Physics Teacher’s Guide – Grade 10 PDF

Physics Teacher’s Guide – Grade 10 FEDERAL DEMOCRATIC REPUBLIC OF ETHIOPIA MINISTRY OF EDUCATION Physics Teacher’s Guide...

Physics Teacher’s Guide – Grade 10 FEDERAL DEMOCRATIC REPUBLIC OF ETHIOPIA MINISTRY OF EDUCATION Physics Teacher’s Guide Grade 10 FEDERAL DEMOCRATIC REPUBLIC OF ETHIOPIA MINISTRY OF EDUCATION  Physics Teacher’s Guide Grade 10 Contributors: Fikadu Eshetu (Ph.D), Writer Mideksa Kasahun (MSc), Writer Moges Tsega (Ph.D), Content Editor Samuel Assefa (Ph.D), Curriculum Editor Felekech G/Egziabher (Ph.D), Language Editor Umer Nuri (MSc), Illustrator Derese Tekestebrihan (Ph.D fellow), Book Designer Evaluators: Zafu Abraha (MSc) Girmaye Defar (MSc) Dessie Melese (MSc) First Published xxxxx 2022 by the Federal Democratic Republic of Ethiopia, Ministry of Education, under the General Education Quality Improvement Program for Equity (GEQIP-E) supported by the World Bank, UK’s Depart- ment for International Development/DFID-now merged with the Foreign, Common wealth and Development Office/FCDO, Finland Ministry for Foreign Affairs, the Royal Norwegian Embassy, United Nations Children’s Fund/UNICEF), the Global Partnership for Education (GPE), and Danish Ministry of Foreign Affairs, through a Multi Donor Trust Fund. © 2022 by the Federal Democratic Republic of Ethiopia, Ministry of Educa- tion. All rights reserved. The moral rights of the author have been asserted. No part of this textbook reproduced, copied in a retrieval system or trans- mitted in any form or by any means including electronic, mechanical, magnetic, photocopying, recording or otherwise, without the prior written permission of the Ministry of Education or licensing in accordance with the Federal Democratic Republic of Ethiopia as expressed in the Federal Negarit Gazeta, Proclamation No. 410/2004 - Copyright and Neighboring Rights Protection. The Ministry of Education wishes to thank the many individuals, groups and other bodies involved – directly or indirectly - in publishing this Text- book. Special thanks are due to Hawassa University for their huge contri- bution in the development of this textbook in collaboration with Addis Ababa University, Bahir Dar University and Jimma University. Copyrighted materials used by permission of their owners. If you are the owner of copyrighted material not cited or improperly cited, please con- tact the Ministry of Education, Head Office, Arat Kilo, (P.O.Box 1367), Addis Ababa Ethiopia. PHOTO CREDIT: Printed by: xxxxxxxx PRINTING P.O.Box xxxxxx xxxxxxx, ETHIOPIA Under Ministry of Education Contract no. xxxxxxxxxxx ISBN: 978-999944-2-046-9 Foreward Education and development are closely related endeavors. This is the main reason why it is said that education is the key instrument in Ethiopia’s de- velopment and social transformation. The fast and globalized world we now live in requires new knowledge, skill and attitude on the part of each individual. It is with this objective in view that the curriculum, which is not only the Blueprint but also a reflection of a country’s education system, must be responsive to changing conditions. It has been almost three decades since Ethiopia launched and imple- mented new Education and Training Policy. Since the 1994 Education and Training Policy our country has recorded remarkable progress in terms of access, equity and relevance. Vigorous efforts also have been made, and continue to be made, to improve the quality of education. To continue this progress, the Ministry of Education has developed a new General Education Curriculum Framework in 2021. The Framework cov- ers all pre-primary, primary, Middle level and secondary level grades and subjects. It aims to reinforce the basic tenets and principles outlined in the Education and Training Policy, and provides guidance on the preparation of all subsequent curriculum materials – including this Teacher Guide and the Student Textbook that come with it - to be based on active-learning methods and a competency-based approach. In the development of this new curriculum, recommendations of the edu- cation Road Map studies conducted in 2018 are used as milestones. The new curriculum materials balance the content with students’ age, incorpo- rate indigenous knowledge where necessary, use technology for learning and teaching, integrate vocational contents, incorporate the moral edu- cation as a subject and incorporate career and technical education as a subject in order to accommodate the diverse needs of learners. Publication of a new framework, textbooks and teacher guides are by no means the sole solution to improving the quality of education in any coun- try. Continued improvement calls for the efforts of all stakeholders. The teacher’s role must become more flexible ranging from lecturer to motiva- tor, guider and facilitator. To assist this, teachers have been given, and will continue to receive, training on the strategies suggested in the Framework and in this teacher guide. Teachers are urged to read this Guide carefully and to support their students by putting into action the strategies and activities suggested in it. For systemic reform and continuous improvement in the quality of cur- riculum materials, the Ministry of Education welcomes comments and suggestions which will enable us to undertake further review and refine- ment. ADDIS ABABA, ETHIOPIA FEDERAL DEMOCRATIC REPUBLIC OF ETHIOPIA xxxxx 2022 MINISTRY OF EDUCATION Contents 1 Vector Quantities 5 1.1 Scalars and vectors........................ 6 1.2 Vector representation...................... 8 1.3 Vector addition and subtraction................ 10 1.4 Graphical Method of Vector Addition and Subtraction... 14 1.5 Vector resolution......................... 20 2 Uniformly Accelerated Motion 27 2.1 Position and Displacement................... 28 2.2 Average velocity and instantaneous velocity......... 31 2.3 Acceleration............................ 37 2.4 Equations of motion with constant acceleration...... 41 2.5 Graphical representation of uniformly accelerated motion 46 2.6 Relative velocity in one dimension............... 51 3 Elasticity and rigid body in static equilibrium 59 3.1 Elasticity and plasticity...................... 60 3.2 Density and Specific Gravity................... 62 3.3 Stress and Strain......................... 65 3.4 Young’s Modulus......................... 67 3.5 Static equilibrium......................... 71 4 Static and Current Electricity 81 4.1 Charges in Nature........................ 82 4.2 Methods of Charging a Body.................. 84 4.3 The Electroscope......................... 86 4.4 Electrical Discharge........................ 88 4.5 Coulomb’s Law of Electrostatics................ 91 4.6 The Electric Field......................... 93 4.7 Electric circuits.......................... 96 4.8 Current, Voltage and Ohm’s law................. 99 4.9 Combination of Resistors in a Circuit............. 107 4.10 Voltmeter and Ammeter Connection in a Circuit...... 113 vi CONTENTS vii 4.11 Electrical Safety in General and Local context........ 116 4.12 Electric Projects.......................... 118 5 Magnetism 131 5.1 Magnet............................... 132 5.2 Magnetic Field........................... 134 5.3 The compass and the earth’s magnetic field......... 138 5.4 Magnetic field of a current carrying conductor........ 140 5.5 Magnetic force on a moving charge.............. 142 5.6 Magnetic force on a current carrying conductor....... 144 5.7 Magnetic force between two parallel current carrying con- ductors............................... 146 5.8 Applications of magnetic forces and fields.......... 149 6 Electromagnetic wave and geometrical optics 155 6.1 Electromagnetic Waves..................... 156 6.2 EM Spectrum........................... 158 6.3 Light as a wave.......................... 161 6.4 Laws of reflection & Refraction................. 164 6.5 Mirrors and Lenses........................ 174 6.6 Human Eye and Optical Instruments............. 188 6.7 Primary colors of light and human vision........... 192 6.8 Color addition of light...................... 194 6.9 Color subtraction of light using filters............. 196 Index 203 CONTENTS 1 Introduction to the Teacher’s Guide Generally, physics contributes to the development of our country in many ways. A knowledge and understanding of physics help students to under- stand the world and appreciate how it works. It contributes to a society that benefits from this understanding, and produces people who realize how the environment can be exploited in a sustainable way for the benefit of society. It prepares students for employment, both in a general way and as a preparation for careers that require knowledge of the subject, such as engineering or communications. However, a study of physics does not just mean learning facts. Physics, as with the other sciences, requires the student to develop creativity and problem-solving skill. The Secondary physics curriculum takes a competency-based, active learning approach, underpinned by three broad outcomes: knowledge, values and attitudes, and skills. The Students’ Book and Teacher’s Guide places emphasis on learner centered classroom and field activities, not only to help students to acquire knowledge, but also to develop problem-solving and decision- making skills, as well as a good attitude to society and the world around us. The teacher must make the students aware that science is a dynamic activity, a body of knowledge that constantly grows and is modified by experimentation. He or she can utilize new approaches to teaching and learning, involving a range of teaching styles, along with practical activities and field work, summarize in the ’Teaching Methods’ section below. General objectives of the Grade 10 physics course When students have completed Grade 10 physics they should: Acquire knowledge and understandings of vector representation, vector addition and subtraction, and properties of vectors. Develop skills of resolving and composing vectors. Develop interest in solving problems using vector approach. Gain knowledge and understanding on uniform and uniformly ac- celerated motion in one dimension 2 CONTENTS Develop skills in applying equations of uniformly accelerated mo- tion in solving problems Develop skills in drawing and interpreting graphs representing uni- form and uniformly accelerated motion Design and conduct investigations on the displacement, velocity, and acceleration of an object; analyze everyday phenomena in terms of these motions Gain elementary knowledge on basic properties of bulk matter such as elastic limit, density, tensile stress and strain. Apply the knowledge acquired now to the later advanced concepts, such as thermal expansion and fluid pressure. Understand and relate the principle of static equilibrium to everyday experience understand the basic properties of electric charge; item produce charges in different charging process and explain the charging pro- cess; have a conceptual understanding of Coulomb’s law and the factors which effect electrical force; understand the concept of an electric field qualitatively and quanti- tatively; understand the relationship among voltage, current and resistance; describe arrangement of resistors in a combination circuit and its practical implications; apply the concept of electricity in solving problems in their real-life situations. understand the nature and characteristics of magnets; understand what is meant by the magnetic field; CONTENTS 3 understand the concepts related to magnetic force; solve problems related to magnetism; appreciate simple applications of magnetism in your everyday life. Understand the properties and transmission of light in various me- dia and their applications. Investigate the properties of light through experimentation illustrate using diagrams and optical instruments. Predict the behavior of light through the use of ray diagrams and algebraic equations; Appreciate the contributions to such areas as entertainment, com- munications, and health made by the development of optical devices and other technologies. Each unit of study has specific learning competencies, and these are listed at the beginning of each unit of this Teacher’s Guide, period needed for each section and teaching activity and providing a useful answer checklist for teachers. Teaching methods The subject content can be delivered in different ways in order to achieve the specific objectives. The type of teaching method used will affect the skills and attitudes that the students develop. The teacher will want to use the most effective methods for teaching a particular topic. In Physics, it is recommended that the teacher use more than one teaching method in a single lesson – the discussion method might be suitable for the beginning of the lesson, followed by the discovery method, or a practical activity. Unit 1 Vector Quantities This unit should fill approximately 9 periods of teaching time. At the end of this unit, students will be able to: understand vectors and scalars; comprehend the techniques of vector addition and resolution; demonstrate vectors representation graphically; apply vector addition techniques to solve problems; discuss how vectors can be used to solve problems in real life situation; apply vector decomposition techniques to solve problems. Finding the best way to teach physics is to show students how the con- cepts are connected together, get them to relate the concepts to their experiences and elaborate on them in their own words. It’s always better to deepen understanding, reconstruct the ideas, and experiment around than just drill for the exam. Dear teacher, you would agree that a good way of introducing any concept in physics is to relate it to your students’ everyday experiences and make 5 6 Unit 1 Vector Quantities them understand why they need to study it. If you could also put in some activities, it would surely add to their interest. So here are some sugges- tions about how you could teach vector quantities to your students.You have 9 periods at your disposal for teaching the section. 1.1 Scalars and vectors This section should fill approximately 1 periods of teaching time. At the end of this section, students will be able to: define scalar and vector quantities; list down examples of scalar and vector quantities; describe the difference between vector and scalar quantities; compare and contrast vector and scalar quantities based their characteristics. Lesson 1: Scalars and vectors Starting off Before introducing the daily lesson, ask your student, for example, what is physical quantity? What can you tell me about a physical quantity like a mass? Is it a scalar or vector? What is the difference between mass and weight? Based on your student’s response, remind them about the defini- tion of physical quantity, scalars and vectors. Lesson description Introduction Dear teacher, after you remind the student about scalars and vectors using the oral question from the previous. Now you can introduce the lesson based on your students’ response. Vectors are physical quantities that have magnitude and direction. 1.1 Scalars and vectors 7 In put and model After you introduce the lesson, give the definition of scalar and vectors, explain if possible using PhET simulation, make it clear by identifying their differences and similarities. Relate the lesson with the students’ daily life experience. Engage your students to do an exercise 1.1 and 1.2. Evaluate your work and summarize the lesson. Guide Students through Their Practice While the students are doing the activities, you are expected to guide the students to learn by themselves. Check for understanding Check for students’ understanding while they are exploring by utilizing your own oral questions or the question below. 1. Explain how vectors differ from scalars. Give some examples. Exercise 1.1 Answer Dear teacher, remind your students about scalars and vectors. Direction is for only vectors and help them to elaborate by an example. Exercise 1.2 Answer Dear teacher, students give their own answer based on their previous knowledge, and help them while they list scalars and vectors. For example impulse, momentum, torque etc are vectors. Where next? Dear teacher, you have to encourage your students to start thinking about how vectors are represented. And remind your student to have a protractor and a ruler for the next topic:vector representation. Closure 8 Unit 1 Vector Quantities To close the lesson, allow students to describe verbally what they under- stood about scalars and vectors. After taking their idea, try to summarize the important concepts of the lesson. Answers to review questions 1. A vector quantity has a magnitude and a direction, while a scalar has only a magnitude. You can tell a given quantity is a vector or scalar: by whether or not it has a direction associated with it. Exam- ple: Speed is a scalar quantity, but velocity is a vector that specifies both a direction as well as a magnitude. 2. Force, weight and velocity have magnitude and direction, so that they are vectors. But other quantities (temperature,volume and age) have only magnitude, are scalars. 1.2 Vector representation This section should fill approximately 1 period of teaching time. At the end of this sectiion, students will be able to: identify the magnitude and direction of a vector; discuss how vectors can be represented graphically. Lesson 2: Vector representation Starting off Dear teacher, remind the student about scalars and vectors. Then you could ask your students this question: how can you represent vectors? Based on their response, try to correlate the lesson with daily life experi- ence and start off the lesson. Lesson description Introduction 1.2 Vector representation 9 Dear teacher, introduce the lesson, motivate you student to follow the lesson that you are going to deliver. In put and model Give short note, present the lesson, explain a parallel and anti parallel vectors. use demonstration using a computer and PhET simulation. Show them how to use ruler and protractor to represent vectors. Additionally, help your the students; when they practice activity 1.1 and exercise1.3. Guide the Students through Their Practice While the students are doing an activity 1.1, you are expected to guide and help the students, on scale measurement and using protractor to learn by themselves. Exercise 1.3 Students own answer. Activity 1.1 Dear teacher, while they are doing this activity in their group or indi- vidually, they should have a ruler and a protractor. Remind your stu- dents to put a scale of measurement before they go to measure. For example,B⃗ = 300km east is given. To represent graphically our scale should be 1: 100. and help them while they are doing this activity. Check for Understanding To assess students learning, you may ask your own oral questions or use review questions. Where next? You have to encourage students to start thinking about the importance of studying about an vector representation for their daily life activity. Closure To close the lesson, allow students to describe vector representation. After taking their idea, try to summarize lesson. 10 Unit 1 Vector Quantities Answers to review questions 1. Vectors are represented algebraically and geometrically. For example: C⃗ = 20 m nor t h. ⃗ = 100 km; 30o sout h o f east F 2. For example: If you use scale of measurement: scale 1 cm:1km for question number 2(a) and 1cm:1m/s for the next question and use Figure 1.1 Vector s the compass to determine the direction. You can get the vectors shown in the 1.1 and 1.2 1.3 Vector addition and subtraction This section should fill approximately 2 periods of teaching time. At the end of this sectiion, students will be able to: Figure 1.2 vector v Apply vector addition and subtraction techniques to solve real-life problems; define the resultant vector. Lesson 3: Vector addition Starting off Dear teacher, remind your student about vector representation. Ask your student, can two parallel vectors be added? Can velocity and force be added? If they say no, why? Again, use your own oral question and try to motivate your student to actively participate. Lesson description Introduction Introduce the lesson Using the students response of the question stated above and use your own approach. 1.3 Vector addition and subtraction 11 Input and model Based on the students response, try to give the short notes on the vector addition and subtraction. Dear teacher, there are some special case of two vector( ⃗ ⃗ ) additions. A and B a) When the Two Vectors are Parallel (Same Direction), the resultant vector ⃗ becomes: R (R) ⃗=⃗ A +B⃗ b)When the Two Vectors are Acting in Opposite Direction, the resultant ⃗ R vector(R): ⃗=⃗ ⃗ A −B ⃗ R c)When the two vectors are perpendicular, the resultant vector (R): ⃗= p A2 + B 2 Dear teacher, your students are new for inverse trigonometric function. So that, give an introduction and show, how to get the inverse trigonometric function using scientific calculator. The inverse tangent function (arctan(θ)) is defined as the following. The inverse tangent function is a function denoted by the t an −1 (x) or arctan(x) that assigns to each real number x the unique number y in (−π/2, π/2) such that x = t an(y). Read the user’s manual for your scientific calculator and find the tangent inverse of: (a) arctan(0.021) and (b) t an −1 (2) and help your student to use their on scientific calculator. Guide Students through Their Practice While the students are doing exercise 1.4 and 1.6 try help them. Exercise 1.5 Answer Dear teacher, two perpendicular vectors are joined either head to tail or tail to tail. So that you can use the triangle method or the parallelogram method of vector addition. Remind your student about Pythagoras’ theo- rem and trigonometry to determine the magnitude and direction of the resultant vector. Check for Understanding To assess students learning, you may ask them review questions or your 12 Unit 1 Vector Quantities own question. Where next? You have to encourage students to start thinking about the importance of studying about vector addition and subtraction for their daily activity. Closure To close the lesson, allow students to describe the vector addition and subtraction. After taking their idea, try to summarize the lesson. Lesson 4: Vector subtraction Starting off Dear teacher, remind your student about vector addition. Ask your student, can two parallel vectors be subtract? Can velocity and force be subtract? If they say no, why? Again, use your own other oral question and try to motivate your student to actively participate on the lesson. Lesson description Introduction Introduce the lesson Using the students response of the question stated above and use your own approach. Input and model Based on the students response, try to give the short notes on the vector subtraction. Dear teacher, For the two vector( ⃗ ⃗ ) acting in Opposite A and B ⃗ direction, the resultant vector(R): ⃗=⃗ R A −B⃗ Guide Students through Their Practice Exercise 1.4 Answer Dear teacher, actually the sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. Try to help the student to explain this concept using a daily activity. 1.3 Vector addition and subtraction 13 Check for Understanding To assess students learning, you may ask them review questions or your own question. Where next? You have to encourage students to start thinking about the importance of studying about vector subtraction for their daily activity. Closure To close the lesson, allow students to describe the vector subtraction. After taking their idea, try to summarize the lesson. Answers to review questions 1. Vector subtraction is the process of taking a vector difference, and is the inverse operation to vector addition. 2. The resultant vector is the result of adding two or more vectors together. When you add vectors, you need to add both a magni- tude and a direction. In other words, the individual vectors can be replaced by the resultant where the overall effect is the same. 3. → − Given: V = 5 uni t → − X = −5 uni t ⃗ =? required: R Solution: → − → − → − The resultant of anti parallel vectors is: R = V − X → − R = 5 uni t − 5 uni t = 0 When two vectors are exactly opposite in direction and equal in magnitude, The magnitude of the resultant vector is zero. 4. The sum of two vectors can only be zero if they are equal in mag- nitude and opposite in direction, the resultant becomes twice the magnitude of the given vector when they have equal magnitude and 14 Unit 1 Vector Quantities in the same direction. 5. Three vectors of unequal magnitude can add to give the zero vector. For example, As shown in the Figure 1.3, a vector 10 N long in the positive x direction added to two vectors of 4 N and 6 N each in the negative x direction will result in the zero vector. Figure 1.3 Zero resultant vector 1.4 Graphical Method of Vector Addition and Sub- for given three vectors. traction This section should fill approximately 3 periods of teaching time. At the end of this section, students will be able to: describe the graphical method of vector addition and subtrac- tion; use the graphical method of vector addition and subtraction to solve problems. Lesson 5: Triangle law of vector addition Starting off Start the topic by asking students about vector addition using triangle law of vectors through encouraging students. Remind the concepts of numerical vector addition. This helps you to know the students’ level of understanding. And it is crucial for shaping their knowledge if, in case, they have misconceptions about the concept vector addition using graphi- cal method(head to tail method). Lesson description Introduction Dear teacher introduce the graphical method of vector addition and sub- traction when the two vectors form the side of triangle. 1.4 Graphical Method of Vector Addition and Subtraction 15 Input and model Dear teacher, before you are going to deliver the lesson, read the materials and prepare demonstration-based teaching. Order your students to have a ruler and a protractor. Discuss the three graphical techniques: the triangle method, the parallelogram method, and the polygon method of graphical vector additions. Give a short note and show the resultant vector using scale measurement: triangle and parallelogram and polygon methods Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding To assess students learning, you may ask your on oral question and check their understanding. Closure Evaluate the lesson using oral questions or your own class room activity. Summarize the lesson using the triangle method. Lesson 6: Parallelogram law of vector addition Starting off Start the topic by asking students for prior knowledge about vector addi- tion and subtraction using triangle method through encouraging students. Remind the concepts of vector addition. This helps you to know the stu- dents’ level of understanding. And it is crucial for shaping their knowledge if, in case, they have misconceptions about the concept vector addition and subtraction using graphical method(head to tail method). Lesson description Introduction Dear teacher introduce the graphical method of vector addition and sub- traction when the two vectors form the side of triangle. 16 Unit 1 Vector Quantities Input and model Dear teacher, before you are going to deliver the lesson, read the materials. Prepare simple demonstration in order to deliver the lesson, your students to have a ruler and a protractor. Introduce a parallelogram method vector addition. For the two vectors ⃗A and B⃗ joined head to head and is the side ⃗ of the two vector is diagonal of the parallelogram, the resultant vector R of the parallelogram. Give a short note on parallelogram law of vector addition and show the resultant vector using scale measurement: head to tail method. Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Activity 1.2 Answer Dear teacher, here two vectors (A and B) are given on the text book, help the student while they measure the magnitude of the two vectors and draw the two vectors as the given instruction using head to tail method to get the length of the resultant vector R using the protractor and ruler. Check for Understanding To assess students learning, you may ask your on oral question and check their understanding. Closure Evaluate the lesson using oral questions or your own class room activity. Summarize the lesson using the following key therms. The triangle, paral- lelogram and polygon methods. Lesson 7: Polygon law of vector addition Starting off Start the topic by asking students about a polygon method of vector addi- 1.4 Graphical Method of Vector Addition and Subtraction 17 tion through encouraging students. Remind the concepts of triangle and parallelogram law vector addition. This helps you to know the students’ level of understanding. And it is crucial for shaping their knowledge if, in case, they have misconceptions about the concept vector addition and subtraction using graphical method(head to tail method). Lesson description Introduction Dear teacher introduce the a polygon method of vector addition and sub- traction when the more than two vectors form the side of polygon. Input and model Dear teacher, before you are going to deliver the lesson, read the materials and prepare demonstration-based teaching. If possible use PhET simula- tion. Discuss about graphical techniques: the polygon method of vector additions. Give a short note and show the resultant vector using scale measurement: triangle and parallelogram and polygon methods Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Activity 1.3 Answer Dear teacher, here two vectors (A and B) are given on the text book, help the student while they measure the magnitude of the two vectors and draw the two vectors as the given instruction on activity 1.3 i.e join the two vectors tail to tail and draw the diagonal of the parallelogram. And its the length is the magnitude of resultant vector R using the protractor and ruler. Activity 1.4 Answer Dear teacher, for the three vectors given, using polygon method of vector addition the resultant vector can be determined. a)Represent each vector graphically with an arrow, labeling the first A , the second B , and the third C , making the lengths proportional to the distance and the directions as specified relative to an east-west line. The head-to-tail method outlined 18 Unit 1 Vector Quantities above will give a way to determine the magnitude and direction of the resultant vector. as shown in the Figure??. b) Place the vectors head to tail retaining both their initial magnitude and direction. As shown in the Figure 1.5. c) Draw the resultant vector, as shown in the Figure1.5. d) Use a ruler to measure the magnitude ofR, and a protractor to mea- sure the direction of R..In this case, R is seen to have a magnitude of 50.0 m and to lie in a direction 7.0o south of east. By using its magnitude and direction, this vector can be expressed as R = 50.0 m and θ = 7.0o south of east. Figure 1.4 (a) Graphical representation of the three vectors. Figure 1.5 (b) The resultant vector of the three vectors. 1.4 Graphical Method of Vector Addition and Subtraction 19 Check for Understanding To assess students learning, you may ask your on oral question and check their understanding. Closure Evaluate the lesson using oral questions or your own class room activity. Summarize the lesson using Key concept your student should remind about a polygon methods. Answers to review questions 1. In triangle law of vector addition the two vectors are sides of triangle and the third side of the triangle is the resultant but in parallelogram law of vector addition the diagonal is the resultant. 2. For finding the resultant vector of several vectors using head to tail method. 3. Using a polygon method of vector addition, when the given six vectors are joined in head to tail then tail of the first vectors and head of the last vector is joined. So that, the magnitude of the resultant vector is zero. 4. C 5. Given: ⃗ =6m C ⃗ = 10 m D ⃗ Required: R:? ⃗ , D) Graphically the two vectors (C ⃗ and the resultant vector(R) ⃗ is shown as the in Figure1.6. Using Pythagoras theorem, the magni- ⃗ of two vectors (C tude of the resultant vector R ⃗ , D) ⃗ will be: p R = C 2 + D2 p R = 6m 2 + 8m 2 p R = 36 + 64 m Figure 1.6 The resultant vector of C and D 20 Unit 1 Vector Quantities p R= 100 m R = 10m 1.5 Vector resolution This section should fill approximately 1 period of teaching time. At the end of this section, students will be able to: resolve a vector into horizontal and vertical components; find the resultant of two or more vectors using the component method. Lesson 8: Vector resolution Starting off Start the topic by asking students for prior knowledge about graphical vector addition and subtraction through encouraging students to relate the concepts of vector addition and subtraction in the case of the paral- lelogram method and vector resolution. This is crucial for shaping their knowledge if, in the case, they have misconceptions about graphical vector addition and subtraction. Lesson description Introduction Dear teacher, before the lesson, remind the students about trigonometric relations and Pythagoras’ theorem. Define the resultant vector. Input and model Explain to the students that they will be exploring resolving vectors. To do this, try to encourage students to do exercise 1.8 and 1.9, discussing in groups. And relate this topic with daily life activities. 1.5 Vector resolution 21 Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Exercise 1.6 Answer Dear teacher, Let us consider ⃗ A having two components A ⃗x and A⃗y. The magnitude of A⃗x = Acos θ and A⃗y = Asin θ. when you compere the magni- tude of the two component it is always less the magnitude of ⃗ A due to the trigonometric values. Exercise 1.7 Answer 1. Dear teacher, a nonzero vector can have a zero component, for example any nonzero vector a long the y-axis has a zero component on the x-axis of a graph. (or vice-versa). A = 2.0m east has non zero value on east direction but zero magnitude along north direction. 2. The two equal vectors have equal magnitude and direction so that they have equal components. Check for Understanding To assess students learning, you may ask them different questions similar to those given at the end of this section, i.e. 1. Draw simple vector diagrams and resolve them into two components. 40 N at an angle of 30◦ from the horizontal. Closure Evaluate the lesson understanding of your students using oral question, and class room activity. To close the lesson, give students a chance to summarize the important concepts of the lesson. Based on their idea, try to summarize the important concepts. Answers to review questions 1. Resolution of vectors: Any vector directed at an angle to the hor- izontal (or the vertical) can have two components that lie on the axes( horizontal and vertical). The process of identifying these two components is known as the resolution of the vector. 22 Unit 1 Vector Quantities 2. (a) Given: F=40 N;θ = 30o Figure 1.7 shows the vector diagram. The two components of the F are:³ p ´ p 3 F x = F cos θ = 40N cos3 0 = 40N 2 = 20 3N F y = F si nθ = 40N si n3 0 = 40N 12 = 20N ¡ ¢ (b) Given: v=10m/s;θ = 80o Figure 1.8 shows the vector diagram. The two components of the v are: v x = vcosθ = 10m/s cos 80o = 10m/s(0.17) = 1.7m/s Figure 1.7 Resolving vector. v y = v si nθ = 10m/s sin 80o = 10m/s(0.98) = 9.8m/s (c) Given: S=1900 km;θ = 40o Figure 1.9 shows the vector diagram. The two components of the s are: s x = s cosβ = 1900km (cos 40o ) = 1900km(0.76) = 1444kmkm s y = s si nβ = 1900km (sin 40o ) = 1216km 3. The vector diagram, for the car in motion is given as in Figure??. And the resultant displacement can be determined graphically using Figure 1.8 Resolving vector. scale of measurement. for example 1cm = 1km. But algebraically using Pythagoras theorem. Figure 1.9 Resolving vector. 1.5 Vector resolution 23 q → − → − 2 →−2 S = S1 +S2 − p → S = 10km 2 + 5km 2 − p → S = 1125km 2 → − S = 11.2km Figure 1.10 displacement oftwo vectors. And the direction of displacement opposi t esi d e tanθ = Ad j ecent si d e 5km tanθ = 10km θ = tan−1 (0.5) θ = 26.6 0 The resultant displacement is 11.2km; 26.6o west of north. Figure 1.11 4. As shown in Figure 1.11 of the graphical representation of displace- ment Resultant displacement of the given motion. S E = S (cos25o ) = 3.10 × 0.9 = 2.79km S E = S (si n25o ) = 3.10 × 0.4 = 1.24km t ot al d i st ance(s) = 2.79 + 1.24km = 4.03km Lesson 9: Virtual experiment Starting Off Start the lesson by summarizing the important points of the unit. Lesson Description Introduction Explain to the students that they will be going to do some selected virtual experiments. To do this, try to encourage students to recall what they 24 Unit 1 Vector Quantities already learnt. Input and Model Show students how to do the virtual experiments. Guide Students through Their Practice While doing the experiments, you are expected to guide the students to learn by themselves. Check for Understanding To assess students’ learning, you may ask them different questions related to the experiment. Where next Students have to use the knowledge that they obtained here in solving other problems. Closure Before closing the lesson, try to summarize the important concepts related to the unit as well as the experiment. Answers to end of unit questions and problems 1. Two vectors of unequal magnitude can never add to give the zero vector. The only way that two vectors can add up to give the zero vec- tor is if they have the same magnitude and point in exactly opposite directions. 2. C 3. Two vectors A and B is given. The resultant vector C is → − →− → − A) C = A + B = 6.8cm + 5.5cm = 12.3cm Figure 1.12 → − →− → − B) C = A + (− B ) = 6.8cm + (− 5.5cm ) = 1.3cm 1.5 Vector resolution 25 → − → − → −´ c) C = B + (− A = 5.5cm + (− 6.8cm ) = −1.3cm 4. For adding vectors, place the tail of the second vector at the head of the first vector. The tail of the third vector is placed at the head of the second vector. The resultant vector is drawn from the tail of the first vector to the head of the last vector this method is head to tail method. 5. Triangle, parallelogram and polygon methods. 6. The parallelogram law of vector addition is used to add two vectors when the vectors that are to be added form the two adjacent sides of a parallelogram by joining the tails of the two vectors. Then, the Figure 1.13 The resultant vec- sum of the two vectors is given by the diagonal of the parallelogram. tor of the three vectors. 7. Polygon law of vector addition states that if a number of vectors can be represented in magnitude and direction by the sides of a polygon taken in the same order, then their resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite order.For example the three vectors A,B, C, the result vector R is shown as the Figure1.13 8. The vectors for the given problem are drawn approximately as in Figure 1.14 The magnitude the Figure1.14 shown. The resultant has a length of 17.5 m and a and direction of the resultant direction 19o north of east. vector. If calculations are done, the actual resultant should be 17 m at 23o north of east. Keeping one more significant figure would give 17.4 m at 22.5o. this shows that analytical method is more accurate than graphical method. 9. Graphically the displacement can be shown as in the Figure 1.15 26 Unit 1 Vector Quantities DR south west The resultant displacement of the car is given by; D = D west + D sout h Figure 1.15 The displacement of a car. displacement is (98 km) sin 45◦ = 69.3 km. The resultant displace- ment has a magnitude of 69.3 294.32 + 69.32 = 302 km. The direction is θ = tan−1 ( 294.3 ) = 13◦ south of west. 10. Given: Vx =9.80 unit and V y =-6.40 unit Solution: the magnitude of V is given by q p V= Vx2 + V y2 = 9.802 + (−6.40 ) 2 = 11.70uni t ¡ −6.40 ¢ The direction will be θ = tan−1 9.80 = −33.10 Figure 1.16 The magnitude 11. Given: ⃗ A = 21cm nor t h and direction of the resultant vector. ⃗ = 26cm sout h C ⃗ = 16cm east and joined head to tail. As shown in the Figure 1.17 B ⃗ ⃗ are anti parallel vectors. So that (A ⃗ A and C −C ) =? (A ⃗ −C ) = 21+(−26) = −5cm north and it is perpendicular to B which is 16 cm east. The resultant a magnitude: p R = (−5)2 + 162 = 16.76 cm ≈ 17 cm and a direction of tan−1 ( −5 16 ) Figure 1.17 The magnitude = 17◦ south of East. and direction of the resultant vector. Unit 2 Uniformly Accelerated Motion This unit should fill approximately 13 periods of teaching time. At the end of this unit, students will be able to: know how position and displacement are used to describe a uniformly accelerated motion; understand the different types of motions to describe physical phenomena; comprehend the nature of uniformly accelerated motion in one dimension; understand relative velocity in one dimension. Dear teacher, you would agree that a good way of introducing any concept in physics is to relate it to your students’ everyday experiences and make them understand why they need to study it. If you could also put in some activities, it would surely add to their interest. So here are some suggestions about how you could teach a uniformly accelerated motion to your students.Have confidence in your students’ abilities, engage them in different activities. You have 8 periods at your disposal for teaching uniformly accelerated motion. 27 28 Unit 2 Uniformly Accelerated Motion 2.1 Position and Displacement This section should fill approximately 1 period of teaching time. At the end of this section, students will be able to: define terms such as position, displacement, and distance describe the difference between of distance and displacement determine the total distance traveled by a certain object. calculate the total displacement given the position as a func- tion of time. Lesson 1: Position and Displacement Starting Off Start the topic by asking students prior knowledge about concept of posi- tion using objects in motion in your surrounding and about inertial frame of reference for an that object in motion. Dear teacher start the lesson use the brain storming given on the text book. Lesson Description Introduction Explain to students about motion is relative and frame of reference should be considered. There is change in the position for an object in given frame of reference. Input and Model Based on the response that you received from the students, try to give a short notes on the definition of Position, distance and displacement. Help the student while they are doing activity 2.1 and 2.2. Explain using practical motion observed or you may use PhET simulation. Help student if worked example is not clear for students. Ask oral question to check their understanding of the topic. 2.1 Position and Displacement 29 Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding Check for students’ understanding while they are exploring by utilizing review questions. Activity 2.1 A student’s own answer. Activity 2.2 Dear teacher, any measurement: position, distance and displacement must be made with respect to a reference frame. While you teach a physics lesson in class, you can use it to explain about frame of reference, displace- ment and distance. For example, mark your initial position using your chalk and change your position and again mark it again. Assume your initial position is at zero coordinate, ask your student to differentiate and explain about initial position, final position, distance and displacement using frame of reference. Based on your student response, you may give a short summary of this activity 2.1. Position is a measurement of a location, with reference to an origin. Distance is the actual path that is traveled by a moving body. Displacement is defined as its change in position (final position minus initial position). Exercise 2.1 Answer Yes! If the body travels in a straight line, then the magnitude of its displace- ment is equal to the magnitude of distance covered. For example: A car moves 20m in a straight line. Exercise 2.2 A student’s own answer. Activity 2.3 A student’s own answer. Dear teacher, Let us consider, the basketball field that your students mea- sure is 28 m length and 15 m width. The total distance traveled to measured p is 43 m. But the displacement should be: s = 152 + 282 = 31.76 m with 30 Unit 2 Uniformly Accelerated Motion Figure 2.1 Position, distance and displacement of an an object. 15 direction θ = t an −1 ( ) = 28o to the side of the length of the basket field. 28 Were next You have to encourage the students to start thinking about average velocity and instantaneous velocity. Closure To close the lesson, allow students to describe verbally what they under- stood about position in particular frame of reference, displacement, and distance. After taking their idea, try to summarize important concepts of: frame of reference, Position, distance, displacement. Answer to review questions 1. Position is the location of the object. As shown in the Figure 2.1 the position of the object is at point O, C, B, and A with the coordinates of 0, 25 m, 35 m, and 60 m respectively with origin as frame of refer- ence and at a given particular time. Displacement is the difference in the object’s position from one time to another. For example again as shown in the figure 2.1 when an object moves from initial to final position (Point o to C) the dis- placement is 25 m in the given direction. Displacement is a vector quantity. 2. For example: A student walking to her school which is 4 km north from her start point, then she is moving 2 km south from her school. From this daily life activity example: The distance traveled: s = 4km + 2km Displacement is 2.2 Average velocity and instantaneous velocity 31 s = 4km − 2km = 2km nor t h s=2 km north. and the magnitude of displacement is 2 km. 3. Given: S AB = 15 m S BC = 20 m Required: Distance(∆S) =? Di spl acement =? Solution: Distance is the total length of the path taken in going from the initial position, s o to the final position, S. But displacement the shortest path between the initial and final position. As shown in the Figure 2.2 distance is sum of the magnitude of two perpendicular vectors and Displacement is the magnitude of the two components. ∆s = s AB + S BC = 15 m + 20 m = 35 m −s = p225 + 400 =25 m → Where as the direction becomes: θ = t an −1 (20/15) θ = 53.1o Figure 2.2 Two perpendicular There fore the magnitude of displacement and direction is: ⃗ s = 25 m; vectors and their resultant. θ = 53.1o to the horizontal. 2.2 Average velocity and instantaneous velocity This section should fill approximately 3 period of teaching time. 32 Unit 2 Uniformly Accelerated Motion At the end of this section, students will be able to: describe instantaneous and average velocity of a body in mo- tion; describe the difference between average velocity and instan- taneous velocity; solve problems related to the average velocity. Lesson 2: Average velocity Starting Off Start the lesson through asking students a brain storming question and remind about Position and displacement. Lesson Description Introduction Dear teacher, introduce about an average velocity based on previous knowledge of the students responses. Input and Model Dear teacher, after you remind about position and displacement, define average velocity and average speed. Average velocity tells us how much an s − so object’s position changes in time;v av = , does not convey any infor- t − to mation about how fast you were moving or the direction of the motion at any instant during the trip. So that we use instantaneous velocity to know the motion a body at the given instant time. remind your student about the s − so difference and similarity between average speed and velocity. v = t − to when t − t o → 0 For practical application of this physical concept of this section in their daily life use your own example.ask them to do exercise2.3. Guide Students through Their Practice While doing the activities and worked example of this section, you are expected to guide the students to learn by themselves. 2.2 Average velocity and instantaneous velocity 33 Check for Understanding Check for students’ understanding while they are exploring by utilizing questions/prompts like those listed below. Exercise 2.3 Answer Dear teacher, average velocity is defined as the change in displacement over the time of travel, while instantaneous velocity is the velocity of an object at a single point in time. For example, a car driver is driving down the highway at a constant velocity of 30km/h. The average velocity of the car is 30km/h, and no matter what time you measure, the instantaneous velocity at that moment is always 30 km/h. Exercise 2.4 Answer No, the speed can be different from the magnitude of velocity. For exam- ple, you drive to a store and return home in half an hour. If your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero because your displacement for the round trip is zero. Exercise 2.5 Answer Dear teacher, as you know, cars speedometer gives information about the speed of the car at instant of time only. Activity 2.4 Answer Dear teacher, the two students are walking at different speeds. The speed of the second student is lower than the first student. displacement is con- stant in every second. Where next Students need to extend their knowledge of the average velocity and aver- age speed for their daily activities. Closure To close the lesson, allow students to describe verbally the physical con- cept of average velocity and average speed. Avoid the miss conception of average velocity and average speed. Based on their idea, try to summarize 34 Unit 2 Uniformly Accelerated Motion the important concept. Lesson 3: instantaneous speed and velocity Starting Off Start the lesson through asking students a brain storming question and remind about average speed and velocity. Lesson Description Introduction Dear teacher, introduce the lesson: instantaneous speed and velocity. Input and Model Dear teacher, after you remind about average speed and average velocity, define instantaneous speed and instantaneous velocity. Average veloc- s − so ity tells us how much an object’s position changes in time;v av = t − to , does not convey any information about how fast you were moving or the direction of the motion at any instant during the trip. So that we use instantaneous velocity to know the motion a body at the given instant s − so time. v = when t − t o → 0 For practical application of this physical t − to concept of this section in their daily life use your own example.ask them to do exercise2.6. Guide Students through Their Practice While doing the activities and worked example of this section, you are expected to guide the students to learn by themselves. Check for Understanding Check for students’ understanding while they are exploring by utilizing questions/prompts like those listed below. Exercise 2.6 Answer Student’s own answer. 2.2 Average velocity and instantaneous velocity 35 Where next Students need to extend their knowledge of the average velocity and in- stantaneous velocity for their daily activities. Closure To close the lesson, allow students to describe verbally the physical con- cept of instantaneous speed and velocity. Avoid the miss conception of instantaneous speed and velocity. Based on their idea, try to summarize the important concept. Review questions Answer 1. Consider an object is moving between two point a and b. The initial position is (S o ) and final position (s) in the given interval of time ∆t s − so the average velocity expressed using this formula. ⃗ s=. ∆t 2. The main difference between average speed and average velocity is that the first one is known to be a scalar quantity, whereas the latter one is a vector quantity. Moreover, the average speed can never be a negative. It is either positive or zero. Where as in the case of average velocity, it can either be a positive quantity or zero, sometimes even a negative quantity. The Average Speed of an object can be calculated by dividing the distance it has covered by the time it has taken to cover the latter. The average speed can help in determining the average rate that a particular body will take to cover the given distance. 3. Average speed and the magnitude of average velocity are differ- ent. There difference is shown in the following example. For ex- ample, a car moves 12 km north then turns and runs 16 km east in three hours.For this given example the average speed and the p magnitude of average velocity are: ∆s = 122 + 162 km = 20km Aver- ∆s 20km ⃗ v av = age velocity(v av): = = 6.7km/h The direction is in ∆t 3h same to displacement. The average speed is total distance divided by total time Average speed(v av ): 36 Unit 2 Uniformly Accelerated Motion Tot al d i st ance 28km v av = = = 9.3km/h. The average speed t ot al t i me 3h of the car is 9.3km/h, but its average velocity is 6.7km/h, in the direction of the displacement. 4. 20 m/s 5. Given: v⃗av = 48 km/h east ⃗ = 144 km east ∆s Required: ∆t =? Solution: ⃗ ∆S V⃗av = ∆t 144km/h ∆t = 48km ∆t = 3 h 6. Given: ⃗ S N = 12 km ⃗ S E = 16 km Required: Figure 2.3 The Possible dis- d el⃗t as =? and v⃗av =? placement. The possible displacement of an athlete run is shown in the Figure 2.3 a) −→ q ∆S = (S N )2 + (S E )2 q −→ ∆S = (12 km)2 + (16 km)2 −→ ∆S = 20 km; opposi t e si d e 16 km t anθ = = = 1.33 ad j cent si d e 12 km θ = tan−1 (1.333) θ = 53o −→ ∆S = 20 km; 53o north east 2.3 Acceleration 37 b) Average velocity(Vav )? ⃗ ∆S V⃗av = ∆t 20km Vav = 3h Vav = 6.66km/h; in the direction of the displacement Tot al d i st ance t r avel ed c) Vav = Tot al t i me t aken 28km Vav = = 9.3km 3h 2.3 Acceleration This section should fill approximately 3 period of teaching time. At the end of this section, students will be able to: explain acceleration in one dimension; distinguish between instantaneous acceleration and average acceleration; compute average acceleration. lesson 4: Average acceleration Starting Off As usual, try to start the topic by asking students to remind the class about the topics that they learn in their previous lesson, i.e., about average accel- eration. Lesson Description Introduction 38 Unit 2 Uniformly Accelerated Motion Introduce the lesson using the response of the students of brain storming question. Input and Model First you need to start teaching the students using the previous lesson: average velocity and instantaneous velocity. Remind about the definition of acceleration they learn in grade 9. Now you are going explain about average acceleration. Activity 2.5 is about deceleration and negative ac- celeration. After the student give their feedback and remind them the difference between them. If somebody want to now accelerating body at specific time rather than average acceleration the instantaneous accelera- tion can describes the motion. so that encourage the student to correlate the concept to the next topic. Summarize lesson. Guide Students through Their Practice While student discuss in their group, you are expected to make all partici- pate on the discussion and motivate all to gain knowledge in the topic. While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding Check for students’ understanding while they are exploring by utilizing questions/prompts like those listed below. Exercise 2.7 Answer Dear teacher, when velocity is constant, change in velocity is zero. So that acceleration is zero.deceleration always refers to acceleration in the direction opposite to the direction of the velocity. Deceleration always reduces speed. Negative acceleration, however, is acceleration in the nega- tive direction in the chosen coordinate system. Use daily activity example, and try to elaborate for you students. Exercise 2.8 Answer Dear teacher, a zero velocity does not necessarily mean that the accelera- tion is zero, nor does a zero acceleration mean that the velocity is zero. (a) 2.3 Acceleration 39 For example, when you put your foot on the gas pedal of your car which is at rest, the velocity starts from zero but the acceleration is not zero since the velocity of the car changes. (How else could your car start forward if its velocity weren’t changing-that is, accelerating?) (b) As you cruise along a straight highway at a constant velocity of 100 km/h, your acceleration is zero: a = 0, v ̸= 0. Where next Encourage students to understand about average acceleration and apply in their daily life activity. Closure Give short summary on the physical meaning of average acceleration. lesson 5: Instantaneous acceleration Starting Off As usual, try to start the topic by asking students to remind the class about the topics that they learn in their previous lesson, i.e., about acceleration. Lesson Description Introduction Introduce the lesson using the response of the students of brain storming question. Input and Model First you need to start teaching the students using the previous lesson: average acceleration. Remind about average acceleration they learn in previous lesson. Now you are going explain instantaneous acceleration. An accelerating body value of acceleration at specific time is shown using instantaneous acceleration rather than average acceleration. The instan- taneous acceleration describes the motion at the given instant of time and it is calculated for an interval of time ∆t which includes the instant t, approaches as the interval of time ∆t gets smaller and smaller, i.e., as 40 Unit 2 Uniformly Accelerated Motion ∆t approaches 0. As the time interval over which you are measuring the change in velocity gets smaller and smaller, the ratio of change in velocity to time interval as the time interval approach zero is instantaneous accel- eration. Summarize lesson. Guide Students through Their Practice While student discuss in their group, you are expected to make all partici- pate on the discussion and motivate all to gain knowledge in the topic. While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding Check for students’ understanding while they are exploring by utilizing questions/prompts like those listed below. Exercise 2.9 Answer Uniform motion Activity 2.5 Answer Deceleration always refers to acceleration in the direction opposite to the direction of the velocity. Deceleration always reduces speed. Negative ac- celeration, however, is acceleration in the negative direction in the chosen coordinate system. Activity 2.6 Answer Student’s own answer. Where next Encourage students to appreciate the applications of the stress and strain in their daily life. Closure Give short summary on the physical meaning of acceleration, average acceleration and instantaneous acceleration. Answer to review questions 2.4 Equations of motion with constant acceleration 41 1. Similarity: They are defined using the ratio of velocity to time. And for constant acceleration motion, the instantaneous acceleration does not vary in value with time and it is equal to average ac- celeration. Their units are m/s, km/h, mil/s etc Deference: Average acceleration gives an information about the motion of the given body based on initial and final velocity. But considering the initial and final velocity of an object in motion, it is difficult to know about its motion in every second whether in motion or stop. Instantaneous acceleration varies with time. It is acceleration at any particular moment of time. 2. a) positive acceleration. b) negative acceleration and deceleration. 3. Vo = 0 ⃗ v = 15 m/s west t=1.8 s Required: a⃗av =? Solution: 15.0 m s −0 a av = V −V t o = 1.8 s =8.33 m/s2 west 4. V0 = 14 ms V = 0 ms t=5.0 s Solution: a av = V −V t o = 0−14 5 s m/s = -2.8 m/s2 The negative in this case indicate the motion the car is deceleration. 2.4 Equations of motion with constant accelera- tion 1. This section should fill approximately 4 period of teaching time. 42 Unit 2 Uniformly Accelerated Motion At the end of this section, students will be able to: describe the nature of motion in a straight line; derive the equations of motion with constant acceleration; use appropriate equations of motion to solve motion-related problems. Lesson 6: Equations of motion with constant acceleration Starting Off In the previous section, the students learned about acceleration. Remind the mathematical expression for average velocity and average acceleration. Then, based on your students’ explanation, ask students from their daily experience to give an example of acceleration of constant motion. Lesson Description Introduction Explain to students that they will be exploring about equation of constant acceleration. Input and Model Before teaching students about the equation of constant acceleration mo- tion, provide a note for the students. Present the lesson. Help the student while doing activity 2.7. After their feedback. You can then proceed to the topic. Solve the problem related to the topic. Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding Check for students’ understanding while they are exploring by utilizing review questions. Exercise 2.10: Student’s own answer. 2.4 Equations of motion with constant acceleration 43 Exercise 2.11: Velocity is constant. Where is next Encourage students to think about the equation of acceleration constant motion in their daily life. Closure To close the lesson, give students a chance to summarize the important concepts of the lesson. Based on their idea, Show all the equations of constant acceleration motion. Try to summarize the important concept. Lesson 7: Examples of motion with constant acceleration Starting Off In the previous section, the students learned about the equations of uni- formly accelerated motion. Lesson Description Introduction Explain to students that they will be doing examples about equation of constant acceleration. Input and Model Solve the problem related to the topic. Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding Check for students’ understanding while they are exploring by asking ques- tions. Where is next 44 Unit 2 Uniformly Accelerated Motion Encourage students to think about the equation of acceleration constant motion in their daily life. Closure To close the lesson, give students a chance to summarize the important concepts of the lesson. Based on their idea, show all the equations of constant acceleration motion. Try to summarize the important concept. Lesson 8: Free fall Starting Off In the previous section, the students learned about the equations of uni- formly accelerated motion. Remind the mathematical expression for uni- formly accelerated motion. Then, based on your students’ explanation, ask students from their daily experience to give an example of free fall motion. Lesson Description Introduction Explain to students that they will be exploring about free fall. Input and Model Before teaching students about the equation of free fall, provide a note for the students. Present the lesson. Help the student while doing activity 2.7 and 2.8. After their feedback. You can then proceed to the topic. Solve the problem related to the topic. Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding Check for students’ understanding while they are exploring by utilizing review questions. 2.4 Equations of motion with constant acceleration 45 Activity 2.7 Answer Dear teacher, what are your student observations? Can you explain free fall in which air resistance is neglected? If air resistance neglected the two object reach the ground at the same time and similarly free fall. Activity 2.8 Answer Dear teacher, While velocity of released body speed its acceleration is constant. Where is next Encourage students to think about the equation of acceleration constant motion in their daily life. Closure To close the lesson, give students a chance to summarize the important concepts of the lesson. Based on their idea, Show all the equations of constant acceleration motion. Try to summarize the important concept. Answers to review questions 1. A freely falling body moves under the acceleration due to gravity and therefore, its acceleration is constant. So, it is a uniformly accelerated motion. 2. Vo = 5.6m/s a = 0.6m/s t = 4.0s required: S=? V=? Using equation of constant acceleration motion 1 S = Vo t + at 2 2 1 S = (5.6m/s)(4s) + (0.6m/s 2 )(4s 2 ) 2 S = 27.2m From V = Vo + at you can get the value of V. V = Vo + at V = 5.6m/s + (0.6m/s 2 (4s) V = (5.6 + 2.4)m/s 46 Unit 2 Uniformly Accelerated Motion V = 8.0 m/s 3. V0 = 0 t = 8.0s g = 9.8 m/s2 Required: v =? and h =? Solution: a V = V0 + g t = 0 + 9.8m s × 8.0s = 78.4m/s 2 b h = 12 g t 2 = 0.5 × 9.8 × 64 = 4.9 × 64m = 313.6 m 2.5 Graphical representation of uniformly accel- erated motion This section should fill approximately 3 periods of teaching time. At the end of this section, students will be able to: draw graphs of position-time, velocity-time and acceleration- time graph; explain the concept of instantaneous velocity using displacement-time graphs; distinguish between instantaneous acceleration and average acceleration using graphical method. Lesson 9: Position-time graph of uniformly accelerated motion Starting Off Start the lesson by asking the students about position -time for the uniform motion from their previous knowledge. Remind distance-time graph of uniform motion. Lesson Description Introduction 2.5 Graphical representation of uniformly accelerated motion 47 Introduce the topic: Position-time graph Input and Model Dear teacher, provide a short note. Before starting the lesson summarize the graph of uniform motion. And using the motion of the body, draw graphs of position-time graph for uniformly accelerated motion. Show the instantaneous velocity of uniformly accelerated motion using position- time graphs. You need to ask students to do and discuss exercises 2.12 and 2.13. Finally, explain about the slope of Position -time graphs. Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding To assess students learning, you may ask your own oral questions and may use review questions and: 1. What information can you obtain from a position - time graph? Exercise 2.12 Answer Student’s own answer. Exercise 2.13 Answer Dear teacher, for constant acceleration motion, the s-t graph is a curve like quadratic function graph as shown in the Figure 2.4. Where is next Encourage students to think of about the importance of studying about graphical representation of uniformly accelerated motion in their daily life. Figure 2.4 Position-time graph. Closure To close the lesson, give students a chance to summarize the important concepts of the lesson. Based on their idea, try to summarize the impor- tant concept for them. 48 Unit 2 Uniformly Accelerated Motion Lesson 10: Velocity -time graph of uniformly accelerated motion Starting Off Start the lesson by asking the students about velocity -time for the graph for uniform motion from their previous knowledge. Remind velocity-time graph of uniform motion. Encourage your student and introduce the les- son. Lesson Description Introduction Introduce the velocity-time graph for the uniformly accelerated motion. Input and Model Dear teacher, provide a short note. And using the motion of the body, draw graphs of velocity - time graph for uniformly accelerated motion. Show the instantaneous acceleration of uniformly accelerated motion using velocity-time graphs. You need to explain about slope and area under of the graph of velocity - time graph. Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding To assess students learning, you may ask your own oral questions and may use review questions and: 1. What information can you obtain from a velocity-time graph? Exercise 2.14 Answer Acceleration. Where is next Encourage students to think of about the importance of studying about graphical representation of uniformly accelerated motion in their daily life. 2.5 Graphical representation of uniformly accelerated motion 49 Closure To close the lesson, give students a chance to summarize the important concepts of the lesson. Based on their idea, try to summarize the impor- tant concept for them. Lesson 11: Acceleration - time graph of uniformly accelerated motion Starting Off Start the lesson by asking the students about acceleration - time for the graph for uniform motion from their previous knowledge. Remind ac- celeration - time graph of uniform motion. Encourage your student and introduce the lesson. Lesson Description Introduction Introduce the acceleration - time graph for the uniformly accelerated mo- tion. Input and Model Dear teacher, provide a short note. And using the motion of the body, draw graphs of acceleration - time graph for uniformly accelerated mo- tion. Show the instantaneous acceleration and average acceleration of uniformly accelerated motion are similar using acceleration - time graphs. You need to explain about slope and area under of the graph of accelera- tion - time graph. Guide Students through Their Practice While doing the activities, you are expected to guide the students to learn by themselves. Check for Understanding To assess students learning, you may ask your own oral questions and may use review questions 50 Unit 2 Uniformly Accelerated Motion 1. What information can you obtain from a acceleration - time graph? Exercise 2.15 Answer Student’s own answer. Exercise 2.16 Answer In Uniform Velocity Motion a body will be moving with a constant (unchanging velocity moving in a particular direction and thus ac- celeration will be zero whereas in Uniform accelerated motion a body will move at constant acceleration and its velocity will keep changing with time at a constant) steady rate. Activity 2.9 Answer Figure 2.5 postion - time graph Based on the given table of the position of an object in the given for the given table. time, the position- time graph becomes as shown in the Figure 2.5 2.6, the Velocity time graph can be drown as shown in the 2.7. By taking any arbitrary point on position - time graph you can draw the tangential line and it is shown as in the figure 2.6. Based on the slope of the three tangential line shown in the figure Again from the slope of velocity - time graph values you can draw acceleration - time graph and it is shown as in the figure2.8 Where is next Figure 2.6 Tangent line for postion - time graph of the Encourage students to think of about the importance of studying about given table. graphical representation of uniformly accelerated motion in their daily life. Closure To close the lesson, give students a chance to summarize the important concepts of the lesson. Based on their idea, try to summarize the impor- tant concept for them. Answers to review questions 1. From velocity-time graph, you can get the following information. (a)Area under the curve of velocity-time graph is a displacement covered by an object in motion. Figure 2.7 Velocity - time (b) The slope of the graph is an acceleration of an object in motion. graph. 2.6 Relative velocity in one dimension 51 If the slope is positive, it is accelerated motion. if slope is negative, it is retarded motion and if slope is zero acceleration is zero. 2. In mathematics, slope is used to describe the steepness and direc- tion of lines. By just looking at the graph of a line, you can learn some things about its slope. The slope of a line is the ratio of the amount that y increases as x increases. A velocity-time graph is the graph of the given motion shows how its velocity changes as it travels in a given time. The slope of the line on a velocity versus time graph is equal to the acceleration of the object. For example: if the object is moving with an acceleration of +4m/s 2 (i.e., changing its velocity by 4 m/s per second), then the slope of the line will be +4 m/s/s. 3. S 1 = Ar ea = 1/2(∆V × ∆t ) = 20 m × 1.0 s = 20m/s S 2 = ar ea = 1/2(∆V × ∆t ) = 40 m × 2.0 s = 40 m/s 2.6 Relative velocity in one dimension This section should fill approximately 1 period of teaching time. At the end of this section, students will be able to: describe the relative velocity in 1-D using frame of reference; calculate the relative velocity of two motions in a straight line. Lesson 12: Relative velocity in one dimension Starting Off Start the lesson by asking the students about a frame of reference and what do mean by relative velocity in one dimension. Lesson Description Introduction Starting from your student response, introduce the lesson and give direc- 52 Unit 2 Uniformly Accelerated Motion tion that you are going to do. Try to encourage students to give responses to lesson. Input and Model Dear teacher, provide a short note. Remind your students about frame of reference. Consider observer on the ground and measuring the speed of the two object moving in similar direction and approaching each other, the relative velocity(v AB ) is v AB = v A − v B and v AB = v A + v B respectively. You need to ask students to do and discuss exercises 2.17. Finally, explain about the relative velocity in one dimension and elaborate using a daily life activities. Guide Students through Their Practice While doing the worked example, you are expected to guide the students to learn by themselves. Check for Understanding To assess students learning, you may ask your own oral questions and may use review questions. Where is next Students are required to think of about the relative velocity in one dimen- sion. And try to use in their daily life. Closure To close the lesson, give students a chance to summarize the important concepts regarding relative velocity in one dimension. Based on their idea, you need to summarize the important concept. Remind the formulas of relative velocity. Answers to review questions 1. Speed of motorcycle v m = 120km/h Speed of car v c = 90km/h 2.6 Relative velocity in one dimension 53 The relative velocity is defined as, v mc : v m c = v m − v c = 120km/h − 90km/h v mc = 30km/h 2. Solution Va = 80km/h Vt = 60km/h Required: Vat = v a + v t Vat = 80km/h + 60km/h Vat = 140km/h 3. Time to reach the thief (t)? → − → − → − V tp = V t − V p → − V t p = 10m/s − 9m/s → − V t p = 1m/s This the relative velocity of the thief with respect to the police. Vt p = ∆s ∆t 1m/s = 100m ∆t ∆t = 100s So that, Answer: D Lesson 13: Virtual experiments Starting Off Start the lesson by summarizing the important points of the unit. Lesson Description Introduction Explain to the students that they will be going to do some selected virtual experiments. To do this, try to encourage students to recall what they 54 Unit 2 Uniformly Accelerated Motion already learnt. Input and Model Show students how to do the virtual experiments. Guide Students through Their Practice While doing the experiments, you are expected to guide the students to learn by themselves. Check for Understanding To assess students’ learning, you may ask them different questions related to the experiment. Where next Students have to use the knowledge that they obtained here in solving other problems. Closure Before closing the lesson, try to summarize the important concepts related to the unit as well as the experiment. Answers to end of unit questions and problems 1. For constant acceleration motion, acceleration is constant and the interval of acceleration is zero in given interval of time. Figure 2.9 Figure 2.9 shows a-t graph. 2. Acceleration is the time rate of change of velocity, so that can be found from the slope of a tangent to the curve on a velocity-time graph in Figure 2.10. During each interval, the acceleration is con- stant as the straight line segments. Velocity increase or decrease with equal interval for equal interval of Figure 2.10 time. 2.6 Relative velocity in one dimension 55 3. v o = 0 a = 2m/s 2 v 1 = 20m/s t 2 = 20s v 2 = 20m/s and constant t 2 = 5s Required: S =? v av =? From constant acceleration equation of motion, you have the fol- v − vo 20/m/s − 0 lowing: t 1 = t1 =