: Learners can sketch speed–time graphs for various scenarios. Volunteers can come and do
this on the board.
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2 The 4 × 100 m relay (20–30 minutes)

Learning intention: To apply understanding of speed–time graphs to a real-life situation.
Resources: Coursebook chapter 2, activity 2.2.
Description and purpose: See Coursebook. Learners should work in pairs to arrive at the answers.
Practical guidance: Learners can participate in a relay activity, preferably in conjunction with the PE / games
department. Learners will need to measure distances and times and apply what they learned from Chapter 1.
Safety: If learners are actually to be running a relay race, this must be done on an appropriate track and
with appropriate clothing and footwear.
Support – learners understand that two runners should be travelling at the same speed and in the same
direction when the baton is handed over.
Challenge – learners can suggest values for the speeds and times of each runner.
Assessment idea: Learners can discuss their answers to each of the questions with other pairs in the class to
reach a consensus as to what the correct answers are.
3 Gradient and area under the graph (20 minutes)
Learning intention: to show learners how to work out acceleration and distance travelled from a speed–
time graph.
Description and purpose: Learners should have already covered acceleration as the concept of change in
speed per unit time. Ask them to recall this. Sketch a speed–time graph with a constant positive gradient.
Ask learners how to work out the gradient of a line (in this case, change in speed divided by change in time).
Make the link between the quantities used to work out the gradient and the equation for acceleration – they
are the same. Hence, the gradient of a speed–time graph is acceleration.
Learners could be asked to comment on the gradient of a curve (it is constantly changing) and then to
suggest how we could work out the gradient at any one point on a curve. Learners should be shown how to
draw a tangent by placing their ruler on the outside of the curve. The edge of the ruler should come close
to, but not touch the curve to allow for the width of a pencil line. When the tangent in ruled, it should just
touch the curve once and not cut across the curve. The gradient of the tangent can then be calculated as
usual for a straight line. Next, ask learners to recall the equation relating speed, distance and time, and to
rearrange this to give distance (speed × time). Now sketch a speed–time graph that is just a horizontal line
(no change in speed). Ask learners how they could carry out the speed × time calculation from the graph.
Point out that this is represented by a rectangle between the line and the time axis.
Do the same for a constant acceleration from rest speed–time graph. Here, the area is a triangle
= _  12 × base × height.
base × height
Note, some learners may find it easier to use the form: base × height ÷ 2, or  ____________
    
2
Support – learners can recall what can be determined from the gradient and from the area under a
speed–time graph.
Challenge – learners could use the equation for the area of a trapezium to calculate distance from some
speed–time graphs.
Assessment ideas: Learners can be given questions with speed–time graphs where they have to calculate
distance and/or acceleration. This can be self-assessed if the answers are provided later. Exercise 2.6 in the
Workbook provides questions on drawing and interpreting speed–time graphs and using these in calculations.
Plenary ideas
1 Give me five (3–5 minutes)
Description and purpose: Learners work individually to write five things that they learned in the lesson and
hand these in as they leave (exit-slips).
Assessment idea: The teacher should check what has been written after the learners leave, to inform
planning for the next lesson.
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2 Speed–time graph word search (5 minutes)

Resources: Prepared word search containing key words from the topic (see ‘Links to digital resources’ for a
free word search maker).
Description and purpose: Learners work individually or in pairs to find as many words as they can in the
allocated time.
Assessment idea: Either a list of the words or a list of clues to the words could be provided.
Homework ideas
Learners can answer questions 11–13 on speed–time graphs and question 14 on calculating distance travelled.
Learners can work through Exercise 2.5 to practise using the equation for acceleration. Learners can work
through Exercise 2.6 to practise sketching distance–time graphs.
2.4: Calculating speed and acceleration

LEARNING PLAN
Core: • Use the gradient of a Learners can calculate

Calculate speed from the gradient distance–time graph to speed from the gradient of a
of a straight-line section of a calculate speed. distance-time graph.
distance–time graph.
Supplement: Define and calculate Learners can calculate

Define acceleration as change in acceleration; understand acceleration and
velocity per unit time; recall and deceleration as a deceleration from
use the equation negative acceleration. speed–time graphs and
∆v  Use the gradient of a from numerical data.
a =  ___
∆t speed–time graph to
Determine from given data calculate acceleration.
or the shape of a speed–time
graph when an object is
moving with:
Calculate acceleration from
the gradient of a straight-line
section of a speed–time graph.
15
Many learners find the concept Ask learners to describe, Ask what acceleration is (change of
of changing acceleration to be in words or by sketching a speed per unit time). So what might
challenging because they think speed–time graph, how speed a greater acceleration be? (A greater
of acceleration as a change will change when acceleration change of speed per unit time.).
in speed. The idea of two is (a) increasing (b) decreasing. How is acceleration worked out
quantities changing becomes from a speed–time graph? (gradient)
more complex. So how would increasing acceleration
appear? (increasing gradient – or a
curve bending upwards).
Work through the same process for
decreasing acceleration.
Starter ideas
1 Different acceleration (5 minutes)
Description and purpose: Learners work in groups of two or three to make lists of things that accelerate
rapidly and things that accelerate slowly. For example, a bullet being fired from a gun accelerates rapidly,
but a long freight train accelerates slowly.
What to do next: Use the activity to lead into acceleration.
2 Largest acceleration (2–3 minutes)
Resources: Picture of a leafhopper insect (optional).
Description and purpose: Ask learners to suggest what animal has the greatest acceleration. They may
suggest the cheetah, but its acceleration is around 9 m/s2. One of the largest accelerations in the animal
kingdom is the leafhopper insect. When jumping, its acceleration can reach 150 m/s2! The maximum
acceleration that humans can survive is around half of that.
What to do next: Use the activity to lead into calculation of acceleration.
Main teaching ideas

1 Introducing the equation (10–15 minutes)
Δv
Learning intention: To introduce the equation for acceleration, a = ___   , and explain the terms.
Δt
Description and purpose: This may be the first time that learners have met the delta symbol in an equation, so
this needs to be explained so they do not think it is another variable. Remind learners how they determined
acceleration from a speed–time graph (the gradient). Ask them to explain how to calculate the gradient of
any graph (change in y divided by change in x). Ask them to write this in words, then ask if short-hand
would make this easier. The Greek upper-case letter delta is used in science to mean ‘change in’ as a sort of
Δv
shorthand. Learners will meet this again during the course. Write the equation as a =  ___  and ask learners to
Δt
read this out in words (acceleration equals change in speed divided by change in time). Then explain that Δv
can be written as v − u where v is final speed and u is starting, or initial, speed.
Provide some example calculations. Start these with an initial speed of zero, then progress to ones where the
initial speed and initial times are not zero.
Support – learners recognise the upper-case delta symbol to mean ‘change in’.
Challenge – ask learners how the acceleration of an object, such as a trolley going down a ramp, could
be determined (difference in speed between the top and the bottom divided by the time taken).
Assessment ideas: Learners can be given questions and can self-assess these when the answers are provided.
Exercise 2.5 in the Workbook provides calculations which use the equation for acceleration and Exercise 2.7 in the
Workbook provides questions on supplementary content on calculating acceleration from speed–time graphs.
16
2 Using ticker tape to find the acceleration of a trolley down a ramp (15–30 minutes
depending on whether practical work is actually carried out or not)
Learning intention: To explain how ticker tape and a ticker timer can be used to determine acceleration.
Resources: Activity 2.3 in the Coursebook.
Description and purpose: See Coursebook. If the ticker tape and ticker timer method of measuring speed was
introduced before, then remind learners of this. Otherwise explain the concept. A timer makes dots on paper
at regular intervals. A long strip of paper (called ticker tape) can be attached to a moving object and pulled
through the timer. The greater the distance between the dots, the greater the speed of the tape.
Support – learners understand why the dots are further apart when the tape is moving faster.
Challenge – ask learners if they can see a pattern in the spaces between the dots. (When acceleration is
constant, the ratio of the distances between these goes up in odd numbers, i.e. 1 : 3 : 5 : 7 : 9 : 11…)
Assessment idea: Learners can peer-assess the answers to the questions.
3 Galileo’s odd number rule (20 minutes)
Learning intention: To discuss the work done by Galileo on the acceleration of free fall.
Resources: Graph paper, calculators, pictures of Galileo’s ramp (optional).
Description and purpose: Galileo was an Italian polymath who lived around 400 years ago. He tried
to determine the acceleration of free fall, but lacked the timing equipment to make the necessary
measurements. Instead, he made a ramp and used timers such as his pulse, a water clock and a pendulum
to time a ball rolling down the ramp. Galileo discovered that the ball rolled down the ramp through an
increasing distance in every equal time interval.
Ask learners to sketch (with a ruler) a speed–time graph of a ball rolling down a ramp on graph paper. Their
line should be showing constant acceleration from an initial speed of zero (straight line through the origin).
The gradient does not matter but it must be constant, and have a value less than 10.
Ask learners to recall how to work out the distance travelled from a speed–time graph (area under the graph).
Ask them to divide their graph into equal time intervals by ruling vertical lines. This will give a right-angled
triangle and a series of trapeziums.
Ask learners to work out the area of each of these areas and then determine the simplest ratio of the areas
(divide all the areas by the smallest one). Their results should be 1 : 3 : 5 : 7, and so on.
Galileo noticed that this was true for every angle of ramp, so predicted that it would also be true for an
object falling vertically.
Learners should then compare their graphs. They will show different gradients but the same ratio. That
reflects Galileo’s results.
Support – learners could be asked why a pendulum would be a better timing method than the human pulse.
Challenge – learners could be asked to calculate the actual distances that an object would fall through in
1 s, 2 s, etc. when dropped in the absence of air resistance (using a speed–time graph with a gradient of
9.8 m/s2) or to determine the link between the total distance travelled and the time (the total distance is
proportional to the time squared, so increases in the ratio 1, 4, 9, 16, …).
Assessment idea: Learners can self-assess as they now know what the ratios should be.
Plenary ideas
1 Learning the equation (3–5 minutes)
Description and purpose: Learners work in pairs to devise a way to remember at the equation for acceleration.
Assessment idea: Learners can swap their method with other groups or share with the class for discussion.
2 What others learned (5 minutes)
Description and purpose: Learners move randomly around the room and pair up with a partner – one group
of three is possible of there is an odd number. Learners have 20 seconds to tell their partners what they
learned. The teacher can then ask volunteers to tell what their partner learned.
17
Homework ideas
Learners can answer question 16. Learners following the supplementary part of the syllabus can answer
questions 17–20 on calculating acceleration and question 21 on calculating acceleration from
distance–time graphs.
Learners can work through Exercise 2.5 to practise using the equation for acceleration in calculations.
Exercise 2.7 provides questions for the supplementary content, calculating acceleration from
speed–time graphs.
Links to digital resources

• GCSE revision: speed: www.cambridge.org/links/pctd7011
• GCSE revision: distance-time graphs: www.cambridge.org/links/pctd7012
• Using and interpreting graphs: www.cambridge.org/links/pctd7013
• Free online word search maker: www.cambridge.org/links/pctd7014
• The world’s biggest vacuum: www.cambridge.org/links/pctd7015
CROSS-CURRICULAR LINKS
Maths: use of graphs, gradients and areas under the lines; equations with substitutions and
rearrangements.
Project guidance
The objective is for learners to produce their own detailed lesson plans for how they would deliver a revision
session focussing on the use of graphs and equations to describe motion. In this topic, learners often have the
most difficulty with distance–time and speed–time graphs, so learners doing this project will need to understand
these thoroughly before starting.
Encourage learners to think about what they found more challenging and how they would best help others
to understand these concepts. This is essentially an exercise in metacognition, where learners think about the
process of learning, however they need to be aware that not all learners will learn in exactly the same way.
Allowances need to be made for this, and also for differences in the level of support that some learners may need.
18

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CAMBRIDGE IGCSE™ PHYSICS: TEACHER’S RESOURCE

Topic Approximate Learning content Resources

Topic Approximate Learning content Resources

TEACHING SKILLS FOCUS

2.1: Understanding speed

Syllabus learning objectives Learning intentions Success criteria

Core: • Define speed and calculate Learners can state what is

2 Coursebook ‘Science in context’ discussion activity (5–10 minutes)

Main teaching ideas

2 Determining speed in the laboratory (15–30 minutes)

3 Running with the wind behind you (15–20 minutes)

2 What I would like to know (2–3 minutes)

2.2 Distance–time graphs

Syllabus learning objectives Learning intentions Success criteria

2 Meanings of words (2 minutes)

Main teaching ideas

2 Understanding the gradient (15 minutes)

3 Real life distance–time analysis (10 minutes)

2.3: Understanding acceleration

Syllabus learning objectives Learning intentions Success criteria

Core: • Plot and interpret speed– Learners can sketch and

Supplement: Distinguish between Learners can describe

Main teaching ideas

2 The 4 × 100 m relay (20–30 minutes)

2 Speed–time graph word search (5 minutes)

2.4: Calculating speed and acceleration

Syllabus learning objectives Learning intentions Success criteria

Core: • Use the gradient of a Learners can calculate

Supplement: Define and calculate Learners can calculate

Main teaching ideas

Links to digital resources

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