Physics Grade 9 Textbook PDF

P h y s i c s S t u d e n t Te x t b o o k – G r a d e 9 FEDERAL DEMOCRATIC REPUBLIC OF ETHIOPIA MINISTRY OF EDUCATION Physics Studen...

P h y s i c s S t u d e n t Te x t b o o k – G r a d e 9 FEDERAL DEMOCRATIC REPUBLIC OF ETHIOPIA MINISTRY OF EDUCATION Physics Student Textbook Grade 9 FEDERAL DEMOCRATIC REPUBLIC OF ETHIOPIA MINISTRY OF EDUCATION  Physics Student Textbook Grade 9 Contributors: Menberu Mengesha (Ph.D), Writer Nebiyu Gemechu (Ph.D), Writer Moges Tsega (Ph.D), Content Editor Samuel Asefa (Ph.D), Curriculum Editor Felekech G/Egziabher (Ph.D), Language Editor Umer Nuri (MSc), Illustrator Derese Tekestebrihan (Ph.D fellow), Book Designer Evaluators: Girmaye Defar (MSc) Dessie Melese (MSc) Zafu Abraha (MSc) iv First Published August 2023 by the Federal Democratic Republic of Ethiopia, Min- istry of Education, under the General Education Quality Improvement Program for Equity (GEQIP-E) supported by the World Bank, UK’s Department for Inter- national Development/DFID-now merged with the Foreign, Common wealth and Development Office/FCDO, Finland Ministry for Foreign Affairs, the Royal Norwegian Embassy, United Nations ChildrenâĂŹs Fund/UNICEF), the Global Partnership for Education (GPE), and Danish Ministry of Foreign Affairs, through a Multi Donor Trust Fund. © 2023 by the Federal Democratic Republic of Ethiopia, Ministry of Education. 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MOE/GEQIP-E/LICB/G-01/23 ISBN: 978-99990-0-032-1 Contents 1 Physics and Human Society 1 1.1 Definition and Nature of Physics................... 2 1.2 Branches of Physics........................... 3 1.3 Related Fields to Physics........................ 3 1.4 Historical Issues and Contributors.................. 5 2 Physical Quantities 11 2.1 Scales, Standards, Units (prefixes)................... 12 2.2 Measurement and Safety........................ 20 2.3 Classification of Physical Quantities................. 26 2.4 Unit conversion............................. 29 3 Motion in a Straight Line 39 3.1 Position, Distance and Displacement................. 40 3.2 Average Speed and Instantaneous Speed............... 45 3.3 Average Velocity and Instantaneous Velocity............ 47 3.4 Acceleration............................... 50 3.5 Uniform Motion............................. 52 3.6 Graphical Representation of Motion................. 53 4 Force, Work, Energy and Power 63 4.1 The Concept of Force.......................... 64 4.2 Newton’s Laws of Motion....................... 66 4.3 Forces of Friction............................ 73 4.4 The Concept of Work.......................... 74 4.5 Kinetic and Potential Energies..................... 76 4.6 Power................................... 80 5 Simple Machines 85 5.1 Simple Machines and their Purposes................. 86 5.2 Simple Machines at Home....................... 89 5.3 Simple Machines at Work Place.................... 91 5.4 Classification of Simple Machines.................. 93 5.5 Mechanical Advantage, Velocity Ratio and Efficiency of Simple Machine.................................. 96 vi CONTENTS 5.6 Designing Simple Machine....................... 113 6 Mechanical Oscillation and Sound Wave 119 6.1 Common Characteristics of Waves.................. 120 6.2 String, Pendulum and Spring..................... 122 6.3 Propagation of Waves and Energy Transmission.......... 129 6.4 Sound Waves............................... 131 6.5 Superposition of Waves......................... 137 6.6 Characteristics of Sound Waves.................... 138 7 Temperature and Thermometry 145 7.1 Temperature and Our Life....................... 146 7.2 Extreme Temperature Safety...................... 148 7.3 Temperature Change and its Effects................. 149 7.4 Measuring Temperature with Different Thermometric Scales.. 152 7.5 Types of Thermometers and Their Use................ 158 7.6 Conversion between Temperature Scales.............. 162 7.7 Thermal Expansion of Materials.................... 166 Unit 1 Physics and Human Society Introduction You learnt about general science in lower grades. General science includes sub- Brainstorming jects like Biology, Chemistry and Physics. Therefore, in this grade level and in Questions higher grades, you will learn about each of the three subjects and explore their t Explain science beauty. In this unit you will learn about physics and the human society. In par- and its broad cate- ticular, you will learn about definition of physics, different branches of physics, gories. relationship between physics and other fields of study, contributions of promi- t What are the nent scientists in advancing physics, and the way physics knowledge was evolving main branches of and changing in history. natural science? At the end of this unit, you should be able to: define physics in different ways; describe the different branches of physics; describe the relationships between physics and other fields of study; discuss the contributions of prominent scientists in advancing physics at different periods of time; describe how aspects of physics are used in other sciences (e.g. biology, chemistry, engineering, etc.) as well as in everyday technology; and discuss how physics knowledge was evolving and changing in history. 2 Unit 1 Physics and Human Society 1.1 Definition and Nature of Physics Exercise 1.1 t In your own At the end of this section, you should be able to: words, define what define physics in different ways. physics is. t Name other tech- Have you ever thought about some modern technological devices such as nological products computers, smart phones, tablets etc? Also think about the fact that our histor- in your locality that ical heritages such as Harar Jugol, Fasciledes Castle, the Obelisk of Axum and rely on the principle rock-hewn churches of Lalibela buildings have kept their balance and survived of physics. for hundreds of years. The working principles of all these rely on physics. The word physics is thought to have come from the Greek word phusis, mean- ing nature. Hence, physics is a branch of natural science aimed at describing the fundamental aspects of our universe. These include what things are in it, what properties of those things are noticeable, and what processes those things or their properties undergo. In simpler terms, physics attempts to describe the basic mechanisms that make our universe behave the way it does. For example, Activity 1.1 Physics enables you to understand the working principles of cars, airplanes, t By discussing in space-rockets, refrigerators, radios, televisions,etc as well as many of your groups, mention im- daily utensils and tools. portance of physics other than those Physics explains physical phenomena such as the difficulty of walking on a mentioned above. smooth plane, and why an electric fan rotates etc. t What other physi- cal phenomena may Physics helps you discover some of the unknown parts of nature and makes you understand in you familiar with the modern world. your locality using physics? Physics helps you to understand some concepts in other subjects like: t What is a physi- Biology, Chemistry, Geology, Astronomy, etc. cist? Studying physics helps you understand concepts, relationships, principles and laws of nature. A person who studies physics is called a physicist. In addi- tion to understanding the concepts, relationships, principles and laws of nature, studying physics has various career opportunities. Some of te fields in which physics is applicable include: The field of transportation The field of aviation and space science 1.2 Branches of Physics 3 The field of medicine The field of forensic and military science the field of meteorology and metrology etc Key Concept: t Physics is a 1.2 Branches of Physics branch of natu- ral science that At the end of this section, you should be able to: attempts to describe describe the different branches of physics. the basic mecha- nisms that make our As our technology evolved over the centuries, physics has expanded into universe behave the many branches. Some of the branches of physics are summarized in Table 1.1. way it does. Exercise 1.2 t List as many physical phenomena in your surroundings as you can. Describe in which branch of physics each physical phenomenon can be categorized. Key Concept: Activity 1.2 t The branches of physics include: Mechanics, Acoustics, Optics, Ther- t Discuss in groups modynamics, Electromagnetism, Nuclear Physics, etc. and list some other fields or areas of sci- ence where physics is applicable. 1.3 Related Fields to Physics At the end of the lesson, you should be able to: Key Concept: identify different general fields of physics and their applications in life; tPhysics is the discuss the relationships between physics and other sciences and fields foundation of many important scientific like transport, traffic, quality control and standards, etc. disciplines including, Chemistry, Engi- Physics is the foundation of many important scientific disciplines. Some of neering, Geology, them are discussed below. Biophysics, Geo- Chemistry: Chemistry deals with the interactions of atoms and molecules. physics, Medical Physics etc. However, it is rooted in atomic and molecular physics. 4 Unit 1 Physics and Human Society Table 1.1 Some branches of physics and their descriptions Branch Description Mechanics Mechanics is the branch of physics which deals with the motion of an object without or with the reference of force. Mechanics can be further divided into two branches namely quantum mechanics and classical mechanics. Quantum mechanics deals with the behavior of smallest particles like neutrons, protons, and electrons, while classical mechanics is the branch that deals with laws of motion of forces and physical objects. Acoustics Acoustics is the branch of physics which deals with the study of sound and its transmission, production, and effects. Optics Optics is the branch of physics which deals with the behav- ior, propagation, and properties of light. Thermodynamics Thermodynamics is the branch of physics which studies thermal energy and the transfer of heat. Electromagnetism Electromagnetism is the branch of physics which deals with the study of electromagnetic force like electric fields, light, magnetic fields, etc. There are two aspects of electromag- netism which are "electricity" and "magnetism" Nuclear physics Nuclear physics is the branch of physics which deals with the structure, properties and reactions of the nuclei of atoms. Astrophysics Astrophysics is a science that employs the methods and principles of physics in the study of astronomical objects and phenomena. Engineering: Most branches of engineering also apply physics. For exam- ple, in architecture, physics is at the heart of determining structural stability, acoustics, heating, lighting, and cooling for buildings. Geology: Parts of geology, the study of nonliving parts of Earth, rely heavily on physics; including radioactive dating, earthquake analysis, and heat transfer across Earth’s surface. Biophysics: Biophysics applies principles and methods used in physics to study biological phenomena.Physics uses mathematical laws to explain the 1.4 Historical Issues and Contributors 5 natural world, and it can be applied to biological organisms and systems to gain insight into their workings. Geophysics: Geophysics applies the principles and methods of physics to the study of the Earth Medical Physics: Diagnostics and medical therapy, such as x-rays, mag- netic resonance imaging (MRI), and ultrasonic blood flow measurements involves principles of physics. 1.4 Historical Issues and Contributors At the end of the lesson, you should be able to: recognize at least three issues and four prominent physicists with signifi- cant contributions to the development of physics; collect and use pictures and texts from a library and the internet to present prominent figures in the history of physics. Over the last few centuries, the growth of scientific knowledge has resulted in ever-increasing specialization and branching of physics into separate fields. Physics, as it developed from the renaissance to the end of the 19th century, is called classical physics. Revolutionary discoveries starting at the beginning of the 20t h century transformed physics from classical physics to modern physics. Many laws of classical physics have been modified during the 20t h century, re- sulting in dramatic changes in technology, society, and our view of the universe. Discoveries of physics find applications throughout the natural sciences and in technology. Some of the physics discoveries that changed the world are discussed below.. Isaac Newton contributions laid the foundations for classical physics/clas- sical mechanics. He contributed to the Scientific Revolution of the 16th and 17th century by formulating three laws of motion, known as NewtonâĂŹs laws of motion and showed how the principle of universal gravitation could be used to explain the behavior not only of falling bodies on the earth but also planets and other celestial bodies in the heavens. 6 Unit 1 Physics and Human Society Michael Faraday contributed a lot to the field of electromagnetism. In 1821 he succeeded in producing mechanical motion by means of a permanent magnet and an electric current. Ten years later he converted magnetic force into electrical force, thus inventing the world’s first electric generator.In general Michael Faraday changed the world with magnet. James Prescott Joule studied the nature of heat, and discovered its rela- tionship to mechanical work. This led to the law of conservation of energy. Joule’s work helped lay the foundation for the first of three laws of thermo- dynamics that describe how energy in our universe is transferred from one object to another or transformed from one form to another. Marie Curie conducted pioneering research in the field of nuclear physics, particularly on radioactivity. She is considered as the mother of modern nuclear physics. She discovered elements polonium and radium. Albert Einstein is known for developing theory of relativity. This revolution- ary theory had a profound impact on classical mechanics and the under- lying philosophy of physics. He is widely acknowledged to be one of the greatest physicists of all time. Einstein also made important contributions to the development of the theory of quantum mechanics. Exercise 1.3 t Mention some other well-known historical contributors in physics and describe their roles. Key Concept: t Revolutionary discoveries starting at the beginning of the 20th century transformed physics from classical physics to modern physics. Many laws of classical physics have been modified during the 20t h century, resulting in dramatic changes in technology, society, and our view of the universe 1.4 Historical Issues and Contributors 7 Unit Summary The following are the main points you learnt in this unit. Science is a systematized knowledge arising from observation, study and experimentation. Physics is the branch of natural science which describes the basic mechanisms that make our universe behave the way it does. Physics is the study of everyday phenomena. A person who studies physics is called a physicist. Physics has several branches such as mechanics, acoustics, optics, thermodynamics, electromagnetism, nuclear physics, astrophysics etc. Physics is the foundation of many important scientific disciplines such as chemistry, engineering, geology, biophysics, geophysics, medical physics, etc. There are several well-known scientists and engineers that have contributed a lot for the advancement of physics. End of Unit Questions 1. The Greek word ’phusis’ for nature is appropriate in describing the field of physics. Which one of the following is the best answer for this? (a) Physics is a natural science that studies life and living organ- isms on habitable planets like Earth. (b) Physics is a natural science that studies the laws and principles of our universe. (c) Physics is a physical science that studies the composition, structure, and changes of matter in our universe. (d) Physics is a social science that studies the social behavior of living beings on habitable planets like Earth. 2. A moving car suddenly comes to a rest after applying brakes. Which 8 Unit 1 Physics and Human Society branch of physics do you think is appropriate to explain this phe- nomenon? (a) Mechanics (b) Acoustics (c) Electromagnetism (d) Nuclear physics (e) None of the above 3. Which of the following is not one of the branches of physics? (a) Thermodynamics (b) Optics (c) Classical physics (d) Evolution 4. Which of the following is not a historical contributor in physics? (a) Willebrod Snell (b) Daniel Bernoulli (c) Thomas Young (d) Charles Darwin 5. Which of the following institution/project does not apply the princi- ple of physics? (a) Ethiopian Aviation Industry (b) Grand Ethiopian Renaissance Dam (GERD) (c) Quality and Standard Authority of Ethiopia (d) Ethiopian Radiation Protection Authority (e) None of the above 6. Which branch of Physics is most important when studying the na- ture and behavior of light? (a) Quantum Mechanics 1.4 Historical Issues and Contributors 9 (b) Nuclear Physics (c) Optics (d) Thermodynamics 7. Galileo’s famous experiment at the leaning tower of Pisa demon- strated that (a) what goes up must come down (b) all objects fall to earth at the same rate, regardless of their mass (c) heavier object falls faster than lighter object of the same size (d) gravity does not act on a falling object Unit 2 Physical Quantities Introduction Brainstorming Physics begins with observations of phenomena, events, matter or energy. Questions Through demanding and controlled experimentation and logical thought 1. What types of dif- process, the physical phenomena are described quantitatively using mathe- ferent measurement matical tools. Any quantitative description of a property requires compari- scales are used in son with a scale of different measuring devises. For example, length needs your surroundings? a meter-stick, time needs a watch, and mass needs a beam balance. In this 2. What is physical process, we recognize a very obvious fact that properties of different kinds quantity? How can you measure mass, cannot be compared. You cannot compare the time of travel from point A to length and time? B with the distance between the two points, although the two quantities may What are their units be related. The time of travel (time) is a physical quantity and the distance of measurement? (length) is also a physical quantity. They are completely different types of 3. How can you physical quantities measured by different measuring devices and units. In classify physical this unit you will learn different types of scales, measurement, classification quantities? of physical quantities, and conversion from one system of units to another. At the end of this unit, you should be able to: list physical quantities. measure different physical quantities with accuracy. perform the measurement activities of different physical quantities. 12 Unit 2 Physical Quantities In grade 8 General Science, you learned about scientific measurement. Differ- ent types of scales are used in measurement. 2.1 Scales, Standards, Units (prefixes) Scales At the end of this section, you should be able to: identify measurement scales in their surrounding (multiple and fractions of the scales); state and use standard units of measures and their relationship with units in their surrounding. A scale on a measuring device contains the markings that show a certain amount of whatever is being measured. The number of marks on a measurement device depends on how accurate a measurement can be. As the number of marks in the measuring device increases the precision of the device also increases. Figure 2.1 shows that there is a difference of 1 between the successively numbered values and there are ten spaces between them. As the result each space is one-tenth and each smaller mark represents one-tenth (0.1) of the distance to the next larger number. Measurements with this device can be precise to two decimal places. So, we can add a last digit which is estimated. Figure 2.1 Reading scales for a given space. 2.1 Scales, Standards, Units (prefixes) 13 Example 2.1 Determine the length of the red line to two decimal places. Figure 2.2 Reading the measured value of a red line. Solution: The red line goes just past 3.3 but not quite to 3.4. We can estimate the second decimal place. It looks like the line goes roughly half way between 3.3 and 3.4. So, we will say 3.35. Example 2.2 Show the following values on each of the scales below. Figure 2.3 Different scales of measurement. Solution: The red arrows in the following figure indicate the values. 14 Unit 2 Physical Quantities Activity 2.1 Determine the length of the red line in Figure 2.5 to three Figure 2.4 Arrows indicating the reading for the given values in example 2.2. decimal places in a group and compare your result with other groups result. Exercise 2.1 1. Read the scales of the mass measuring devices shown in Figure 2.6. Figure 2.5 Red line and number of divisions for a given span. 2. Write down the values on each of the scales shown in Figure 2.7. 3. Write down the reading of tempera- ture scales shown in Figure 2.8. Figure 2.6 Different scales of mass measuring devices. 2.1 Scales, Standards, Units (prefixes) 15 Figure 2.7 Different scales showing the values of measurement. Key Concept: t In physics scale is a set of numbers, amounts, etc., used Figure 2.8 Different readings of temperature scale. to measure or com- Thanks to technology, today we have digital instruments that indicate the pare the level of measured value in digital format which is the number with its unit. It is very easy something. to read compared to the usual analog instruments. Moreover, it is an accurate measurement. Activity 2.2 1. What is your mass in kilograms? 2. In group observe measurement activities in the surrounding (home, local market and work places) for two days and prepare a report on the what, the where, and the how of the measurements observed. 3. Based on your observation discuss the traditional and commonly used scales and units of measurement for length, mass, time, volume and tem- perature. People in different community measure physical quantities such as length, time, volume, and mass using traditional measuring units. However, each unit has different values at different time, position and conditions. 16 Unit 2 Physical Quantities Standards Brainstorming Ay the end of this section, you should be able to: Questions discuss about the measures used in their local environment and comment What is a standard on the practice; in measurement? In list standard units of measures and their relationship with units in their your local area peo- surroundings. ple measure volume, mass and area using different measuring In the previous section you have learned different types of scales. Now, you are devices. Do these going to earn about measures used in your local area and the standard units of measurements have basic quantities. The laws of physics are expressed in terms of basic quantities standards? Discuss that require a clear definition. In physics, the seven basic quantities are length in groups. (l), mass (m), time (t), temperature (T), current (I), amount of substance (n), and luminous intensity (I V ). All other quantities in physics can be derived from these Figure 2.9 Traditional measuring units. 2.1 Scales, Standards, Units (prefixes) 17 seven basic or fundamental physical quantities. Table 2.1 Measurement of mass at different places. No. Name of student Place Measured value 1 Student A Location A 1.6 unit 2 Student B Location B 2.1 unit Activity 2.3 3 Student C Location C 2.5 unit 4 Student D Location D 3.0 unit t Suppose six grade 5 Student E Location E 1.1 unit 9 students in differ- 6 Student F Location F 3.5 unit ent parts of Ethiopia are given the same object and mea- If your teacher orders you to report the results of a measurement to someone who sured its mass in wishes to reproduce this measurement, a standard must be defined. Whatever is the same unit as chosen as a standard: shown in Table 2.1. Discuss whether the it must be readily accessible and possesses some property that can be measurement has a measured reliably. standard or not re- gardless of personal measurements taken by different people in different places must yield the errors. same result. Lack of standard in measurement has many negative consequences. In Ethiopia, for instance, people use their palm to measure the amount of cotton and footsteps Exercise 2.2 to measure length. The one with a bigger palm collects much cotton than the one t What are the with a smaller palm. Thus, using a palm or footsteps as a measuring device has SI units of length, mass, and time? no standard. It creates inaccuracy on measured value and bias among people. In 2019, an International Committee revised a set of standards for length, mass, time and other basic quantities. The system established is an adaptation of the metric system and is called the SI system of units (see Figure 2.10 or CLICK HERE for further reading ). Length: Meter is the standard or international system (SI) unit for length. There are also other non-SI units of length. These are centimeter (cm), millimeter (mm), and kilometer (km). Today, the meter (m) is defined as a distance traveled by light 1 in vacuum during a time of 299792458 s. Time: It is defined as the interval between two events. It is a fundamental quantity. The unit of time in SI system is second (s). The non-SI units of time are minute Figure 2.10 The SI system after the (min), hour (hr), day, month and year. The second (s) is defined as 9 192 631 770 2019 redefinition 18 Unit 2 Physical Quantities times the period of vibration of radiation from the caesium-133 atom. Mass: The kilogram (kg) is the standard or international system (SI) unit of mass. The non-SI units of of mass are gram (g), milligram (mg), and tonne. The kilogram (kg) is defined by taking the fixed numerical value of the Plank constant h = m2 6.62607015 × 10−34 when expressed in the units of J s (which is equal to kg s ), where the meter and second are defined in terms of the speed of light in vacuum h∆ f (c) and the frequency of the Caesium 133 atom (∆ f ). [1kg = 1.4755214 × 1040 c2 ] Activity 2.4 t Discuss the need for standards of measurement. t Identify problems of non-standard measurement practices in your lo- cality and the country at large. Key Concept: t Standard units are conventional units which are used to measure phys- ical quantity scientifically. 1 t Meter: a distance travelled by light in vacuum during a time of 299792458 s. h∆ f t Kilogram: 1 kilogram (1kg) is 1.4755214 × 1040 c2. t Second: 9 192 631 770 times the period of vibration of radiation from the cesium-133 atom. Scientific Notation In physics, scientific notation is a way of writing measured values that are too large or too small to be conveniently written as a decimal. This can be written more easily in scientific notation, in the general form: d × 10n Exercise 2.3 where d is a decimal number between 0 and 10 that is rounded off to a few decimal places; n is known as the exponent and is an integer. If n > 0 it represents t Write 0.000001256 in how many times the decimal place in d should be moved to the right. If n < 0, scientific notation then it represents how many times the decimal place in d should be moved to the to 3 decimal places. left. For example, 3.24 × 103 represents 3240 (the decimal moved three places to t How many signif- the right) and 3.24 × 10−3 presents 0.00324 (the decimal moved three places to icant figures are in the left). 7800? 2.1 Scales, Standards, Units (prefixes) 19 Significant Figures In a number, each non-zero digit is a significant figure. Zeroes are only counted if they are between two non-zero digits or are at the end of the decimal part. For example, the number 2000 has 1 significant figure (the 2), but 2000.0 has 5 significant figures. You estimate a number like this by removing significant figures from the number (starting from the right) until you have the desired number of significant figures, rounding as you go. For example, 6.827 has 4 significant figures, but if you wish to write it to 3 significant figures it would mean removing the 7 and rounding up, so it would be 6.83. Adding and subtracting experimentally measured values of two different signifi- cant figures (digits) needs to remember the following rule. Exercise 2.4 When two experimentally measured numbers are added or subtracted, the number of significant figure or digit should be equal to the smallest number Write the number for each expression of decimal places of any term in the sum or difference. For example: while with appropriate adding two measured values 9.65 and 8.4, the least closer decimal place is number of signifi- 8.4 cm. The sum of these two numbers is 18.1 and is not 18.05. cant figures. Multiplying or dividing experimentally measured values of two different signifi- t 1.513 + 27.3 t 6.789 − 4.23 cant figures (digits) is based on the following rule. 138.0 t 11.9 When two experimentally measured numbers are multiplied or divided, the t 2.1 × 5.687 number of significant digits in the final answer is the same as the number of significant figures in the quantity having the smallest number of significant figures. For example: While multiplying two measured values 8.65 and 2.035, if you use a calculator your answer is 17.75845 which is completely wrong. The first number 8.65 has three significant figures and the second number 2.035 has four significant figures. According to the rule the smallest number of significant figures is three. So, the correct answer is 17.8. Exercise 2.5 Prefixes Write the following In the previous section you have learned different basic units. When a numerical physical quantities unit is either very small or very large, the units used to define its size may be using appropriate modified by using a prefix. A prefix is an important aspect of dealing with units. prefixes. t The radius of the Prefixes are words or letters written in front that change the meaning. Table 2.2 earth is 6,371,000 m lists a large set of these prefixes. The kilogram (kg) is a simple example. 1 kg is 1000 g, or 1 × 103 g. We can replace the 103 with the prefix k (kilo). t The diameter of our hair is 0.000 0075 m 20 Unit 2 Physical Quantities Table 2.2 Unit Prefixes. Prefix Symbol Multiplier Exponent tera T 1 000 000 000 000 1012 giga G 1 000 000 000 109 mega M 1 000 000 106 kilo k 1 000 103 hecto h 100 102 deka da 10 101 deci d 0.1 10−1 centi c 0.01 10−2 milli m 0.001 10−3 micro µ 0.000 001 10−6 nano n 0.000 000 001 10−9 pico p 0.000 000 000 001 10−12 Key Concept: t Prefix is a letter or a syllable which is written directly before a unit name with no space. t Scientific notation: a system in which numbers are expressed as prod- ucts consisting of a number between 1 and 10 multiplied by an appropriate power of 10. t In a number, each non zero digit is a significant figure. 2.2 Measurement and Safety Brainstorming Ay the end of this section, you should be able to: Questions list different instruments used to measure physical quantities such as t What is meant by length, area, volume, mass, and time in their local area; measurement? list modern length, mass and time measuring devices; t What measuring devices are used to measure length, mass and time using different units. measure volume, mass and length in your local area? 2.2 Measurement and Safety 21 Activity 2.5 Measurement t Observe your Measurement is the process of comparing an unknown quantity with another local environment quantity of its kind (called the unit of measurement). The measurement process and list different has three key elements: instruments used to measure physical The physical quantity to be measured. quantities. t Discuss different The necessary measuring tools. measurement ac- Units of measurements used (standard units). tivities and related issues in life. Twenty-first century civilization is unthinkable without an appropriate measure- ment tools on which everyday life depends. Modern society simply could not exist without measurement. Figure 2.11 shows some measuring devices applicable today. Figure 2.11 Examples of measuring tools of some physical quantities. 22 Unit 2 Physical Quantities Measuring Length When you are measuring the length of objects, you are comparing it with the standard length. The SI unit of length is meter (m) as we discussed before. There are also non SI units of length. These are millimeter (mm), centimeter (cm) and kilometer (km). Key Concept: t Measurement of any physical quantity involves comparison with a cer- tain basic, arbitrarily chosen, internationally accepted reference standard called unit. Figure 2.12 Standard length measuring instruments. 2.2 Measurement and Safety 23 Activity 2.6 t Make groups and measure the length and width of your exercise book in meter, centimeter and millimeter. t Which measuring instrument of length can you use for measuring the diameter of a small spherical marble? t A farmer wants to know the length of his plots of land in meter but he has only a long rope, a 50 cm ruler and a 6 m long stick. How can he easily measure the length of his plot? Discuss in groups. Length is one of the fundamental (basic) physical quantities which describes the distance between two points. Activity 2.7 t Measure the length and width of your blackboard in meter unit. t Calculate the area of the blackboard using the above measured values in meter square unit. Exercise 2.6 t Compare your results with that of your friends’. t What mecha- nisms do people in your locality use to measure the mass of Definition: Every physical quantity can be represented by its numerical an object? value and unit. t Which scientific mass measuring Measurement is the comparison of an unknown quantity with the known instrument is used fixed unit quantity. It consists of two parts: the unit and the number indicating in your locality? how many units are in the quantity being measured. For example: The length of a table is 3 meters. In this example, 3 is the magnitude, and meter is the standard (unit) of that quantity. 24 Unit 2 Physical Quantities Key Concept: t Length is the fundamental physical quantity that describes the distance between two points. t The SI unit of length is meter (m). Activity 2.8 Measuring Mass t Visit different shops in your living Measuring mass is a day to day activity in human life. People in various parts of area and observe the world measure the mass of an object in different ways. the procedure of measuring goods Definition: Mass is a basic physical quantity. It is defined as the amount carefully. Write the of matter contained in a body. procedures and exactness of the The SI unit of mass is a kilogram (kg). There are also non SI units used measurement. to measure the mass of an object. In scientific way mass is measured by an instrument called beam balance. Activity 2.9 t Collect different simple objects such as a) a duster, b) an exercise book, c) one stick of chalk. t Measure the mass of these objects and record the measured values in a table. t Compare your recorded value with that of other groups and discuss. Key Concept: t Mass is a basic physical quantity. It is defined as the amount of matter contained in a body. tThe S.I unit of mass is the kilogram (kg). Measuring Time Figure 2.13 Different scientific mass measuring instruments. How long does it take between the sun rise and set in your location? Do the people in your locality use the sun set and sun rise for measuring time? Some people in the rural parts of Ethiopia traditionally use the position of the sun or the position 2.2 Measurement and Safety 25 of shadows of their house or trees to estimate the time. A traditional clock that shows the time of the day by the shadow of an upright object that falls on to a flat surface marked with hours is called sundial. However, this way of measuring time has no standard and is not accurate. Time is the basic physical quantity. It describes the duration between the beginning and end of an event. The SI unit of time is second (s). The commonly used non SI units of time are: minute, hour, day, week, month and year. Activity 2.10 t Discuss in groups and list the names of scientific time measuring devices. t Record the activities you do from sun rise to sun set. Compare your recorded activities with that of your friend. Some of you are effectively using your time to accomplish different activities. Discuss the wise use of time in relation to its contribution for the development of our country. Key Concept: t Time is a basic physical quantity. It describes the duration between the beginning and end of an event. tThe S.I unit of time is second (s). Figure 2.14 Different scientific time measuring devices. Laboratory Safety rules A systematic and careful laboratory work is an essential part of any science program since laboratory work is the key to progress in science. The equipment and apparatus you use involve various safety hazards, just as they do for working physicists. Students should follow the general laboratory safety guidelines so that working in the physics laboratory can be a safe and enjoyable process of discovery. These safety rules are: Always wear a lab safety goggles. Avoid wearing baggy clothing, bulky jewelry, dangling bracelets, open-toed shoes or sandals. NEVER work alone in the laboratory. 26 Unit 2 Physical Quantities Only books and notebooks needed for the experiment should be in the lab. Read about the experiment before entering the lab. Do not eat, drink, apply cosmetics, or chew gum in the laboratory. NEVER taste chemicals. Do not touch. Report all accidents to the teacher immediately, no matter how mi- nor. Exercise caution when working with electrical equipment. Perform only those experiments authorized by the teacher. Wash hands thoroughly after participating in any laboratory activity. 2.3 Classification of Physical Quantities Brainstorming At the end of this section, you should be able to: Questions classify physical quantities as fundamental and derived physical quanti- What is the differ- ties; ence between funda- describe derived physical quantities in terms of fundamental quantities; mental and derived physical quanti- differentiate between fundamental and derived units; ties? Some physical quantities have only classify physical quantities as scalar and vector quantities. magnitude. How- ever, other physical quantities have Physical Quantities both magnitude and direction. Can Definition: A physical quantity is anything that you can measure. For you mention some example, length, temperature, distance and time are physical quantities. examples of these physical quantities? Quantities that can be measured directly or indirectly are known as physical quantities. The measured values of physical quantities are described in terms of number and unit. Each physical quantity and its unit have a symbol. 2.3 Classification of Physical Quantities 27 In Activity 2.7, you can observe that some physical quantities are directly mea- sured while other physical quantities are measured by combining two or more measurable quantities. For example you measured the width and length of your blackboard directly. However, the area is measured by multiplying the length and width of the blackboard - A = l × w. Physical quantities can be classified into two. Activity 2.11 Fundamental or basic physical quantities t In activity 2.7 Derived physical quantities you measured the length, width and Fundamental or basic physical quantities: are physical quantities which can area of the black- be measured directly. They cannot be described in terms of other physical quan- board. Discuss the tities. The units used to measure fundamental quantities are called fundamental symbols of the phys- units. i.e., the unit of fundamental quantity is called fundamental unit. It does ical quantities and their units. Is there not depend on any other unit. There are seven fundamental physical quantities any difference be- as shown in Table 2.3. tween length, width Table 2.3 The fundamental or basic physical quantities with their units and symbol of and area? units. Basic physical quantities Symbol Basic unit Symbol Activity 2.12 Length l meter m Mass m kilogram kg t Discuss in groups Time t Second s and classify physical Temperature T Kelvin K quantities (length, Current I Ampere A mass, speed, vol- Amount of substance n Mole mol ume, force and Luminous intensity Iv Candela cd pressure) as funda- mental or derived. Exercise 2.7 t Describe volume, density, and speed as combination of fundamental physical quantities. t Determine the units of volume, density and speed using basic units. t Discuss how to use mobile phone (Android) to measure the time, heartbeat and body temperature. 28 Unit 2 Physical Quantities Derived physical quantities: Physical quantities which depend on one or more fundamental quantities for their measurements are called derived physical quantities. The units of derived quantities which depend on fundamental units for their measurement are called derived units. Area, volume, density, and speed are some examples of derived physical quantities. Table 2.4 shows some derived quantities with their units and symbol of units.. Table 2.4 Some derived physical quantities and their units. Physical quantity Symbol Formula Unit Symbol of the unit Distance meter m Speed v Time second s Mass kilogram kg Density ρ Volume meter cube m3 Velocity meter m Acceleration a Time second square s2 kg.m Force F Mass × Acceleration newton(N) s2 kgm2 Work W Force × Displacement joule (J) s2 Force kg Pressure P Area pascal (Pa) m.s2 Scalar and Vector Quantities Physical quantities can also be classified as scalar and vector quantities. Some Activity 2.13 physical quantities are described completely by a number and a unit. A number Discuss in groups with a unit is called a magnitude. However, other quantities have a direction and classify the attached to the magnitude. They cannot be described by a number and unit only. following physical quantities as scalar Thus, physical quantities are grouped into two. These are: or vector quantity: Scalar quantities mass, time, area, speed, velocity, ac- Vector quantities celeration, force, energy, work, pres- A scalar quantity is a physical quantity which has only magnitude but no sure, momentum, direction. electric current, current density, Examples are: distance, mass, time, temperature, energy etc. displacement, and temperature. 2.4 Unit conversion 29 A vector quantity is a physical quantity which has both magnitude and di- rection. When expressing that the car moves 50 km/h to east, this gives full information about the velocity of the car that includes magnitude and direction (50 km/h is the magnitude, and east is the direction). Because of this, velocity is a vector quantity. Examples are: displacement, acceleration, force, etc. A vector can be represented either by a single letter in bold face or by a single letter with arrow head on it. For example: displacement can be represented as ~ S or S. Key Concept: tPhysical quantity: anything that you can measure and describe by a number and unit.. t Fundamental physical quantities: physical quantities which can be measured directly. t Derived physical quantities: Physical quantities which depend on one or more fundamental quantities for their measurements. t Scalar quantities: Physical quantities that are described only by their magnitude. t Vector quantities: Physical quantities that are described by their mag- nitude and direction. 2.4 Unit conversion At the end of this section, you should be able to: Brainstorming convert one unit of length to another unit of length. Question convert one unit of mass to another unit of mass. t How many me- ters, centimeters convert one unit of time to another unit of time. and millimeters are there in one In the previous section you have learned different physical quantities. These kilometer? physical quantities have SI and non SI units. It is possible to convert units from SI t How many grams are there in one kilo- unit to non SI unit and vice versa. Conversion of units is the conversion between gram? How many different units of measurement for the same physical quantity, typically through seconds are there in multiplicative conversion factors. one day? 30 Unit 2 Physical Quantities The relation between meter and other non SI units is given in Table 2.5. 2.4 Unit conversion 31 Example 2.3 The distance between two houses is 200 meter. What is the distance in: a) centime- ter b) kilometer c) millimeter Given: l = 200 m Solution: a) 1m = 100 cm 200 m = ? (200 m × 100 cm) l in cm = = 20000 cm (1 m) b) 1m = 0.001 km 200 m = ? (200 m × 0.001 km) l in km = = 0.2 km (1 m) c) 1m = 1000 mm 200 m = ? 200 m × 1000 mm l in m = 1m = 200000 mm = 2 × 105 mm Table 2.5 Conversion between units of length. 1 kilometer (km) 1000 meter (m) 1 meter (m) 100 centimeter (cm) 1 meter (m) 1000 millimeter (mm) 1 centimeter (cm) 10 millimeter (mm) 1 meter (m) 0.001 kilometer (km) 1 centimeter (cm) 0.01 meter (m) 1 millimeter (mm) 0.001 meter (m) Exercise 2.8 1. Which one of the following is a suitable unit to measure the distance between the Earth and the Moon? 32 Unit 2 Physical Quantities (A) mm (B) km (C) cm (D) m (E) all 2. Which one of the following is a suitable unit to measure the diameter of electric wire? (A) mm (B) km (C) cm (D) m (E) all 3. A hydrogen atom has a diameter of about 10 nm. (a) Express this diameter in meters. (b) Express this diameter in millimeters. (c) Express this diameter in micrometers. The relationship between the SI units and non SI units of mass are shown in Table 2.6. Table 2.6 Relationship between units of mass. 1 kilogram (kg) 1000 gram (g) 1 gram (g) 0.001 kilogram (kg) 1 milligram (mg) 0.001 gram (g) 100 kilogram (kg) 1 quintal 1000 kilogram (kg) 1 tonne Example 2.4 In one of the pans of a beam balance the masses 1.5 kg, 500 g, 250 g, 25 g and 0.8 g are placed to measure the mass of unknown object. What is the mass of an object in gram and kilogram on the other side of the pan if they are in balance? Given: m = 1.5 kg , 500 g , 250 g , 25 g , 0.8 g , Required: Total mass in g and Kg Solution: Total mass =sum of masses in the pan = 1.5 kg + 500g + 250 g + 25 g + 0.8 g 2.4 Unit conversion 33 = 1500 g + 500 g + 250 g + 25 g + 0.8 g = 2275.8 g, 1000 g = 1 kg, 2275.8 g = ? 2275.8 g × 1 kg mass in kg = = 2.2758 kg 1000 g Table 2.7 The relation between different units of time. 1 minute (min) 60 second (s) 1 hour (hr) 60 minute (min) 1 day 24 hours (hrs) 1 week 7 days 1 month 30 days 1 year 365.25 days Example 2.5 Express the following times in seconds. a) 2 hours b) 0.5 hour c) 3/5 hour Solution: a) 1hr = 3600 s , 2 hr × 3600 s 2 hr =? =⇒ t = = 7200 s 1 hr b) 1hr = 3600 s , 0.5 hr × 3600 s 0.5 hr =? =⇒ t = = 1800 s 1 hr c) 1hr = 3600 s , 3 3 5 hr × 3600 s hr =? =⇒ t = = 2160 s 5 1 hr 34 Unit 2 Physical Quantities Exercise 2.9 1. How many hours, minutes and seconds are there in a day? 2. List some traditional ways of measuring time in your community. 3. Express the following time in minutes and seconds. (a) 0.25 hr. (b) 3.2 hrs. (c) 6.7 hrs. Unit Summary Scale is a set of numbers, amounts etc., used to measure or compare the level of something. There are four types of measurement scales: nominal, ordinal, inter- val and ratio. In Physics, most of the scales are ratio scales. Measurement is the comparison of an unknown quantity with a known one (standard unit). Standard units are conventional units which are used to measure physical quantities scientifically. Traditional measuring units are not exact and have no a standard. Prefixes are used to simplify the description of physical quantities that are very big or very small. Quantities that can be measured directly or indirectly are known as physical quantities. Physical quantities are characteristics or properties of an object that can be measured or calculated from other measurements. Physical quantities are classified as fundamental /or basic physical quantities, and derived physical quantities. Length, time, mass, temperature, current, amount of substance and luminous intensity are fundamental quantities in science. All other physical quantities are derived physical quantities. 2.4 Unit conversion 35 Meter, second, kilogram, Kelvin, Ampere, mole and candela are fundamental (basic) units. Physical quantities can be categorized as vectors or scalars. Meter, kilogram and Second are the SI unit of length, mass, and time respectively. SI units can be converted to non SI units and vise versa. End of Unit Questions and Problems Part I. Multiple choice 1. Which one of the following scale allows addition, subtraction, multi- plication and division? (a) Nominal scale (b) ratio scale (c) ordinal scale (d) interval scale 2. Which one of the following is NOT a fundamental physical quantity? (a) Temperature (b) density (c) time (d) mass 3. The SI standard of time is based on: (a) The daily rotation of the Earth (b) The yearly revolution of the Earth about the sun (c) 9 192 631 770 times the period of vibration of radiation from the cesium-133 atom. (d) A precision pendulum clock 4. Which one of the following is a derived SI unit? (a) Second (b) Joule (c) kilogram (d) Kelvin 5. A nanosecond is (a) 109 s (b) 10−9 s (c) 10−6 s (d) 10−12 s 6. Which one of the following method provides a more reliable mea- surement of time in daily life activities? (a) Looking the rotation of stars in the sky (b) Using a digital watch (c) Looking the position of shadows of trees 36 Unit 2 Physical Quantities (d) Looking the position of the sun on the sky 7. Which one of the following pair of physical quantities has the same unit? (a) displacement and distance (b) mass and force (c) speed and acceleration (d) volume and area 8. How many minutes is 3 hour + 10 minute + 120 s? (a) 182 min (b) 202 min (c) 212 min (d) 192 min 9. If the masses of bodies A, B, and C are 2 ton, 100 kg and 1 kg respec- tively. Then the total mass of the bodies is (a) 221 kg (b) 2101 kg (c) 2011 kg (d) 2001 kg 10. Why are fundamental physical quantities different from derived physical quantities? (a) Fundamental physical quantities are derived from derived physical quantities. (b) Derived physical quantities are derived from fundamental physical quantities. (c) Derived and fundamental physical quantities have no relation. (d) All are answers 11. Which of the following would describe a length that is 2.0 × 10−3 of a meter? (a) 2.0 km (b) 2.0 cm (c) 2.0 mm (d) 2.0 µm 12. Which quantity is a vector? (a) Energy (b) force (c) speed (d) time 13. Which one of the following lists is a set of scalar quantities? (a) length, force, time (b) length, mass, time (c) length, force, acceleration (d) length, force, mass Part II: Write true if the statement is correct and false if the statement is wrong. 2.4 Unit conversion 37 1. Second is a device used to measure time. 2. Candela is a derived physical quantity. 3. The unit of force can be derived from the units of mass, length and time. 4. One kilometer is 100 meter. 5. For a very large or very small numbers prefixes are used with SI units. 6. Scalar quantity can be described by its magnitude and direction. Part III: Short answer questions 1. What is the difference between interval scale and ratio scale? 2. How many seconds are there in 12 hours? 3. What is measurement? 4. What is the difference between traditional measuring units and scientific measuring units? 5. Define the following terms: a) Meter b) second c) kilogram d) length e) time f) mass g) Physi- cal quantity h) derived physical quantity i) fundamental physical quantity. j) scalar physical quantity k) vector physical quantity 6. Which SI units would you use for the following measurements? (a) the length of a swimming pool (b) the mass of the water in the pool (c) the time it takes a swimmer to swim a lap 7. Which instrument is used to measure the thickness of a sheet metal? 8. Write some safety rules. 9. Give three examples of scalar and vector quantities. Part IV: Workout problems 38 Unit 2 Physical Quantities 1. In one of the pans of the beam balance the masses 3 kg, 900 g, 90 g and 5 g are placed. What amount of mass should be placed on the other side of the beam balance to make it balanced? 2. For each of the following symbols, write out the unit in full and write what power of 10 it represents: (a) micro g (b) mg 3. The doctor wants to know the age of his patient and asks him how 1 old he is. The patient replies that he is 25 2 years old. What is the age of the patient in month? 4. The student wants to measure the length of the classroom using a tape meter. The tape meter reads 8m and 40 cm. What is the length of the classroom in cm? 5. How many minutes are there in 3 days? 6. If the area of a single ceramic is 0.25 m 2 , how many ceramics are used to cover a floor of a classroom whose area is 40m 2 ? 7. The distance between Sun and the Earth is about 1.5 × 1011 m. Ex- press this distance using prefix. 8. The volume of the Earth is on the order of 1021 m 3. (a) What is this in cubic kilometers (km 3 )? (c) What is it in cubic centimeters (cm 3 )? 9. For each of the following, write the measurement using the correct symbol for the prefix and the base unit: (a) 101 nanoseconds (b) 10 milligrams (c) 72 gigameters. Unit 3 Motion in a Straight Line Introduction In this unit, you will be introduced to the basic concepts of motion. We encounter Brainstorming motion in our day-to-day activities and have enough experience about it. You Question might have learnt in lower grades that everything in the universe moves. It is t What do you because of this that motion is one of the key topics in physics. We use the basic think is motion? concepts of distance, displacement, speed, velocity and acceleration to express Give some examples motion. There are different types of motions. Motion in a straight line is one of of motion that you the simplest forms of motion in a specific direction. The motions of a car on a encounter in your road, the motion of a train along a straight railway track or an object falling freely daily life. are examples of one-dimensional motion. At the end of this unit, you should be able to: describe motion in terms of frame of reference, displacement, speed, ve- locity, and acceleration; draw diagrams to locate objects with respect to a reference; solve problems involving distance, displacement, speed, velocity and acceleration; make practical measurements of distance, displacement, average speed, average velocity and acceleration. 40 Unit 3 Motion in a Straight Line 3.1 Position, Distance and Displacement At the end of this section, you should be able to: define motion, position, and displacement; describe motion in terms of frame of reference; differentiate between position, distance and displacement; draw diagrams to locate objects with respect to a reference frame. The most convenient example to explain about position, distance and dis- placement is your daily travel from your home to your school. When you go to school, your journey begins from your home. Your home is your original position. After some time, you will reach your school. Your school is your final position. In this process, you are continuously changing your position. While traveling from home to school, you are increasing the gap between your present position and your home. This continuous change of position is known as motion. Note that your change of position is observed by considering the distance from your school to home. Your home is taken as a reference frame. Motion is a continuous change in position of an object relative to the position of a fixed object called reference frame. Key Concept: t A frame of reference is a set of coordinates that can be used to deter- mine positions of objects. t Motion is the change in the position of the object with respect to a fixed point as the time passes. A body is said to be at rest in a frame of reference when its position in that reference frame does not change with time. If the position of a body changes with time in a frame of reference, the body is said to be in motion in that frame of reference. The concepts of rest and motion are completely relative; a body at rest in one reference frame may be in motion with respect to another reference frame. For example, if you are 2 m from the doorway inside your classroom, then your reference point is the doorway. Your classroom can be used as a reference frame. In the classroom, the walls are not moving, and can be used as a fixed frame of reference. We commonly use the origin as a fixed reference point to describe motion along a straight line. 3.1 Position, Distance and Displacement 41 Exercise 3.1 t Assume you are sitting on a horse and the horse is moving at a certain speed. Are you at rest or in motion? Discuss it by taking two frames of reference: the horse itself and some fixed point on the ground. Key Concept: t Position is a mea- Position surement of a loca- To describe the motion of a particle, we need to be able to describe the position tion, with respect of the particle and how that position changes as the particle moves. Motion is to some reference the change in the position of the object with respect to a fixed point as the time point (usually an origin). passes. For one-dimensional motion, we often choose the x axis as the line along which the motion takes place. Positions can therefore be negative or positive with respect to the origin of the x-axis. Figure 3.1 shows the motion of a rider in a straight line. Its position changes as it moves. Have you ever used Google Maps to locate your geographical position while you are moving from some place to another? Google Maps is a Web-based service that provides detailed information about geographical regions and sites around the world. In addition to conventional road maps, Google Maps offers aerial and Figure 3.1 A rider in motion changes its position as it moves. 42 Unit 3 Motion in a Straight Line satellite views of many places. Google Maps provides you with the longitude (east-west position) and latitude (north-south position) coordinates of a location or position of a place. You can see how far you have travelled and how you travelled from place to place, such as walking, biking, driving or on public transport. The following steps guide you to get started using Google Maps: Step 1: At first you need to open the Google Maps software application on your Android phone, tablet or computer. For more information, click here to see Google Maps https://www.google.com/maps/ Exercise 3.2 Step 2: Search for a place or tap it on the map. t What is the dis- Step 3: In the bottom right, tap directions. tance around a Step 4: To add destination you have to go to the top right and tap more and then standard football add a stop. field? t Is distance a pos- Distance itive or negative quantity? Distance travelled is a measure of the actual distance covered during the motion of a body. In other words, distance is the total path length traveled by the body. The distance travelled does not distinguish between motion in a positive or negative direction. This means that it is a scalar physical quantity. The SI unit of distance is meter (m), though it can also be measured in other non-SI units such as kilometer (km), miles (mi), centimeter (cm), etc. The symbol for distance is s. Pictorial representation of the distance covered by a runner is shown in Figure 3.2. Figure 3.2 The distance covered by a runner. 3.1 Position, Distance and Displacement 43 Displacement When an object moves, it changes its position. This change of position in a certain direction is known as displacement. A displacement is described by its magnitude and direction. Hence, it is a vector quantity. Displacement is independent of the path length taken. For example, you travel from your home to school. After school, you travel o your home. Therefore, the change in your position when you return back to your home is zero. In this case, we say that your displacement is zero. The SI unit of displacement is the same as the SI unit of distance that is meter (m). Figure 3.3 shows the difference between distance and displacement of the motion covered from point A to point B. ~i at time t i. At a later time, Figure 3.1 shows a student on a bicycle at position X t f , the student is at position X~f. The change in the student’s position, X~f − X ~i , is called a displacement. Thus, displacement ~ S can be written as ~ S = X~f − X ~i (3.1) Figure 3.3 Illustration of distance Key Concept: and displacement. t Displacement is the change in an object’s position. Table 3.1 Difference between distance and displacement. Distance Displacement It is the length of path travelled It is the shortest distance between by an object in a given time. the initial and final positions. It is a scalar quantity. It is a vector quantity. It depends on the path followed It depends o the initial and final by the object. positions of the object, but not necessarily on the path followed. It can be more than or equal to Its magnitude can be less than or the magnitude of displacement. equal to the distance. 44 Unit 3 Motion in a Straight Line Activity 3.1 t Three students walked on a straight line. The first student walked 200 m to the right from a reference point A, then returned and walked 100 m to the left and then stopped. The second student walked 200 m from point A to the right, then returned and walked 300 m to the left and stopped. The third student walked 200 m to the right from point A, then returned and walked 200m to the left and stopped at point A. Discuss in groups about the total distance and displacements of the first, the second and the third student. Example 3.1 A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her displacement? (b) What distance does she ride? (c) What is the magnitude of her displacement? Solution: To solve this problem, we need to find the difference between the final position and the initial position while taking care to note the direction on the axis. a) Displacement: The rider’s displacement is ~ S = X~f − X ~i = 1 km west. The displace- ment is negative if we choose east to be positive and west to be negative. b) Distance: The distance traveled is 3 km + 2 km = 5 km. c) The magnitude of the displacement is 1 km. Exercise 3.3 t What is the dis- placement if the Exercise 3.4 final position is the t Given the following values for the initial position X i and final position same as the initial X f , check whether the value of the net displacement is positive or negative. position? a) X f = (5, 0) and X i = (−1, 0) b) X f = (10, 0) and X i = (−15, 0) c) X f = (6, 0) and X i = (4, 0) 3.2 Average Speed and Instantaneous Speed 45 3.2 Average Speed and Instantaneous Speed At the end of this section, you should be able to: differentiate between average speed and instantaneous speed; compute the average speed of a body; moving in a straight line covering a certain distance in a given time; estimate the speed of moving bodies in your surroundings. Speed is a quantity that describes how fast a body moves. Speed is the rate at which an object changes its location. Like distance, speed is a scalar quantity because it has a magnitude but no direction. Since speed is a rate, it depends on the time interval of motion. Its symbol is v. In other words, speed is the distance covered by a moving body per unit time. The SI unit of speed is meter per second (m/s). Other units of speed include kilometer per hour (km/h) and miles per hour (mi/h). The mathematical equation used to calculate speed is Distance speed = (3.2) time s v = (3.3) t One of the most obvious features of an object in motion is how fast it is moving. Exercise 3.5 In your journey from home to school, you walk slowly for some time, and you run another time to cover the total distance. This shows that the speed for the walk t In Figure ??, what and the speed for the run are different. In this regard, we define average speed. does the speedome- ter read? Speed and average speed are not the same although they are derived from the same formula. The average speed is defined as the total distance travelled divided by the total time it takes to travel that distance: Total distance covered Average speed = (3.4) Total time taken (3.5) Figure 3.4 Speedometer. stot vav = (3.6) ttot 46 Unit 3 Motion in a Straight Line During a typical trip to school by car, the car undergoes a series of changes in its speed. If you were to look at the speedometer readings at regular intervals, you would notice that it changes. The speedometer of a car gives information about the instantaneous speed of the car. It shows the speed of the car at a particular instant in time. The speed at any specific instant is called the instantaneous speed. To calculate the instantaneous speed, we need to consider a very short time interval-one that approaches zero. For example, a school bus undergoes changes in speed. Mathematically the instantaneous speed is given ∆s vins = as ∆t → 0 (3.7) ∆t where, ∆s is the distance travelled during the given very short time interval ∆t. Instantaneous speed and average speed are both scalar quantities. When you solve the