CAMBRIDGE Sea tee eect mates for Cambridge IGCSE™ David Sang, Mike Follows & Sheila Tarpey Ce aed International Education Conese eee eanCAMBRIDGE UNIVERSITY PRESS Physics for Cambridge IGCSE™ COURSEBOOK David Sang, Mike Follows & Sheila TarpeyCAMBRIDGE UNIVERSITY PRESS University Printing House, Cambridge CB2 SBS, United Kingdom (One Liberty Plaza, 20th Floor, New York, NY 10006, USA. 4477 Williamstown Road, Port Mefbourne, VIC 3207, Australi 314-321, 3rd Floor, Plot 3, Splendor Forum, Jasola Dissict Centre, New Delhi ~ 110025, India 79 Anson Road, #06-04/06, Singupore 079906 ‘Cambridge University Presis part of the Univesity of Cambridge. [furthers the University’s mission by disseminating knowledge in the pursuit of| ‘education, earning and research atthe highest international levels of excellence. wurmeambridge-ore Information on is tite: wwweambridgeorg/978-1-108-88807-3, | ‘© Cambridge University Press 2021 “This publication isin copyright. Subject to statutory exception sand tothe provisions of relevant coletive licensing agreements, ‘no reproduction of any part may take place without the watten permission of Cambridge University Press Fics edition 2009 Second edition 2014 Thiel edition 2021 20 19 18 17 16 15 14 13 1211 10987654321 Printed in Dubai by Oriental Press ‘A catalogue record for this publication is available from the British Library ISBN 978-1-108-88R07-3, Coursebook with digital access (2 years) ISBN 978-1-108-97042-6 Digital coursebook (2 years) ISBN 978-1-108-74449-2 Coursebook eBook Additional resources for this publication at www.cambridge.orydlange (Cambridge International copyright material inthis publication is reproduced tinder license and remains the intellectual property of Cambridge Assessment International Education NOTICE TO TEACHERS “The photocopy masters in this publication may be photocopied or distributed [electronically] free of charge for class-o0m use ‘within the school or institution that purchased the publication, Worksheets and copies of them remain in the copyright of Cambridge University Press, and such copies may not he lstributed or used in any wey outside the purchasing institution. Exam-style questions [and sample answers] have been waitten by the authors Tn examinations, the way marks are warded may be lifferent. References 10 assessment and/or assessment preparation are the publisher’ interpretation of the syllabus requirements ‘and may not fully reflet the approach of Cambridge Assessment International Education. NOTICE TO TEACHERS IN THE UK 11s laga to reproduge any part of this work in material form {including photocopying and electronic storage) except under the following circumstances where you ate abiding by «licence granted to your schoo! or institution by the Copyright Licensing Agency: (i) where no such licence exist, oF where you wish to exceed the ‘terms of a fieonee, and you have gained the writen permission cof Cambridge University Press, (Gi) where you ate allowed to reproduce without permission under the provisions of Chapter 3 of the Copyright, Designs and Patents Acr 1988, which covers for example, the reproduction ‘of short passages within certain types of educational anthology land reproduction for the purposes of sling examination questions4 DEDICATED « TEACHER bya AWARDS WINNER Coe Crean) i Cee)‘The coursebook provides coverage of the full Cambridge IGCSE Physies syllabus. Each chapter explains facts Soe ee rete ar ee em tos ‘scientific principles to bring the subject to lie. Together Sere hr eee og Sta een ee ener aspects oftheir scientific study. At the end of each chapter, ‘examination-style questions offer practice opportunities for mea The digital teacher's resource contains detailed guidance for all topies of the syllabus, including common misconceptions identifying areas where learners sight need extra support, as well as an engaging bank of lesson ideas for each syllabus topic. Differentiation is emphasised with advice for identification of different learner needs and suggestions of appropriate interventions to support and streich learners The teacher's resource also contains support for preparing and carrying out all the investigations in the practical workbook, including a set of sample results for when practicals aren't possible. Ged rotaeeete ‘The teacher's resource also contains scaffolded ‘worksheets and unit tests for each chapter. Answers forall components are accessible to teachers for free on the Cambridge GO platform.The skills-focused workbook has been carefully constructed to help et sce ae at a) their Cambridge IGCSE Physics course, providing further pract Sei eet Reece Pee ate ri Co eicortt net cee is supported. The workbook enables independent learning and is Feet og eae ee Sat g ‘The Cambridge IGCSE practical workbook pr ith additional opportunities for hands-on practical work, aiving them full guidance and support that will help them to develop their investigative skills. These skills include planning ee ee reun oer yeaa tte cert hypotheses, recording and displaying results, and analysing Remercnee fr Eker Nee EUR nema ee en ee eee ete ea ee ee oe aT Skills for Cambridge IGCSE Physies write-in workbook has been written in collaboration with the Association of Seience Education, See eae ne Seuss en sty Deere ees nun anton’> CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK > How to use this book Throughout this book, you will notice lots of different features that will help your learning, These are explained below. eh es In the learning intentions table, Supp ndicated with a large arrow and a darker ground, as in the examp This contains questions and activities on subject knowledge you will need before starting the chapter aS ‘Supplement content: Where content is intended for earns Tearmer ho are studying the Supplement content ofthe syllabus as well as the Core, this is indicated in the main text using the arrow and the bar, as om the right here, and the text is in blue, You may also see the blue text with just un arrow (and no bar), in boxed features such as the Key Words or the Getting Started. Symbols in blue are also supplementary content. This feature presents real-world examples and applications of the content in a chapter, encouraging you to look further into topics that may ge beyond the syllabus. There are discussion questions at the end which look at some of the benefits and problems of these appii Questions Boece Appearing throughout the text, questions give you chance to check that you have understood the topic you This feature focuses on developing your practical have just read about. The answers to these questions are skills. They include lists of equipment required and ‘accessible to teachers for free on the Cambridge GO site, any safety issues, step-by-step instructions so you can carry out the experiment, and questions to help you think about what you have learned. Activities give you an opportunity to check your understanding throughout the text in a more ‘active way, for example by creating presentations, posters or taking part in role plays. When activiti have answers, teachers can find these for free on the Cambridge GO site, Key vocabulary is highlighted in the text when it is first introduced, and definitions are given in ‘boxes near the vocabulary. You will alsa find definitions of these words in the Glossary at the this book Important equations which you will need to learn | and remember are given in these boxes.How to use this book Beeson ste ‘At the énd of some activities and experimental skils boxes, you will find opportunities to help you assess your own work, or that of your | classmates, and consider how you can improve the way you learn. ‘Command words that appear in the syllabus and might be used in exams are highlighted in the ‘exam-style questions. In the margin, you will ind the Cambridge Intemational definition. You will also find these definitions in the Glossary, Wherever you need to know how to use an equation to carry out a calculation, there are worked example boxes fo show you how to do this, a bee oe These activities ask you to think about the approach that you take to your work, and how you might improve this in the future aeusem 4 | Projects allow you to apply your learning from the whole chapter to group activities such as making posters or | presentations, or performing in debates. They may give you the opportunity to extend your learning beyond the syllabus if you want to. EIA pace Core ‘Supplement> CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK > Introduction Studying physics Way study physics? Some people study physios for the simple reason that they find it interesting, Physicists study matter, energy and their interactions. They might be interested in observing the tiniest sub-atomic particles, or understanding the vastness of the Universe itself Ona more human scale, physicists study materials to try to predict and control their properties. They study the imeractions of radiation with matter, nctading the biological materials we are made of, ‘Other people are more interested in the applications of physics. They want to know how it can be used, perhaps in an engineering project, or for medical purposes. Depending on how our knowledge is applied, it can make the world a better place. Some people study physics as part of their course ‘because they want to become some other type of scientist pethaps a chemist, biologist or geologist. These branches of science draw a great deal on ideas from ‘physics, and physies may draw on them, Thinking physics How do physicists think? One of the characteristics of physicists is that they ty to simplify problems ~ reduce them to their basies ~ and then solve them by applying some very fundamental ideas. For example, you will be familiar withthe idea that matter is made of tiny particles that attract and repel each other and move about. This is a very useful model, which has helped us to understand the behaviour of matter, how sound travels, how eletrcity lows, and much more. Once a fundamental idea is established, physicists look around for other areas where it might help to solve problems. One of the surprises of 20th eentury physies, ‘was that, once physicists had begun to understand the: fundamental particles of which atoms are made, they realised that this helped to explain the earliest moments in the history of the Universe, at the time of the Big Bang. Medicine is often seen as 2 biological career but this doctor will use many applications of physics, fram X-rays te ebotic limbs, in bar workPhysics relies om mathen quantities and analyse data. They invent mathematical models — ties, Physicists measure CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK In pairs, either take the measurements or write down how you would do the following: ‘+ measure the length, width and thickness of this book and work out its volume + measure the thickness of a sheet of paper that makes up this book + measure the length of a journey (for example, on 2 map) that is not straight. Now discuss how you would work out the density of + aregularshaped solid + an imegular-sheped sol + aliquid People tend to dismiss people who lived in the past as less intelligent than we are. After al, they Used parts of their bodies for measuring distances. Accubit was the length of the forearm from the tip of the middle finger to the eloow. However, the ~ncient Egyptians knew this varied between people. Therefore, in around 3000 BCE, they invented the royal cubit Figure 1.1), marked out on a piece of granite and used this asa standard to produce cubit rods of equal length. Figure 1.2: Eratosthenes used shadews and geometry to work out the circumference of the Earth, Discussion questions Figure 1.1:Cubitrod. 1 You cannot always depend on your eyes to judge lengths. Look at Figure 7.3 and decide The Ancient Egyptians were experts at using very which line is longer? Check by using a ruler. simple tools lke the cubit rod. This enabled them to build their pyramids accurately. Eratosthenes, a brilliant scientist who lived in Egypt in about 300 BCE, showed the same care and attention to detail. This allowed him to work out that the Earth has a circumference of 40000km (Figure 1.2). In contrast, there are many recent examples where 2. Eratosthenes may have hired a man to pace incorrect measurements have led to problems. the distance between Alexandria and Syene Although the Hubble Space Telescope had the most (present-day Aswan) to calculate the Earths precisely shaped mirrar ever made, the criginal circumference. People have different stride images it produced were not as clear as expected, lengths so some people take longer steps than Tiny mistakes in measuring meant that ithad the others. Discuss the possible ways that anyone wrong shape and it took a lot of effort to account with any stride length could have measured for these errors. the distance between these towns accurately1 Making measurements 1.1 Measuring length and volume In physies, we make measurements of many diferent lengths, for example, the length of a piece of wire, the height of liquid in a tube, the distance moved by an ‘object, the diameter of a planet or the radius of its orbit In the laboratory, lengths are often measured using a ruler (such asa metre rule), Measuring lengths with a rulers « familiar task, But when you use a ruler, itis worth thinking about the task and just how reliable your measurements may be. Consider ‘measuring the length of a piece of wire (Figure 1.4). + The wire must be straight, and laid closely alongside the ruler. (This may be tricky with a bent piece of wire) + Look at the ends of the wire. Are they cut neatly, ‘or are they ragged? Ts it difficult to judge where the ‘wire begins and ends? * Look at the markings on the ruler. They are probably | mm apart, but they may be quite wide, Line one end of the wire up against the zero on the seals, Because of the width of the mark, this may be awkward to judge * Look at the other end of the wire and read the scale ‘Again, this may be tricky to judge, ‘Now you have a measurement, with an idea of how precise itis You can probably determine the length of the wire to ‘within a millimetre, But there is something else to think about ~ the ruler itself. How sure can you be that itis correctly calibrated? Are the marks at the ends of a metre ruler separated by exactly one metre? Any etror in this will Tead to an inaccuracy (probably small) in your result, igure 1.5: Making multiple measurements. The point here is to recognise that i is always important to think critically about the measurements you make, however straightforward they may seem. You have to consider the method you use, as well as the instrument {in this ease, the ruler). —————— Perr Tr Figure 1.4: Simple measurements still require careful technique, for exemple, finding the length of a wire. standard: is an absolute or primary reference or measurement precise: when several readings are close together when measuring the same value calibrated: should agree closely with a standard ‘or agrees when 2 correction has been applied More measurement techniques If you have to measure a small length, such as the thickness of a wire, it may be better to measure several thicknesses and then caleulate the average. You can use the same approach when measuring something very thin, such asa sheet of paper. Take a stack of 500 sheets and ‘measure its thickness with a ruler (Figure 1,5). Then divide by 500 to find the thickness of one sheet. 500 sheets, 13 ” " 10> CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK kilogram, kg ‘cubic metre, m? kilograms per cubic metre 1000 kg/m? Kilogram, kg cubic dacimetre, dm? | kilograms per cubic decimetre | 1.Okg/am? gram, 9 ‘cubic centimetre, cm? _| grams ger cubic centimetre 1.0 g/em> Table 1.2: Units of densi Values of density Some values of density are shown in Table 1.3. Gases hhave much lower densities than solids or liquids. ‘An object that is less dense than water will float. Ice is less dense than water which explains why icebergs float in the sea, rather than sinking to the bottom. Only about ‘one tenth of an iceberg is above the water surface. If any part of an object is above the water surface, then it is less dense than water. Gases air 1.29 hydrogen 0.09 helium aie carbon dioxide | 1.98 Liquids | weter 1000) alcohol (ethanod __| 790 mercury 13.600 Solids ice 720 wood 400-1200 polyethene 910-970 glass 2500-4200 steel 7500-8100 lead 11340 silver 10500 gold 19300 Table 1.3: Densities of some substances, For gases, these are a pressure of 10x 10°Pa. given at a temperature of 0°C Many materials have a range of densities. Some types of wood, for example, are less dense than water and will float. Other types of wood (such as mahogany) are more dense and will sink, The density depends on the nature of the wood (its composition) Gold is denser than silver. Pure gold isa soft metal, so {jewellers add silver to make it harder, The amount of silver added can be judged by measuring the density, ‘tis useful to remember that the density of water is 1000kg/m', 1.Okg/dm or 1.0 gfem*. Calculating density To calculate the density of a material, we need to know ‘the mass and volume of 2 sample of the material. A sample of ethanol has a volume of 240 cm. Its mass is found to be 190.0 g. What is the density of ethanol? Step I: Write down what you know and what you want to know. ‘Step 2: Write down the equation for density, substitute values and calculate p. as —_1908 240em* = 0.79 glem? Answer Density of ethanol = 0.79 giem*The easiest way to determine the density of a substance {sto find the mass and volume of a sample of the substance. Fora solid with a regular shape, find its volume by ‘measurement (see Section 1.1). Find its mass using & balance. Then culeulate the density Questions 3. A brick is shown in Figure 1.9. It has a mass of 28 kg. Figure 1.9: A brick labelled with its dimensions, a Give the dimensions of the brick in metres. b Calculate the volume of the brick. © Calculate the density of the brick. 4 A box full of 35 matches has a mass of 6.77 g The box itself has a mass of 3.37 a What is the mass of one match in grams? b What is the volume (in em’) of each mateh. A match has dimensions of 42mm x 2.3mm * 2.3mm? © What is the densi How do you know if these matches will fl of the matches? ‘The Earth has a mass of 6X 10°kg and a radius of about 6400 km, What is the density of the Earth (in kg/m)? The volume of a sphere is given by the equation 7 = 4373, where ris the radius. 40 drawing pins (tiumb tacks) like those shown in Figure 1.10 have a mass of 17.55 g. What is the volume (in mm’) of one pin when they are made of metal with a density of 8.7 gem? Figure 1.10: & pair of drewing pins (thumb tacks) A young gir from the Kayan people in northern ‘Thailand wears a neck ring made of brass (Figure 11D, Itlooks asif there are 21 individual ings but the ring isactually one continuous length of brass fashioned (bent) into a coil, The height ofthe brass coil is 12cm and its average circumference is 40cm. ‘Neck rings are usually only removed to be replaced with a bigger one as the gil grows, However, we can estimate the mass of this neck ring without removing it Vv> (CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK What looks like 21 individual rings around the girl's neck is actually 21 turns of a coil of brass. Each turn has a circumference of 40cm, ‘Calculate (in em) the total length of brass used to make the git!’s neck ring. b Thecoil has a height of 12cm and the coil has 21 turns. Calculate the radius of the brass in em, ¢ If the brass coil is unwound from the girl's neck and straightened out, it would be a long, thin, cylinder. Calculate the volume of this cylinder in em?. The volume of a eylinder is given by the equation ¥ = 32h, where = radius and h = height. Calculate the mass of brass used to make the neck ring and express your answer in kg. The density of brass = 8.73 g/cm’ Finding the density of a liquid Figure 1.12 shows one way to find the density of a liquid. Place a measuring cylinder on « balance. Set the balance to zero. Now pour liquid into the cylinder. Read the volume from the scale on the cylinder. The balance: shows the mass Figure 1.12: Measuring th mass of aliquid ‘When liquids with different densities are poured into the same container, they will arrange themselves so that the liquid with the lowest density will be atthe top and the ones with the highest density will be at the bottom. This is because the denser liquids displace the less dense liquids. This is easier to see when each liquid is given a Gifferent colour. In Figure 1.13, the green liquid is less ease than the red liquid and 30 on. When a distinct layer forms in a mixed solution, the liquids re said to be immiscible, which means they do not mix. Thisis why oil floats on water. However, not all liquids stay separated so you would be disappointed if ‘you tried this at home with squash and water, for example. ‘When liquids mix, itis usually because one liquid dissolves in the other. For example, orange squash is a concentrated syrup that is difuted by dissolving it in water. Figure 1.13: Liquid density owers Apart from making colourful liquid density towers, do variations in the density of liquids have practical consequence? In Chapter 11, you will lara about convection currents in fuids (liquids andl gases), which are driven by differences in density. These convection currents include the thermohaline circulation in the ‘oceans. Colder and saltier water sinks, displacing (pushing up) warmer and less salty water. Finding the density of a regularly shaped solid In pairs, create a worksheet on the computer for Jinding the density of a regularly shaped solid object {for example, a rectangular block) using a ruler and a mass balance. Your worksheet should include: + amethod for measuring the mass and working out the volume ‘+ the equation for calculating density + atable to record the data. You could include an optional task to work out the density of aliquid. After your allotted time, another pair is going to test a copy of your worksheet (perhaps by doing the experiment). They are going to add any steps that are missing or make suggestions to make your worksheet clearer. When you get your worksheet retumed, edit and save a new version of it.NN Finding the density of an irregularly shaped solid Before you start, make a copy of your previous 1 Making measurements Write down one thing that you di really well in this activity worksheet and save it under a new name. Some of what you included in the previous worksheet can be kept and some will need to be edited. Write down one thing that you will ty to do better next time. How will you do this? In pairs, create a worksheet for finding the density of an irregularly sheped solid object using amass balance, a measuring cylinder, some thread, @ pair of scissors and a eureka can (if you have access to cone]. Your method explaining how to measure the mass and how to calculate the density should be the same. However, you should: * explain how to measure volume by displacement * say something about choosing a suitably sized measuring cylinder * change your previous table 1.3 Measuring time The athletics coach in Figure 1.14 i using his stopwatch to time a sprinter. Fora sprinter, a fraction of a second (perhaps just 0.01 s) can make all the difference ‘between winning and coming second or third. different in 2 marathon, where the race lasts for more than ‘two hours and the runners are timed to the nearest second, You could include an optional task to work out the density of an irregularly shaped solid object that is less dense than water. Finding its mass and calculating the density is straightforward. The challenging part is explaining how to work out the volume of an object thet oats. Design a flowchart or decision-tree (optional) Design a flowchart or decision-tree for use by anyone iho wants to work out the density of any liquid or any solid object. Ensure that your flowchart includes enough information so that someone could take the measurements. Ask your partner or someone else who has completed the first two parts to check and correct your flowchart. Figure 1.14: An athletics coach uses a stopwatch to time a hurdler, who can then learn whether she has improved. How dense can you be? In groups of three, write a method showing how you could work out your own density, or that of a friend or of a younger sibling. Alternatively, pian out your strategy and be prepared to share it with the class. There are at least two methods: a dry method and a wet method. Discuss one or both of them. » CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK In the laboratory, you might need to record the temperature of a container of water every minute, or find out how long an electric current is flowing. For measurements like these, stopclocks and stopwatches can be used. You may come across two types of timing device An analogue clock (Figure 1.15) is like a traditional clock whose hands move round the clock’s face. You find the time by looking at where the hands are pointing on the scale. It can be used to measure time intervals to no better than the nearest second. Figure 1.15: An analogue clock. A digital clock (Figure 1.16) or stopwateh is one that ‘gives a direct reading of the time in numerals, For example, a digital clock might show a time of 9.58. A digital clock records time to a precision of at least one hundredth of a second. You would never see an analogue watch recording times in the Olympic Games digital dock started when the gun fired and stopped 9.58 latar when Usain Bolt crossed the finishing line to win the 100m at the 2009 World Championshias in world record time. analogue: display has hands (or @ needle) and is often not very precise digital: display shows numbers and is often precise When studying motion, you may need to measure the time taken for a rapidly moving object to move between two points. In this case, you might use a device called a light gate connected to an electronic timer. This is similar to the way in which runners are timed in major athletics events, An electronic timer starts when the marshal’s gun is fired, and stops as the runner crosses the finishing line, ‘You will lean more about how to use electronic timing instruments in Chapter 2 Measuring short intervals of time Figure 1.17 shows a typical lab pendulum, A mass, called 4 plumb bob, hangs on the end of a string, The string is clamped tightly at the top between two wooden jaws IF you pull the bob gently to one side and release it, the pendulum will swing from side to side, The time for one oscillation of a pendulum (when it swings from left to right and back again) is called its period. A single period is usually too short a time to measure accurately. However, because a pendulum. swings at 2 steady rate, you can use a stopwatch to ‘measure the time for a large number of oscillations (perhaps 20 or 50), and calculate the average time per oscillation. Any inaccuracy in the time at which the stopwatch is started and stopped will be much less significant if you measure the total time for a large number of oscillations KEY WORDS plumb bob: a mass (usually lead) hanging from a string to define a vertical line oscillation: a repetitive motion or vibration period: the time for one complete oscillation or wave; the time it takes an object to return to its original position1 Making measurements 9 A student was investigating how the period of a pendulum varied with the length of the string and obtained the results in Table 1.4. 0.00 0.0 0.20 18.1 0.40 25.1 0.60 28.3 0.80 304 1.00 40.5 1.20 444 1.40 479) Table 1 2 Why did the student record the time for 20 swings? — b Make a copy of Table 14 and, for each length of the pendulum, calculate the time for one Questions ‘oscillation and record the value in the third column of the table © Plota graph of the period of the pendulum against its length (that is, plot the length of the pendulum on the x-axis). Use the graph to work out the ength of the Figure 1.17: A simple pendulum, 8 High-speed video can revord sporting events at a frame rate of 60 frames per second (framels). 2 Whatis the time interval betwen one frame and the next? b If weean see 24 framels as continuous motion, pendulum when the period is 2 seconds. This is by what factor cam the action recorded at the length of pendulum used in a grandfather {6 frame's be slowed down and still ook clock. continuous? Using a pendulum as a clock In 1656 the Dutch scientist Christiaan Huygens invented a clock based on a swinging pendulum. Clocks like these were the most precise in the world until the 1930s. One oscillation of a pendulum is defined as the time it takes for a plumb bob at the bottom of the string to return ta its original position (Figute 1.18). You need to develop a worksheet so that students can plot a Le graph of how the period of oscillation of a pendulum varies with the length of the string. They then need to use the graph to find Figure 1.18: One oscillation is when the ‘the length the pendulum needs to be to give a period of one plus bob swings one way anc! then the second (useful for a clock). Your worksheet needs to: ‘other and returns back to is original position.> CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK CONTINUED + define what an oscillation means (30 that a student knows when to start and stop the stopwatch) + explain why we take the time for 10 or 20 oscillations when we only need the time for one oscillation + provide a labelled diagram of the assembled apparatus (not just a list of equipment) so that students know how to put the equipment together put the eq + amethod (step-by-step instructions) Swap copies of your worksheet with a classmate, Write down suggestions for any improvements on the worksheet you receive before retuming it to its owner. Note down any improvements if you have a class discussion, In groups of three or four, produce a podcast (no more * Explain how a submarine or scuba diver moves up than five minutes long) on one ofthe following options. ‘and down in the water column (or perheps expiain how a Cartesian diver dernonstration works). * Explain how differences in fluid density can. Option 1: Can we build on what we have learned bon cenyy lead t0 convection (something you will meet in ‘This is opportunity to revise what you have leamed Chapter 11). You might want to go on to discuss about density and then consolidate that knowledge how this relates to ocaan currents or wind. and understanding by applying it to one of the two ‘examples below. + You must explain how density is calculated, including the equation. + You should describe how to measure the mass and volume of both regular ang irregular Option 2: What was the solution to the longitude problem? clock based on a pendulum is impractical on the moving deck of a (sailing) ship but knowing the time is important for navigation as this provides your longitude on a spinning Earth, Lines of longitude Sepeaalece are the vertical lines on a map. When you move east * You could describe how tc work out the density Gr west you are changing your longitude; move for of an object that can float. nough snd you change fire zone 1 RSS Titanic = You must start with a short description of the twas claimed that the RSS Titanic was unsinkable. longitude problem. However the ship sank in 1912 on its first voyage * You could describe the various suggested * You must explain why a ship can float despite solutions to the longitude problem. being made of material that's denser then water. © You could describe the final solution to the * You should explain why a ship can sink, in terms. longitude problem. For this, you would need to of changes in density lookup John Harrison and his marine chronometer + Do some research to find out about Sulkheads : How did the Ancient Egyptians build in ships: what are they and what are they for? eee oe Why did the RSS Tite k despite be! Rae eaT oT ae The pyramids are an incredible fest of engineering, even by today’ standards, Using very basic tools, the 2 Submarines and scuba divers prea Carica am patecty arama You could describe one phenomenon that depends 4 You, could start by introducing the dimensions ‘on changes or differences in density. You could think at he GEE aul miliaris ‘of your own or select one of these: reouired td bul _ Sagal Saale TE a CoA ar SEARS A TTY cm)exp 1¢ Egyptians managed to get the sides of their pyramids lined up with ‘true north (without a compess) and how they got the base of them absolutely level at) without a (piri level, Option 4: How did circumference of the. ? Eratosthenes was a brilliant scientist. He was told ‘hat, at the same time every year (12 noon on 21 June), vertical columns in Syene (present day Aswan) cast no shadows while columns where he lived in Alexandria cast shadows. He used this 40 work out that the Earth is round. Eratosthenes may have hired @ man to measure out the distance work out the between Alexandria and Syene. * You could start with a short biography of Fratosthenes. + You should explain why the observation with the shadows shows that the Earth is sphere. You might want to include a diagram like Figure 1.2. * You should try and show how the man hired by Eratosthenes could have worked out his stride-length (the distance of each step) and kept count of his strides (steps). Think about his possible journey: did he follow a straight line; were there any hills in the way? Could this have introduced errors in measuring the distance. between Alexandria and Syenie? ‘+ Finally, you could show how Eratosthenes did the calculation. 1. Making measurements ‘Option 5° Hew did Archimedes really Work out that the goldsmith fiad replaced some of the gold in Hiero's crown with silver? Archimedes was probably the most brilliant scientist of his era, He is s 10 have solved the, problem of how to work out the density of the crown ‘while having @ bath. Legend has it that he then ran into the streets shouting ‘eureka’ ("'ve solved i). + _ You could start with a short biogtaphy of Archimedes. * You could then describe the usual explanation ‘of how he worked out that some gold had been stolen. Silver is less dense than gold so the same mass of silver has a bigger volume and will displace a bigger volume of water. However, it would be difficult to measure the difference in volume, especially since bubbles Of air could cling to the submerged crown and there could be other sources of error, You could describe a better method, which uses a mass balance. You would need to lain why, when the masses are equal, the balance tips towards the denser mass when lowered into water. +. Gold needs some silver impurity or it would 'be too soft and would be easy to bend out of shape. Perhaps the goldsmith was falsely ‘accused? Perhaps this idea could form part of a ‘piece of creative writing (some prose or a play) bbut be sure to include the physics. * For your project, write down some thoughts about what you feel went well and areas where you could improve. * Give yourself @ score out of ten for how much you know and understand the physies you included. If you scored ten, write down how you could have produced a more ambitious project. If you scored less, do you need to thoroughly review the material or are you making careless errors? Write down what concrete steps you need to take to improve for ext time * Give yourself a score out of ten for the quality of your presentation. Write down vihat you thought was good about the other presentations or any effective presentation ideas that you might use next time you present.Length can be measured using a ruler. ‘The period of one oscillation can be measured by measuring the time for 20 oscillations and then dividing the time by 20, ‘The volume of a cube or cuboid can be found by measuring the length of the three sides and multiplying the measurements together. ‘The volume of a liquid can be measured using a measuring cylinder where the bottom of the meniscus appears on the scale when looked at horizontally, All objects that sink in water displace their own volume of water. ‘The volume of an irregularly shaped object can be found from the change in the height of liquid in a measuring cylinder when itis immersed in the liquid. Density is the ratio of mass to volume for a substance: p= % The density of water is 1000kg/m® or 1.0 g/cm ‘Anything less dense than water will float in water and anything denser than water will sink in water. ‘Tee floats because itis less dense than water. ‘One liquid will float on top of another liquid if iti less dense, ‘Time can be measured using a clock or watch. "An analogue clock has hands and can only measure time to the nearest second ‘A digital clock displays numbers and records time to a precision of at least one hundredth of a second. gold 19.30 ; [silver 10.49 ' [lead 11.34 1. Three metal cubes have the same volume but are made of different metals, Each one is lowered into a beaker of water. Use the data in the table to, decide which one will cause the biggest rise in water level, a} A 20d B silver € lead Dall will cause the same rise in water level1 Making measurements eS) 2 Three metal cubes have the same mass but are made of different metals, Each one is lowered into a beaker of water. Use the data in the table to decide which one will cause the biggest rise in water level. ni A gold B silver € lead D all will cause the same rise in water level 3. Astronauts land on another planet and measure the density of the atmosphere on the planet surface. They measure the mass of a S00 cm' conical flask plus stopper as 457.23 g, After removing the air, the mass is 456.43 g (1m! = 1000!itres). What is the best estimate of the density of the air? ni A 0.000001 6 kg/m’ © 0.16kgim* B 0.0016ke/m* D 16kgh 4. The graph shows the mass and volume of several different objects. Mass Which two objects have the same density? ni A 2and3 B lands © 2and4 D 3and4 5. Astudent measures the circumference of a circular copper pipe. ‘He wraps a length of string four times around the pipe and marks it with ink, as shown in the photograph,> CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK 2 The student unwraps the stag and hols agit a ar vith asetinete i 2 ‘The photograph shows the first two ink marks on the string. i Use the photograph to estimate the circumference of the pipe: n ii The student finds that the total length of string for4 turns is 354mm, ‘Caleulate the average (mean) circumference of the pipe using this value. [1] Total: 2) 6 Segue how you would work out the thickness of «single sheet of paper if the only measuring device available was a ruler and its smallest division was Imm. m 7 What is the mass of a microscope slide that has dimensions of 75mm ¥ 26mm * 1 mm and has a density of 2,24 wlem?? (2) 8 Four different liquids are poured into a 100cm measuring eylinder that is 10cm tall. Each liquid has a different density and each has a different colour. Calculate the missing vals in the table. fa) Liquid Mass /g ae / ree clear ethanol i 20.00 | 079 red alycerin | 20.00 1.26 green olive ol 25:90__| 28.80 it blue turpentine | 30.00 | 35.30 v Copy the diagrim below Using the data from the table above, write down the colour ofthe liquid you would expect to find in each layer and how thick the layer would be 2 Colour of Fem 9 Metals are denser than water, Explain why a metal ship can lat, a 10 Suggest how you could work out the density of a drawing pin. re eeu en ened calculate: work out from givon facts, figures or information suggest: apply knowledge and understanding to situations where there are a range of valid responses in order to make proposals/ put forward considerations explain: set out purposes or reasons; make the relationships between things evident; provide why and/or how and support with relevant evidence 16 >1 Making measurements LF-EVALUATION CHECKLIST “Measure length, volume and time. teens ee Calculate the volume of a cube or cuboid from measurements using a rule. Determine the volume of an irregularly shaped object. Measure the size of tiny objects (for example, the thickness of a sheet of paper, the volume of a drawing pin). Calculate density. Predict whether an object will float or sink in water based on its density Describe an experiment to find the density ofa liquid, ‘Predict whether a liquid will float on top of another Kquid if their densities are known and they cannot mix. Describe an experiment to find the density of a cube or cuboid, Describe an experiment to find the density of an irregularly shaped object. ‘Describe the differences between analogue and digital watches or clocks.oa Oi TJ) a4 | Describing define speed and calculate average speed plot and interpret distance-time and speed-time graphs work out the distence travelled from the area under a speed-time graph understand that acceleration is a change in speed and the gradient of @ speed-time graphWork in pairs. (On your own, quickly sketch 2 distance-time graph, pethaps based on your journey to school. Then ask your partner to write a description of it on a separate sheet of paper. Discuss each other's answers ‘Sketch a speed-time graph for a sprinter running the 100m in a time of 9.58. Label it with as much information as you know. Show how your graph could be used to work out the sprinter’s acceleration at the start of the race and the distance he travelled. Compare your sketch with your pariner’s and add to or correct your own work. Be prepared to share your thoughts with the class. 2. Describing motion AROUND THE WORLD IN 80 DAYS The first known cireumnavigation (trip around the world) was completed by a Spanish ship on 8 September 1522. It took more than three years. The French writer Jules Verne wrote the book Le tour du monde en quatre-vingts jours (which means Around the World in Eighty Days) in 1873. In honour of the writer, the Jules Verne Trophy is a prize for the fastest circumnavigation by a yacht, now held by the yacht IDEC Sport, which did it n just under 41 days in 2017. In 2002, the American Steve Fossett was the first to make 2 solo cireurnnavigation in @ balloon, without stopping, taking just over 13 days. In 2006, he flew the Virgin Atlantic GlobalFiyer (Figure 2.1), the first fixed-wing aircraft to go around the world without stopping or refuelling. It took him just under three days. Hypersonic jets are being developed that could fly at 1.7 km per second so they could circurnnavigate the globe in an incredible six and a half hours. Figure 2.1: The Virgin Atlantic GlobalFlyer passes over the Atlas Mountains. Sometimes these epic adventures inspire those who do them to campaign for a better world. The British sailor Ellen MacArthur (Figure 2.2) is just such a person. She held the world record for the fastest solo circumnnavigation, achieved on 7 February 2005. However, she retired from competitive sailing to set up the Ellen MacArthur Foundation, a charity that works with business and education to accelerate the transition to a circular economy. A circular economy would create less waste 2s things should be designed to last a long time and bbe easy to maintain, repair, reuse or recycle. Figure 2.2: Ellen MacArthur celebrates after completing her record solo round the world journey on 7 February 2005 in Falmouth, England, Discussion questi 1. What were the speeds of the six journeys mentioned in the first paragraph? Assume that the Earth's circurnference is 40000 km. 2 How could the fastest boat not win a round- the-world yacht race?>: CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK In the second part of Figure 24, a piece of card, called an interrupt card, is mounted on the trolley. As the ‘trolley passes through the gate, the eading edge of the interrupt card breaks the beam to start the timer. ‘When the trailing edge passes the gate, the beam is no longer broken and the timer stops. The faster the trolley is moving, the shorter the time for which the beam is broken. Given the length of the interrupt card, the trolley’ speed can be calculated. light gates: allow the speed of an object passing between them to be calculated electronically interrupt card: allows the speed of an object passing through a light gate to be calculated; a timer starts when the card breaks the beam and stops when the beam is no longer broken Rearranging the equation It is better to remember one version of an equation and how to rearrange it than to try to remember three different versions. The equation distance speed = S842 time allows us to calculate speed from measurements of distance and time, This equation can also be written in symbols KEY EQUATION This is sometimes known as the instantaneous speed. which is the speed at a particular instant or moment in time, whereas average speed is worked out over a longer time interval. Beware, sin this equation means distance (or displacement) and not speed. We can rearrange the ‘equation to allow us to calculate distance or time. For example, a railway signaller might know how fast 2 train is moving, and needs to be able to prediet where it ‘will have reached after @ certain length of time: distance = speed x time ors Similarly, the crew of an aircraft-might want toknow' how long it will take for their aircraft to travel between two points on its fight path: A spacecraft is orbiting the Earth at a steady speed of 8.0km/s (see Figure 2.5). How long will it take to complete a single orbit, @ distance of 44.000 km? igure 2.5, Step I: Start by writing down what you know, and what you want to know. speed (») = 8.0kin/s distance (s) = 40 000 km time () =? (Choose the appropriate equation, with the unknown quantity, time, as the subject (on the left-hand side). , Substitute values —it can help to include units = 40000 km 8.0 kris Perform the calculation, 1 5000s, Step 4: Answer ‘The time to complete a single orbit (44.000 km) is $5005, ‘This is about 92 minutes (5500 ~ 60 = 91.667). So, the spacecraft t2kes 92 minutes to orbit the Earth once.2. Describing motion Worked Example 2.2ilustrates the importance of looking at the units. Because speed isin km/s and distance isin km, we do not need to convert to m/s and metres. We would get the same answer if we did the conversion: 40000.000m ‘8000 mis = 5000s time = Questions 4° Anaireraft travels 900 metres in 3.0 seconds ‘What isits speed? 5 Acar travels 400 km in 3.Shours. What is the speed of the car in knvh and mis? 6 The Voyager spacecraft is moving at 17000 mis, How far will it travel in one year? Gi in km, Running with the wind behind you In 2011, Justin Gatlin ran 100metres in 9.45 seconds (faster than Usain Bolts world record by 0.13 seconds) However, he was pushed along by a 20m/s tailwind generated by giant fans as part of a Japanese game show. 100m or 200m sprint record can stand only i a tailwind does not exceed 2m/s. Why does this nile not apply to longer events? First, think about how you might approach this problem. The day Roger Bannister ran a mile in four minutes (6 May 1954) he almost decided not to race because it was too windy. Imagine there is a tailwind along the final straight section of a 400m track which speeds you up, and a headwind on the opposite straight section which slows you down. Why do the effects of the tailwind and headwind not cancel out? (Hint: you need to think about the time it would take you to run the straight sections.) 1. Imagine that you are @ 400m runner who can run the distance in 40 (a new world record) at the same average speed of 10 m/s. Assume that the 400m track is equally divided so that the straight sections and bends are each 100m long. jmutes it takes sunlight to reach us from the Sun. Light travels at 3 x 10* m/s and the Sun is about 144 million km away. A cheetah can maintain its top speed of 31 mis over a distance of 100 metres while some breeds of gazelle, such as Thomson's gazelle, have a top speed Of 25 m/s. This question considers how close the. cheetai needs to be to catch the gazelle if they have both just reached top speed a How long does it take a cheetah to cover 100m? bb Whats the closing speed of the cheetah, that is, what is the difference in speed between the cheetah and the gazelle? € How farahead of the cheetah would the gazelle ned to be to escape? (Hint: you need the time you calculated in a and the closing speed you ealeulated in b.) How long would it take the cheetah to cateh the gazelle with the closing speed you calculated in band the distance apart you caleulated in e? Plot your time for the 400m (y-axis) against wind speed (axis). When you are running against the wind on the straight section opposite the finish line, subtract the wind speed from your normal running speed. When you are running with the wind on the final stright section before the finish line, add the wind speed to your normal running speed. For example, if there is a wind speed of 1 m/s, ‘your speed along the straight opposite the finish line will be 9 m/s while it will be 11 m/s along the straight section before the finish line. Then you need to acd the times for each straight section to the 20s for the bends. Repeat this, increasing the wind speed by 1 m/s each time, until you reach 10m/s. Could you have reached the answer without plotting a greph? Discuss whether its realistic to acid or subtract the wind speed to your normal running speed. Design an experiment to test how wind speed affects running speed. You might need to include equipment that you do not have access to (such as the giant fans used on the Japanese game show).Discuss your answers to the activity with the person sitting next to you. Have they thought of anything you haven't included in your answer? Would you add anything to your answers after your discussion? 2.2 Distance-time graphs ‘You can describe how something moves in words, “The coach drove away from the bus stop. It travelled at a steady speed along the main road, leaving town. After five minutes, it reached the highway, where it was able to speed up. After ten minutes, it was forced to stop because of traffic” ‘We can show the same information in the form of a distance-time graph, as shown in Figure 2.63. This graph is in three seetions, corresponding to the three sections of the coact’s journey. Distance travelled Tine / min bs £ 2 6 0 5 10 3 Time / min Figure 2.6 a and b: A graph to represent the motion of 2 ‘coach, as described in the text. The slope of the graph tells, us about the coach’ speed In section A, the graph slopes up gently, showing that the ‘coach was travelling at a slow speed. In section B, the graph becomes steeper. The distance of the coach from its starting point is increasing more rapidly. Itis moving faster. 2)» In section C, the graph is flat (horizontal). The distance of the coach from its starting point is not changing. It is stationary. The slope of the distance-time graph tells us how fast the coach is moving. The steeper the graph, the faster itis moving (the greater its speed). When the graph becomes horizontal, its slope is zero. This tells us that the coach’s speed is zer0 in section C. Itis not moving, Figure 2.6a shows abrupt (instant) changes in specd between A, Band C. It would not be a very comfortable ride for the passengers! Instead of abrupt changes in speed, the speed would change more slowly in the real ‘world and there would be smooth curves joining the sections (Figure 2,6b). The increasing gradient of the upward-sloping curve between A and B would show that the coach was speeding up (accelerating) and the decreasing gradient of the curve between B and C would show that the coach was slowing down (decelerating). However, we will only look at graphs with angled edges as in Figure 2.62, Questions 9 Acar pulled away from the lights and travelled at a steady speed along an empty road, After 8 minutes it joined a main road, where it travelled at about twice the original speed for 12 minutes. The car then meta traffic jam and had to quickly slow down and stop. The traffic cleared after 5 minutes but then the car travelled slowly, at about half the original speed. ‘Sketch a distance-time graph to show the ca’s journey. 10 Figure 2.7 shows the distance-time graph for a woman running a mountain marathon, 40 T | 0 | Distance / kilometres | SP eSREEE EES ESEREE igure 2.7: Distance-time graphHow far did she travel? What was her average speed in km/h’ How many stops did she ma ‘The rules said she had to stop for half an hour for food. When did she take her break? ance © Later she stopped to help an injured runner When did this happen? f What would her average speed have been if she had not stopped at all? g What was hcr highest speed and over what section did this happen? Express trains, slow buses ‘An express train is capable of reaching hhigh speeds, pethaps more than 300km/h. However, when it sets off on its journey, it may take several minutes to reach this, top speed. Then it takes a long time to slow down when it approaches its destination, The French TGY trains (Figure 2.8) run on lines that are reserved solely for their ‘operation, so that their high-speed journeys are not disrupted by slower, local trains A bus journey is full of accelerations and decelerations. The bus accelerates away from the stop. Ideally, the driver hopes to travel at steady speed until the next stop. A steady speed means that you can sit comfortably in your seat, Then there is a rapid deceleration as the bus slows to a halt, A lot of accelerating and decelerating means that youare likely to be thrown about as the bus changes speed. ‘The gentle acceleration of an express train will barely disturb the drink in your cup. The bus's rapid accelerations and decelerations would make it impossible to avoid spilling the drink (Figure 2.) Figure 2.8: France's high-speed trains, the TGV Grande Vitesse), run on dedicated tracks. Their sper made it possible to travel 600km from Marseille in the south to Paris in the north, attend a meeting, and return home again within a single day. 2. Describing motion Figure 2.9: |: can be uncomfortable on a packed bus as it ccelerates and decelerates along its journey. 2.3 Understanding acceleration Some cars, particularly high-performance ones, are advertised according to how rapidly they can accelerate ‘An advert may claim that a car goes ‘from 0 to 100 km/h in 53’. This means that, if the car accelerates at a steady rate, it reaches 20 km/h after 1s, 40km/h after 2s, and so on We could say that it speeds up by 20 km/h every second. In other words, its acceleration is 20km/h per second. So, we say that an object accelerates if its speed increases, Its acceleration tells us the rate at which its speed is, changing, that is, the change in speed per unit time, When an abject slows down, its speed is also changing, We say that it is decelerating. Instead of an acceleration ithas a deceleration Speed and velocity, vectors and scalars In physics, the words ‘speed! and ‘velocity’ have different meanings, although they are closely related: velocity is aan object’s speed in a particular stated direction. So, we could say that an aircraft has a speed of 200 m/s but a velocity of 200:m/s due north. We must give the direction, of the velocity or the information is incomplete. Velocity is an example of a yeetor quantity. Veetors have both magnitude (size) and direction. Another example of a vector is weight — your weight is a force that acts downwards, towards the centre of the Earth Speed is an example of a sestlar quantity. Scalars only have magnitude. Temperature is an example of another scalar quantity. You will learn more about vectors and scalars in Chapter 3. 2 >>. CAMBRIDGE IGCSE™ PHYSICS: COURSEBOOK acceleration: the rate of change of an object's velocity velocity: the speed of an object in a stated direction vector quantity: has both magnitude (size) and direction scalar quantity: is something that has magnitude but no direction Speed-time graphs Just as we ean represent the motion of a moving object by a distance time graph, we can also represent it by a speed-time graph. A speed-time graph shows how the abject’ speed changes as it moves. Always check any’ graph by looking at the axes to see the labels. ‘A speed-time graph has speed on the vertical axis and time on the horizontal axis Figure 2.10 shows a speed-time graph for a bus. The ‘graph frequently drops to zero because the bus stops to let people on and off. Then the line slopes up, as the bus accelerates away from the stop. Towards the end of its journey, the bus is moving at a steady speed (horizontal raph), as it does not have to stop. Finally, the graph slopes downwards to zero again as the bus pulls into the terminus and stops. ‘The slope of the speed-time graph tells us zbout the ‘bus's acceleration + the steeper the slope, the greater the acceleration + anegative slope means a deceleration (slowing down) ‘+ ahorizontal graph (slope = 0) means a constant speed. Speed Figure 2.10: A speed-time graph for e bus on e busy route, At frst, ithas to halt frequently at bus stops. Toward the lend of its journey, maintains a steady spec. Graphs of different shapes Speed-time graphs can show us a lot about an object’s| ‘movement. Was it moving at a steady speed, or speeding up, or slowing down? Was it moving at all? Figure 2.11 represents a train journey. The graph is in our sections. Bach section illusrates a different point ‘+ A:sloping upwards, so the speed increases and the train is accelerating ‘+ Brhorizontal, so the speed is constant and the train, is travelling at a steady speed © Cr sloping downwards, so the speed decreases and. the train is decelerating, + Dshorizontal, so the speed has decreased to 2er0 and the train is stationary. Speed Time Figure 2.11: An example of a speed-time graph fora train during part ofits joumey, ‘The fact that the graph lines are curved in sections A and C tells us that the train's acceleration was changing. Afits speed had changed ata steady rate, these lines ‘would have been straight. Questions 11 Two students live in the same apartment block in Hometown and attend the same school in Schooltown, as shown in Figure 2.12. For this question, work in km and hours, Hometown epaament block station /0.3km_ rs station NR oc Bim o7km Figure 2.12 eo‘Arun gets a lift to schoo! in his mother’s ear. ‘The traffic is heavy so the average speed for the Journey is 40 km/h, How many minutes does it take Arun to get to school? Sofia leaves home at the same time as Arun ‘but she walks the 0.3 km to Hometown station, ‘waits 3 minutes (0.05 hour) for the train, travels on the train to Schooltown station Gourney distance 22 km) and walks the 0.7 km from Schooltown station to the school, The train averages 88 km/h and Sofia walks at $ km/h How many minutes docs it take Sofia to get to school? How many minutes shorter is Sofia’s journey time than Arun's? Draw a speed-time graph for their journeys fon the same axes but assume that any change in speed is instant (do not show the acceleration), 42. Look at the speed-time graph in Figure 2.13. Speed / km/h 0 © 10 20 30 40 50 4 70 80 Time / minutes Figure 2.13 Name the sections that represent: a b « a steady speed speeding up (accelerating) being stationary slowing down (decelerating). 13. Accaris travelling at 20 m/s. The driver sees 1 hazard, After a reaction time of 0.75, she performs ‘an emergency stop by applying the brakes. The car takes a further 3.3 to come to a stop. Sketch a speed.-time graph for her journey from the moment she sees the hazard to the moment she brings her ear to astop. Label the graph with as many details as you can. 2 Describing motion 14 a Copy Tuble 23 and sketch the motion graphs for each motion described. at rest moving at constant speed constant acceleration Gpeeding up) constant deceleration (lowing down) Table 2.3, b Copy Table 2.4 and sketeh the speed-time ‘graphs for each acceleration described. accelerating decelerating Table 2.4 Finding distance travelled ‘A spoed-time graph represents an object’s movement, It tells us about how its speed changes. We can also use the graph to deduce (work out) how far the object travels, To do this, we have to make use of the equation: distance = area under speed-time graph ‘The area under any straight-line graph can be broken down into rectangles and triangles, Then you can calculate the area using: area of rectangle = width » height area ofa triangle = 5 * base * height To understand this equation, consider Worked Examples 23,24and 25, a>