Ap college board ap physics 1 workbook answer key

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Ap college board ap physics 1 workbook answer key

Are you wondering how you can use the AP Physics 1 workbook during remote learning? I was wondering what to do with this 358-page pdf. My classes are fully remote, and I don't want to print the whole thing! I like the questions in the AP Physics 1 workbook and I think it is a very useful tool to prepare students for the AP exam. I have been assigning some of the workbook pages as we go through each unit. Then, I plan to use the workbook more when reviewing and prepping for the AP exam in the Spring. I decided that the only way that I could manage using the workbook would be to transform it into a digital workbook. So, here it is! Here is your Google Slides version... For each unit, the PDF workbook pages have been made into the background of a Google Slide. Then, text boxes and drag-and-drop elements have been added for students to use as they complete each page. The Google Slides file can be shared through your school's LMS for students to access. Each link below will prompt you to make a copy to put in your own Google Drive. Each file will then be your own, and editable in case you want to make any changes to it! Workbooks by Unit: The answer key to the AP Physics 1 workbook is available to all registered AP Physics 1 teachers in the secure documents area of the College Board website. You can login to the AP course audit to access your answer keys. The workbook pages are published by the College Board who holds the copyright to the material. The pages have not been altered in any way, only made available in a student-friendly format for remote learning. These materials are free to use and share with other AP Physics 1 students and teachers. These files are not for commercial use and no compensation has been received for any of this work. For more general information about the AP Physics 1 course please visit the College Board Website. Related Physics 1 Workbook College Board Answers. 30 May 2021 -- Ap physics 1 workbook college board answers. Note that any related adjustments to AP Exams, such as length or content covered, .... Solutions to Physics I Gravity and Kepler's Laws Practice Problems 1. 0)(sin 37.Tag:ap physics 1 workbook key Physics B ? Practice Workbook ? Book 1 Mechanics, Fluid Mechanics and Thermodynamics The following(? is applicable to this entire document ? copies for student distribution for exam preparation explicitly allowed.Tag:ap physics student workbook answers Student's Workbook for College PhysicsPrinceton Review AP Physics 1 Premium Prep 2021AP* Test-Prep WorkbookCollege Physics for AP? CoursesCollege Physics: Reasoning and RelationshipsCollege Physics, Volume 1The PerformanceTag:ap physics 1 student workbook ap-physics-c-practice-workbook 1/2 Downloaded from optimus.test. on October 5, 2021 by guest Kindle File Format Ap Physics C Practice Workbook Getting the books ap physics c practice workbook now is not type of inspiring means.Tag:ap collegeboard physics workbook answers AP Physics 1 & 2 Multiple-Choice Questions For your study guide to AP Physics 1 and 2 multiple-choice, well now go through a few practice questions from the official AP sample questions. AP Physics 1 First, one from AP Physics 1: question 13 (on page 166) at this link. Here you need to rank magnitudes of acceleration by examining the graph.Tag:ap physics workbook answer key book is a compilation of all the problems published by College Board in AP Physics C organized by topic. The problems vary in level of difficulty and type and this book represents anTag:mit ap physics 1 workbook College Board. College Board is a mission-driven, not-for-profit organization that connects students to college success and opportunity. Founded in 1900, College Board was created to expand access to higher education. Today, the membership association is made up of over 6,000 of the world's leading educational institutionsTag:ap physics c workbook Physics; Physics C: Mechanics, Physics C: Electricity and Magnetism Course Description. or "Terms Defined" in the . AP Physics 1: Algebra-Based Course and Exam Description . and the . AP Physics 2: Algebra-Based Course and Exam Description. 5. The scoring guidelines typically show numerical results using the value . g 9.8 m s. 2,but the ...Tag:ap physics c textbook pdf Physics 1- Momentum, Impulse, and Collisions Practice Problems ANSWERS FACT: The product of mass and velocity is a vector quantity known as momentum ( ).The equation for linear momentum is = and has the units kg? , which can also be written as a newton-second (N?s).Now take Newton'sTag:ap physics 1 workbook key Edition Field, Jones, Randall D. ... 3rd Edition Brian Jones, Randall D. ... By now most AP Physics 1 teachers are aware of the new "Workbook", available as a free download from a teacher's College Board course audit page. If you're not, get aware right away! Amy Johnson of the College BoardTag:ap physics student workbook answers Physics C ? Practice Workbook ? Book 1 Mechanics .... The following(? is applicable to this entire document ? copies for student distribution for exam preparation explicitly allowed. ... College Board, Advanced Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, PreAP, SAT, Student Search Service, and the acorn ...Tag:ap physics 1 student workbook Physics C Unit 6 - Rotational Motion 6 Rotational Kinematics 1. Rotational Kinematics with Rotating Disk A circular disk (like a CD, wheel, or galaxy disk), starting from rest, rotates with an angular acceleration given by a = (3 + 4t) rad/s2 a) Derive the expression for ...Tag:ap collegeboard physics workbook answers physics 1 college board workbook answers Enroll in this CourseCourse DescriptionDescriptionThe course provides students with an introductory experience in the concepts and methods of physical analysis, focused on classical mechanics and simple electrical circuits. Building the ability to reason qualitatively and quantitatively is a primary ...Tag:ap physics workbook answer key Physics 1 - Summer Assignment 2019-20 Richard Montgomery High School Welcome to AP Physics 1! AP Physics 1 is an algebra-based, introductory college-level physics course. Students cultivate their understanding of physics through inquiry-based investigations as they exploreTag:mit ap physics 1 workbook This is a free resource that contains a compilation of problems written by master AP Physics teachers and college/university physics faculty to help students master the knowledge and skills in collegelevel physics coursework. This workbook offers more than 100 scenarios, or worksheets, presented in unit order, that were designed to support learning of course content and important skills, such as argumentation, quantitative analysis, data analysis, using representations, and experimental design. The Teacher Edition contains complete solutions, as well as instructional guidance for each scenario provided. Both the Teacher and Student Editions are available through your Course Audit account and on AP Classroom. ?Physics 1TEACHER'S EDITIONContents2 About This Workbook4 Workbook at a Glance6 Embracing Challenges7 Learning Physics as Refining Common Sense8 Unit 1: Kinematics36 Unit 2: Dynamics71 Unit 3: Circular Motion and Gravitation102 Unit 4: Work and Energy141 Unit 5: Momentum180 Unit 6: Simple Harmonic Motion208 Unit 7: Torque and Rotation241 Unit 8: Electric Charge and Electric Force269 Unit 9: DC Circuits300 Unit 10: Mechanical Waves and Sound335 Unit 11: Review Questions367 Appendix368 AP Physics 1 Equation Sheet370 AP Physics 1 Science Practices371 AP Physics 1 Task Verbs Used in Free-Response Questions372 Graphical Methods Summary373 Writing TipsAP Physics 1 WorkbookAcknowledgmentsThe College Board would like to acknowledge the following individuals for their commitment and dedication toward the completion of this project. All individuals and their affiliations were current at the time of contribution.AP Physics Consultants and ReviewersAngela Benjamin, Woodrow Wilson High School, DCBrendon Eaton, Rick Reedy High School, TXRichard Fetzner, McDowell High School, PAJohn Frensley, Prosper High School, TXKristen Gonzales-Vega, Rick Reedy High School, TXPeter Harris, Methuen High School, MADavid Maloney, Purdue University Fort Wayne, INJoe Mancino, Windsor High School, CTTerri McMurray, Career Center High School, NCRebecca Messer, Northfield High School, MNJohn Pinizzotto, Weymouth High School, MAJenny Podel, Northampton High School, MAGay B. Stewart, West Virginia University, WVJames VanderWeide, Hudsonville High School, MIBarbara Watson, JJ Pearce High School, TXCollege Board Curriculum,Instruction, and AssessmentAmy Johnson, Director, Instructional Design and PD Resource Development ? PhysicsClaire Lorenz, Senior Director, Instructional Design and Teacher Resource DevelopmentMichael Robertson, Director, Curriculum, Instruction, and Assessment Process ManagementTanya Sharpe, Senior Director, Advanced Placement STEM Curriculum, Instruction and AssessmentTeacher's Edition | 1AP Physics 1 WorkbookReturn to Table of ContentsAbout This WorkbookBackground The AP Physics 1 course is designed to promote student learning of essential physics content and foster the development of deep conceptual understanding. The instructional approaches utilized in this workbook are informed by research on student learning and knowledge construction, especially with regard to physics principles.Contents This workbook is a compilation of problems written by high school and higher education physics faculty to help students and teachers master the knowledge and skills in college-level physics coursework. The AP Physics 1 Exam requires students to be able to think about physics both conceptually and mathematically as well as to write about physics. Thinking about physics and defending claims with writing may be new and challenging for students, and this workbook provides helpful guidance in supporting students' development of this skill.Scaffolding The units in this workbook are scaffolded so that students can learn the skills such as argumentation , quantitative analysis , and data analysis , alongside course content, so that they will be prepared for the AP Exam by May. As you read through the problems, you will see that the scaffolding slowly decreases as students progress from unit to unit. By Unit 10, students are expected to be able to demonstrate all skills without support. Students start their study of physics with their own unique backgrounds, and it is possible that you will find these questions either too scaffolded or not scaffolded enough for your students. Teachers are encouraged to modify the problems in this workbook as necessary, so that they meet students' needs. If you think some of the questions are too challenging or make too great a leap for your students, consider supplementing with your own scaffolding to help students access these scenarios.Teacher's Edition | 2AP Physics 1 WorkbookReturn to Table of ContentsSolutions and Teacher Notes The answers presented in the teacher version are not inclusive of all possible solutions--that is, they do not represent the only method of solving these problems. Teachers may present slightly different methods and/or different symbols and variables in each topic, but the underlying physics concepts are the same.It is strongly suggested that teachers support the careful use of language suggested in the Physics 1 course framework. While the wording in some cases is somewhat longer than what is traditionally used, this has been done to directly address the misconceptions that can be supported by using briefer descriptions.Teacher's Edition | 3AP Physics 1 WorkbookReturn to Table of ContentsTeacher's Edition | 4AP Physics 1 WorkbookReturn to Table of ContentsWorkbook at a GlanceAlthough each unit in this workbook is unique and focuses on content, skills, and learning objectives for that unit, the overall formats are similar. Each page includes a scenario, which acts as the prompt to focus students' attention on key elements of the problem. Each problem is then broken down into several parts, and headers are added to provide guidance to the students--to key them into the type of question they're going to be asked. The major headings are: Using Representations Quantitative Analysis Argumentation Data Analysis Experimental DesignTeacher's Edition | 5AP Physics 1 WorkbookReturn to Table of ContentsTeacher pages include the Essential Knowledge and Science Practices that are linked to each scenario. Teacher pages also include notes about how to prepare for assigning the page, use it in your classroom ( teach ) and assess that your students have learned key concepts and/or skills. Some of the teacher notes include quick quizzes, lab ideas, or other suggestions for extensions.Embracing ChallengesTeachers should consider the noncognitive dimension to teaching and learning when working with AP Physics 1 students. What a teacher or student believes about how success is achieved may affect the learning process. As educators, it's important to take into account our own perceptions about student success and how we can empower students as they encounter new academic challenges. A student who believes that success is possible embraces challenges as new opportunities to learn, makes concerted efforts to improve, and believes that their ability and potential is not fixed or static but can grow over time. A teacher who believes that success is possible measures improvement over time and believes that effort is the linchpin of success. This way of thinking counters the self-defeating notions that ability is static and permanent and extra effort has no benefits because success is determined by innate ability or talent.The messages that teachers send to students, along with all classroom practices, can encourage students to take risks, make mistakes, learn, and grow. This culture is beneficial in an AP class where frustration can short-circuit the learning process. Teachers who can coach students through such moments, and train them to see academic setbacks as stepping stones rather than stumbling blocks, can set students up for success. Students new to AP, or students who seem to be struggling with the challenges of AP, may benefit from specific strategies such as: Encouragement to attend after-school tutoring Assistance in finding online resources for instruction Assistance in forming study groups to work with other students on developing and deepening their understandingTeacher's Edition | 6AP Physics 1 WorkbookReturn to Table of ContentsLearning Physics asRefining Common SenseThere is a quote attributed to Albert Einstein that "science is refined common sense." One clear implication of this idea is that students who are taking a course in physics are bringing to the course their common-sense understanding of how the physical world works. Physics education research over the last 30 years has identified many of the ideas students are going to have initially. Since we humans build new knowledge by using our current understanding (i., our current framework), to try to make sense of what we are being taught, knowing the content of students' around "common-sense" frameworks is an important pedagogical tool.The research has shown that students' common-sense frameworks contain both useful ideas and counter productive ideas about the behavior of physical systems. The task of learning physics can be thought of as helping each student refine his or her common-sense framework to bring it into closer alignment with the physically accepted ideas. So, the refinement process involves helping students learn which components of their framework will help them correctly analyze the behavior of a physical system, or solve a problem correctly, and which components they need to modify or replace with new ones.It is important for instructors to get students to realize that they have useful ideas that they can use with confidence as well as helping them modify or change other ideas. One of the primary reasons for paying explicit attention to having the students use "correct" ideas from their frameworks is motivational. If the focus is always on problematic ideas in their frameworks (i., misconceptions), students can become discouraged because it can seem like they are "always wrong." Knowing and using components that are correct or that can readily be tweaked to be useful can enable the students to realize that they already have some productive tools available to them.If the pedagogical focus is to be on refining common-sense frameworks, it is critical that each student be an active participant of the process since each student will have a different framework. Consequently, each student needs to have multiple opportunities to think the ideas through for her- or himself and to test her or his ideas against the ideas and reasoning of other students as well as actual empirical evidence.--David Maloney, TIPERS Co-author; Professor of Physics Purdue University, Fort Wayne, INTeacher's Edition | 7AP Physics 1 WorkbookReturn to Table of Contents####### UNIT 1Kinematics####### MisconceptionsEven some of the best students struggle with in-depth conceptual understanding and resort to using memorized terms to answer conceptual questions. Although factual misconceptions can often be easily corrected, insisting that students dismiss their preconceptions or misconceptions is not always effective. If a student already has a nonscientific model to explain a phenomenon, new concepts, models, and representations are difficult to learn. Before embracing the concepts held to be correct by the scientific community, students must confront their own beliefs and then attempt to reconstruct the knowledge necessary to understand the scientific model being presented. This process is most effective when the teacher first identifies students' misconceptions or preconceptions and then provides a forum for students to confront them.It is very important to set the stage for learning by helping students understand that most of the common ideas that do not align with accepted knowledge are based on incomplete understanding, not incorrect understanding. Aristotle believed the same things many of our students believe. Friction is not readily apparent, and if its presence is neglected when it does exist, your observation would be that you do need to push something to keep it moving, for example. Helping students understand that the modifications they need to make are based on better scientific evidence puts them in the position of real scientists.In kinematics, it is crucial to help students distinguish among kinematic ideas such as speed, velocity, distance, displacement, and acceleration. In physics, these ideas are distinct for important reasons. In everyday contexts, concepts that are physically distinct are taken as synonyms. For example, students often do not distinguish between scalar quantities and their vector counterparts (distance and displacement; speed and velocity) and confuse speed/velocity with acceleration. While students often know that these terms are distinct, they commonly do not differentiate between them because the differences are either not important in everyday contexts or will be acknowledged in another way. It can be useful to have students consider situations in which they must distinguish such concepts to plant the idea that they will need to alter their thinking when doing physics. For example, students readily recognize that if they were to fly at 100 kilometers per hour ( km/h ) for two hours in a straight line due east compared to 100 km/h due west for an hour, they would not end at the same final location. So, there are times when students know that direction is an important aspect of motion. It can be beneficial to point out that analyzing physics correctly does not require students to think differently but instead requires them to use familiar ideas more systematically. Teacher's Edition | 8AP Physics 1 WorkbookReturn to Table of ContentsA related challenge is helping students develop the graphical skills that are used throughout physics. Part of the challenge here is that many students struggle with the nature of graphical representation and how to make connections between graphical and other forms of representation. Some students perceive graphs as a literal picture of a determined motion. For example, they might interpret a rising line with a steep slope as a hill or any straight line as representing constant velocity. Before leaving Unit 1, students should be comfortable graphing position, velocity, and acceleration as functions of time; moving back and forth between these graphs; and using these graphs as evidence to support claims or solve mon misconceptions in Unit 1: Kinematics and the pages that provide students with the opportunity to confront their misconceptions are summarized in the table below:Scenario Misconception 1 Distance and displacement are interchangeable. 1 Two objects side by side must have the same speed.1, 1 Motion always begins at the origin (0, 0). 1 Velocity is absolute and not dependent on frame of reference.1 Acceleration and velocity are always in the same direction. 1 If velocity is zero, then acceleration must also be zero.1, 1, 1 An object that is speeding up has a positive acceleration and an object that is slowing down has a negative acceleration.1, 1 Freely falling bodies can only move downward. 1 Average and instantaneous velocities are equivalent.Teacher's Edition | 9AP Physics 1 WorkbookReturn to Table of Contents####### SkillsThe design of the AP Physics 1 course and exam focuses on seven overarching practices that capture important aspects of the work of scientists. Science practices describe the skills and abilities that students should learn and demonstrate, integrated with content knowledge, to reach a goal or complete a learning activity. While the skills listed below are critical to student success, most of them are scaffolded skills necessary for students to be successful at the science practice listed with each skill.Science Practice Related Skill Prompt Heading Scenario 1 Plot data on a graph. Using Representations 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11 Draw a bestfit line. Using Representations 1, 1, 1, 1, 1 1 Scale and label axis. Using Representations 1, 1, 1, 1, 1, 1, 1 1 Find the area under a curve. Quantitative Analysis 1, 1, 11 Find the slope of a best-fit line. Quantitative Analysis 1, 1, 1, 1, 1 1 Relate the slope to a physical quantity. Quantitative Analysis/Data Analysis 1, 1, 1, 1, 1, 1, 1, 1, 1 1 Relate the area under a curve to a physical quantity. Quantitative Analysis/Data Analysis/ Argumentation1, 1, 1, 11 Linearize a graph. Using Representations 1, 1 1 Re-express one type of graph as another. Using Representations/Argumentation 1, 1, 1, 1, 1, 1 2 Defend the use of an equation to solve a specific problem. Quantitative Analysis 12 Identify an equation that can be used to solve a problem. Quantitative Analysis 1, 1, 1 2 Rearrange an equation to solve a specific problem. Quantitative Analysis 1, 14 Choose correct data to answer a question. Data Analysis 1, 1 4 Choose equipment to conduct a scientific experiment. Experimental Design 1, 1 5 Determine if data is reliable. Data Analysis 15 Use a linearized graph to answer a question about a physical quantity.Quantitative Analysis 1, 1A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.Teacher's Edition | 10AP Physics 1 WorkbookReturn to Table of ContentsTeacher's Edition | 11AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsDisplacement EK 3.A, 4.A SP 1, 1.Prepare At first glance, this scenario may seem too introductory for students. However, it provides a suitable entry point for all students regardless of their backgrounds or previous experience with physics. Note that more advanced learners will move through this worksheet quickly.Teach In Part C, most of the writing has been done for students so that they know how to structure responses. Students should see good writing before they are asked to create good writing on their own.Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:The diagram above illustrates a car that, starting from the origin, x0 travels 4 km right, and then 7 km left. What is the net displacement of the car? What is the total distance traveled by the car? Create another diagram with different position labels (i., put zero in a different place) and recalculate the displacement of the car and the distance traveled on the new coordinate system. Explain how your answers to the first set of questions are different and/or the same as your answers to the second set.What's the point? We make up coordinate systems to be able to communicate with each other. We need a common language to discuss what is happening in a very precise way. So, choosing zeros and a direction to be positive allows us to have a common language with which to discuss physical scenarios.Teacher's Edition | 12AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsPosition and Velocity EK 3.A, 4.A SP 1, 2.Prepare Creating, interpreting, and using representations are critical skills for the AP Physics 1 Exam. While students can be trained to find an equation and plug in numbers to find an answer, research shows this does not create a lasting understanding. Creating and then using a representation as evidence for a claim may seem much more difficult but builds toward deep conceptual understanding. While using the "big three" kinematic equations represents one analysis technique, there are many more that they need to be familiar with including analyzing graphs of position, velocity, and acceleration vs. time as well as motion maps.Teach If your students are using their calculator to calculate the slope, they need to indicate that they used their calculator to do the linear regression by stating it on the exam. Students who simply state the slope given to them by their calculator will receive zero points for this calculation. In a beginning physics course, it is best to have students determine the slope of the line without the use of their calculator.Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below: The position vs. time graph above represents the motion of two objects. One object is traveling at 8 m/s , while the other object is traveling at 5 m/s_. Which line on the graph represents the object traveling at_ 8 m/s_? Explain using evidence._What's the point? Representations come in many forms, including equations! You will need to be able to create more than one representation for a physical situation to be able to show that you understand relationships among physical quantities.Teacher's Edition | 13AP Physics 1 Workbook Kinematics UNIT 1 | |?Return to Table of ContentsAverage vs. Instantaneous Speed EK 3.A, 4.A SP 4, 4, 4, 5.Prepare A foundational concept for students to learn in AP Physics 1 is the difference between average and instantaneous velocity. Year after year, the Chief Reader Report on AP Exam performance highlights the fact that students still--even in May--get confused between average and instantaneous velocity, how to measure them and how to calculate them. Just because teachers move on from Unit 1 doesn't mean students never have to consider these concepts again. Bring average vs. instantaneous velocity up every time you talk about velocity. Ask students which one they need to consider for the physical situation presented to them and how they could measure it. ??Students need to be able to differentiate between average velocity, instantaneous initial velocity, and instantaneous final velocity for an accelerating object and understand that "delta distance over delta time" only gives the average velocity. ? If an object starts from rest and attains some final speed with constant acceleration, that final speed is DOUBLE the average speed. If it takes T seconds and D meters to reach the final speed, then it takes 1 2 T seconds to reach average speed and 1 4 D meters to reach average speed. Mistakes Kids Make: ? Students want to assume that D/T is the final velocity, not just the average of initial and final. ??Upon understanding that D/T is the average and not the final speed, students assume that the object reaches an instantaneous speed equal to its average speed at half the time (correct) and half the travel distance (which is wrong). ??All comments above are only true for CONSTANT accelerations; if an acceleration is changing (like in AP Physics C, where an object is subject to air resistance) an object attached to a spring, or an object going down a ramp with nonconstant incline slope, then average velocity is still D tbut the object may attain its average speed at a time before or after 12 Tdepending on the nature of the changing acceleration.Teacher's Edition | 14Teach Writing a good experimental procedure does not always require the use of a lot of words. The experimental procedure should be short and to the point. In later units, there are more scaffolded lab questions where students can practice designing experiments. Consider doing the "meeting point challenge" with your students. Each group is given two constant motion vehicles (one with two batteries and one with a battery and a "slug" made from aluminum foil), and the students need to design an experiment to determine the speeds of each vehicle. They are then given a distance (they will start the cars this distance apart) and a time (the second car is released after set time), and the students must predict where the two vehicles will meet. They may use equations, but that should not be their only representation. (For example, they should have at least one set of graphs to use as evidence for their claim.)For Part C, it may be helpful to demonstrate the second claim by setting up a set of photogates (as suggested in the argument) with a pull-back car (not constant velocity) to see if this procedure can determine the instantaneous speed. There are several ways of testing the claim made by the toy company in Part C. Have the students come up with their own method!Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:In order to perform an experiment, two students need to determine the velocity of a cart just as it reaches the bottom of a ramp. Is this the average or instantaneous velocity that they are looking for? In a few short sentences, describe an experimental setup that they could use to determine the needed velocity of the cart at the bottom of the ramp.Return to Table of ContentsWhat's the point? Data is more than just numbers. Every number in physics has meaning, and we need to analyze that data to determine its meaning.Teacher's Edition | 15AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsVelocity Is a Vector! EK 3.A, 4.A SP 1, 1, 1, 2, 6.Prepare If students are still unsure about position and velocity with one object, they may need more scaffolding for this worksheet. The key takeaways here are that velocity and displacement are vectors and direction matters!Teach Follow-Up Questions: When do Angela and Blake meet? How do you know? What other evidence could you produce to show that they meet at this time? What would a position vs. time graph of someone running at 7 m/s look like? How would that graph show a greater speed than the original 5 m/s (or -3 m /s)? What would a graph of position vs. time look like for someone who took a break in the middle of running?Suggested Activities: Walking Graphs Lab Have students act out for themselves the suggested lab in the AP Physics B question #2 from 2006.Teacher's Edition | 16Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:The above graph represents the position as a function of time for an object moving in a straight line to the right. Which of the following is true?A. The object's velocity increases. B. The object's velocity decreases. C. The object's velocity remains unchanged. D. The object stays at rest. E. More information is required.Explain.Return to Table of ContentsWhat's the point? The slope relationship between position and velocity is one in a series of relationships you will discover throughout the course. In math class, the slope of a line is a number. In physics, it correlates with a physical quantity, such as velocity.Teacher's Edition | 17AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsRelative Velocity EK 3.A, 4.A SP 2, 2, 6.Prepare This is relatively easy to replicate in the lab with long sheets of paper and constant-motion cars. If you have access to these materials, consider letting your students experiment either before or while they are working on this worksheet.Teach For Part D, we specifically chose numbers so that a student who is not considering direction will gravitate toward Scenario A. A related question that always stumps the students because it involves water instead of a moving train is as follows: Suppose you and a pair of life preservers are floating down a swift river as shown. You want to get to either of the life preservers for safety. One is 3 meters downstream and one is 3 meters upstream from you. Which can you swim to in the shortest time? A preserver upstream B preserver downstream C require the same time. The Answer is C: Both require the same time. Switch up the situation so that it is Blake again with Angela 3 meters in front and Carlos 3 meters behind as the train moves. Which friend can Blake walk to the fastest? Since Blake, Carlos, and Angela are all traveling on the train together, they can be considered to be at rest relative to each other. Therefore, Blake can walk to either friend just as quickly!Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below: The motion diagram below represents a cart moving to the right. Is the cart speeding up? Slowing down? Or moving at a constant speed? Explain.What's the point? Velocity is RELATIVE, meaning that is depends on your reference frame. When analyzing a physical scenario, the first step is to choose a frame of reference including a zero position and positive and negative directions.Teacher's Edition | 18 Return to Table of ContentsTeacher's Edition | 19AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsConstant Velocity EK 3.A, 4.A, 4.A SP 1, 1, 2Prepare Understanding the meaning of representations is key to understanding physics. Sometimes students see graphs as busy work they must do before they can get down to the business of solving the equation for the "answer." Encourage students to focus less on finding an answer and more on what evidence the students can find to back up their claims about physical situations.Teach If you have access to constant-motion vehicles and motion sensors, you could have students replicate this experiment and collect their own data. Additional questions: What would the position vs. time graph look like for this vehicle? What about the acceleration vs. time? What is the relationship between the velocity graph and the position graph? The velocity vs. time graph is the most "powerful" graph because in just one representation, students can find evidence about the displacement (the area under the curve), the velocity, and the acceleration (the slope of the curve).Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below: The position vs. time graph of a moving object is shown at right. Sketch the velocity vs. time graph for the same object during the eight seconds shown. Explain how you know what to sketch.What's the point? The area relationship between velocity vs. time graph and position is yet another relationship you will discover throughout the course. In math class, the area under a line is a number. In physics, it corresponds to a physical quantity.Teacher's Edition | 20AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsGraphs of Velocity EK 3.A, 4.A, 4.A SP 1, 1, 2, 2Prepare This scenario can be demonstrated by releasing a cart from rest at the top of an incline with a motion sensor on the track to record the velocity as a function of time. Students could also use a fan cart and motion sensor to recreate this graph.Teach Problems that are extremely difficult to solve with equations can become much simpler to analyze with graphs. The better your students become at using graphs as evidence for claims, the better prepared they will be for the AP Physics 1 Exam.Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below: Two objects start from the same position at the same time from rest but with different magnitudes of positive accelerations. Sketch displacement vs. time, velocity vs. time, and acceleration vs. time graphs for the two objects. Explain your reasoning in creating the graphs.What's the point? There are so many ways to analyze a graph! The three ways shown here are 1) reading a quantity directly off the graph, 2) analyzing the slope, and 3) analyzing the area under the curve. When given a graph, think about the meaning of all the different pieces of information presented there!Teacher's Edition | 21AP Physics 1 Workbook Kinematics UNIT 1 | |?Return to Table of ContentsRelationships Between Position, Velocity, and Acceleration EK 3.A, 4.A, 4.A SP 1, 1, 1, 2, 2Prepare Have students walk this graph in front of a motion detector, so they have the opportunity to physically feel that they are not at zero position but at zero velocity at t = 3 s. If you haven't already done a "walking the graphs" lab, you should consider doing it before assigning this worksheet. If the laboratory equipment is not available, have students use an online simulator like PhET to recreate motion graphs.Teach Part D is very tricky for students. And in fact, many students feel like deer in the headlights when faced with a blank grid on which to create a graph. Remind students that they are not expected to know immediately what shape they should graph. Have them plot the points they know. For example, for Part D, they should be able to verbalize that the initial position of the car was x = 10 m (given in the prompt) and that they can find the position later (at t = 3 seconds) by finding the area under the velocity vs. time graph from t = 0 to t = 3 s. Now that they have two points plotted, they have to decide whether there is a line or a curve connecting the points and if it is a curve, whether it will be concave up or down. However, even if they only can plot these two points and then guess about the connection, they will have more points on the AP Exam than if they left the grid blank or just scribbled nonsense. Scaffolding for sketching position graphs: ? Step 1: What are the beginning and end points? ?? Step 2: What is the general shape of the graph? Linear (constant velocity, even if its zero)? Curvy (accelerating)? ?? Step 3: If accelerating, is the velocity positive and increasing (or negative and decreasing) or is the velocity positive and decreasing (or negative and increasing)? A simpler way to think of this is, if the change in velocity (the acceleration) is negative, the curve of a position-time graph is concave down (and concave up if it is positive). An object speeds up when its acceleration and velocity are in the same direction, so if it is speeding up, the acceleration has the same sign as the velocity.Teacher's Edition | 22 Return to Table of ContentsAssess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:to write a narrative of how they created the two graphs in Part D (i., explain the thoughts they had that helped them create the correct graphs). For example,"I first plotted the point ( 0 s 0 m , ) because I knew the object started at position zero. The object stops at t = 3 because that is where the velocity changes direction. The area between 0 and 3 is the farthest distance that the object travels forward, which is 18. So, I then plotted the point ( 3 s , 18 m ). Now I know that the graph before three seconds slopes up (the velocity is the slope and is positive) and the slope is becoming less steep as the speed decreases. After time three, the slope is negative and getting steeper as the object goes faster backward."What's the point? Moving between representations of the same situation is an important skill in AP Physics 1. Next time you are asked to create a representation (graph, sketch, diagram, etc.) challenge yourself to see if you can create a second representation of the same situation.Teacher's Edition | 23AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsThe Chase EK 3.A, 4.A SP 1, 1, 1, 2, 2, 6Prepare This is very similar to the classic fugitive catching a train problem. Although in this iteration, the police car doesn't have a maximum speed, in real life, the police car would have a maximum speed. Adding that into the problem (like in the fugitive problem) makes the mathematical approach much more difficult but doesn't affect the difficulty of the graphical solution. Remind your students that the graphical approach for motion is often simpler and provides clearer evidence for understanding than just finding a numerical answer. On the AP Physics 1 Exam, it is currently unlikely that they will be asked to solve for a numerical answer, but it is extremely likely that they will be asked to create and/or use a graph of motion to justify a claim.Teach Remind students that you cannot catch someone by going the same speed. Try this out with your constant-motion vehicles. Start one and then 5 seconds later, start the other from where the first one started. Can the second car ever catch the first car if it is traveling at the same speed? For Part C, students might need a graph for a longer time than what they drew initially. If your students have the time t 1 at the far-right corner of the grid, encourage them to draw a bigger graph incorporating more time.Additional Questions: Determine, using the graph, the approximate time when the car and truck are in the same location. Double-check, using another representation, the time at which the car and truck are in the same location.Teacher's Edition | 24 Return to Table of ContentsAssess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:At t = 0 s , two cars are located at the starting line. Car 1 is traveling at 10 m/s , and Car 2 is at r 2 m/s 2est. Car 1 continues traveling at 10 m/s while Car 2 accelerates at. Sketch a velocity vs. time graph for each car on the same axis. (Differentiate the lines and make a key so it is clear which graph belongs to which car.) Mark on the graph t 1 where the two cars have the same velocity. Mark on the graph t 2 the time when Car 2 catches up to Car 1. How did you know where to mark t 1 and t 2_?_What's the point? While position and velocity are related, they are not linked, meaning that just because two objects are side by side, they are not necessarily going the same speed, or just because two objects are going the same speed, they are not necessarily side by side.Teacher's Edition | 25AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsVertical Motion EK 3.A, 4.A, 4.A SP 1, 1, 1, 2, 2, 6Prepare This worksheet can be paired with the next one for deeper questions about the motion of the rocket.Teach Additional Questions: What is the relationship between the graphs drawn in Parts A and B? Are there ways to check that the graphs are self-consistent? What would the acceleration of the rocket be at 12 seconds? What would the graph of velocity vs. time look like from the time of launch until the time the rocket reaches its maximum height? How would you represent the time when the rocket reaches the maximum height on the velocity vs. time graph? How could you determine the maximum height of the rocket only using the velocity vs. time graph? How could you use a velocity vs. time graph to determine how long it would take the rocket to land back on Earth? How would you know from the velocity vs. time graph that the rocket had landed back on Earth? What would a position vs. time graph look like for the rocket for the first 10 seconds? Until the rocket reaches the maximum height? Until it reaches the ground?Teacher's Edition | 26Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:A ball is thrown straight up into the air from the ground. It reaches a maximum height and returns back to the ground. Sketch two vectors that represent the velocity and the acceleration of the ball on the way up.Sketch two vectors that represent the velocity and acceleration of the ball at the maximum height.Sketch two vectors that represent the velocity and acceleration of the ball on the way down.Using the diagrams you just drew, make a claim about the direction of the acceleration and velocity and when the ball is speeding up or slowing down.What's the point? In math class, you are used to reaching for an equation to solve a problem. In physics, representations are often easier and faster to help you determine an answer or support a claim.Return to Table of ContentsTeacher's Edition | 27AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsFree Fall EK 3.A, 4.A, 4.A SP 1, 1, 1, 2, 2, 6Prepare This worksheet can be paired with the one before for deeper understanding.Teach Students consistently hunt for equations that look like they can give them the answer they need without thinking through the meaning of the physical situation, the variables they are given, or the limitations of the equations. Finding the time when the rocket lands back on Earth is a classic AP Physics B "type" problem. It is mathematically a little tricky and requires two steps to solve correctly. To make this into an AP Physics 1 question, take out the need for a solution to the question. Ask simply, how could you find the time? Ask the students for more than one method. Using an equation is fine, but can they explain how they would use the equation? Can they then create a graph that they could use to double-check their solution and/or provide more evidence to justify a claim?Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below: A hot air balloon moving upward at 10 m/s drops a sandbag as the balloon is 10 meters above the ground. Sketch a velocity vs. time, position vs. time, and an acceleration vs. time graph for the sandbag. What is the maximum height reached by the sandbag? Provide evidence for your claim. (Equations should not be your only evidence!) How long does it take the sandbag to reach the ground? Provide evidence for your claim. (Equations should not be your only evidence!)What's the point? Equations are tools. If you try to use a hammer to clean a window, you'll make a mess. You must make sure you use the right equation for the job. Equations include mathematical models of physical behavior and are another way to communicate relationships among physical variables.Teacher's Edition | 28 Return to Table of ContentsTeacher's Edition | 29AP Physics 1 Workbook Kinematics UNIT 1Return to Table of ContentsLinearizing Graphs EK | 3.A, 4.A SP | 1, 1, 2, 2, 5, 6Prepare Consider printing out the table at the bottom right with the most common relationships used in AP Physics 1 for your students. Being able to repeatedly reference this will help them see the patterns and feel more confident in making claims about the relationships between physical quantities. Linearization is a tough mathematical concept. Consider doing an activity to introduce the idea before assigning this worksheet. Give each lab group a set of paper circles (printed from the internet or cut from craft paper with a circle cutter). Have each group measure the diameter of each circle (pre-mark each circle with the area--you can calculate this--it is tedious to have students determine area by counting boxes and not the point of this activity). Students will then have data about the area and diameter of a circle. If they graph area vs. diameter (or radius if that makes it easier), is it linear? What is the relationship between the two variables? (Compare with the chart at bottom right). What should they graph to make a linearized graph? (Students can graph A vs. r 2 and the slope will be , or if they graph A vs. D 2 , the slope will be /4.Teach You can keep this lesson going by asking students to sketch a graph of drop height vs. time squared (that they calculated in Part C). Then have them sketch in a line of best fit. Try to have the line as close as possible to all points and as many points above the line as below. Next, students can find the slope of their line of best fit by choosing points on the line (not data points), marking them on the graph, and using these points with the point slope equation. Students can then calculate the acceleration due to gravity by setting the value of the slope equal to 12 g. Students should be able to explain in a short paragraph or set of sentences how and why they are performing each of these steps listed above.Teacher's Edition | 30 Return to Table of ContentsAssess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:Give students a set of data collected about the radius and volume of a set of spheres. (This can also be done as an activity where students determine the volume of the spheres by water displacement.) Have the students graph volume vs. diameter (or radius). Is it linear? What is the relationship between volume and diameter (or radius)? What should be graphed to make a linearized graph? What would the slope be? (If students graph volume vs. r 3 , the slope will be 4 /3 .)Ask students for other equations that they may have learned in other classes in which they could have theoretically collected data. What would they graph? Would it be linear? How could they linearize the data?What's the point? Not all relationships are linear, but when you manipulate the data so that the graph is a line, it is easier to get useable information from the graph to be able to draw conclusions as well as construct equations.Teacher's Edition | 31AP Physics 1 Workbook Kinematics UNIT 1 |Return to Table of ContentsProjectile Motion EK | 3.A, 4.A SP 2, 2, 6Prepare This worksheet can be paired with the next one for deeper understanding.Teach Students develop personal "theories of motion" by generalizing the ideas they acquire from the observation of objects in everyday life. Many student misconceptions result from a pre-Newtonian impetus theory of motion. This theory attributes motion to an impetus that is given to an object initially and then is gradually used up over time. (This is the cartoon theory of motion.) Common misconceptions include: ??An object moves in the direction it is launched. Only after some "impetus" has been used up can gravity act, causing the object to fall to the ground ??An object that is dropped from a moving object (i., a car, train or airplane) does not receive any impetus, and so falls straight down. ??Falling objects possess more gravity than stationary objects, which may possess none at all. (i., an object at the top of its path does not have an acceleration.) It is important to be both aware of these misconceptions and provide students with opportunities to confront them. You can continue this page by asking students the following question: Part F: If you throw the ball at an angle, it increases the time that the ball is in the air and decreases the horizontal speed, so will the ball go farther or not as far if it is thrown at an angle of 20 degrees above the horizontal rather than being thrown horizontally?Teacher's Edition | 32 Return to Table of ContentsAssess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the question below:A 0 -kilogram red ball is thrown horizontally at a speed of 4 m/s from a height of 3 meters. A 0 -kilogram green ball is thrown horizontally from the same height at a speed of 8 m/s_. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is_A. half as much. B. the same. C. four times as much. D. one-quarter as much. E. twice as much.What's the point? When asked to write or derive an equation relating variables, start with an equation that is already familiar to you. When you are finished, make sure that you have used ONLY the variables given to you!Teacher's Edition | 33AP Physics 1 Workbook Kinematics UNIT 1 | |Return to Table of ContentsProjectile Motion EK 3.A, 4.A SP 1, 1, 1, 6Prepare This worksheet can be paired with the one before for deeper understanding.Teach There are many correct answers here. On a question like this, students can get hung up on what the "correct" answer is. They need to be taught that in response to an open-ended question, the AP Exam is looking for common properties that all correct graphs will have in common. For example, for Part B of this question, all correct vertical velocity vs. time graphs will have a vertical intercept that is a positive non-zero value and will have the same slope. Peer grading can be a powerful tool. Students need opportunities to see that there are other correct responses and to argue the differences and similarities between correct representations.Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below: A ball of mass m is thrown into the air at an angle of 37 degrees above the horizontal. What happens to the magnitude of the ball's vertical acceleration during the total time interval that the ball is in the air? A. Acceleration decreases and then increases. B. Acceleration decreases and then is constant. C. Acceleration increases and then decreases. D. Acceleration increases and then is constant. E. Acceleration stays the same.What's the point? When sketching graphs of velocity vs. time for projectile motion, take special care to differentiate what is happening in the vertical and horizontal directions. See AP Physics B 1994 #3 for more practice drawing graphs of velocity vs. time for objects undergoing projectile motion.Teacher's Edition | 34AP Physics 1 Workbook Kinematics UNIT 1 |Return to Table of Contents2D Motion EK 3.A, 4.A SP | 1, 1, 2, 2, 5, 6Prepare If you have access to projectile launchers and carbon paper, this experiment can be replicated by your students. Another option is to purchase a set of dollar-store suction-cup launchers and have your students replicate. The dollarstore suction-cup launchers may or may not have a constant launch speed, which will add an interesting spin to the data analysis! If you use the suction-cup launchers, make sure you do the experiment before your students so that you are aware of any possible problems they may have to overcome.Teach For more linearization practice, have your students derive an expression for the distance D to the target in terms of the vertical distance H, the speed of the dart, and fundamental constants as necessary. Have them graph D vs. H. Is this linear? What can we say about the relationship between D and H? What could we graph instead so that the graph is linear? If the students graph D 2 vs. H, the slope will be 2 v 2 /g. The speed of the dart they calculate should be about 60 m/s. Suppose the "real" speed of the dart is 65 m/s, what could explain the difference? Have students find the percent error between their speed and the known value.Teacher's Edition | 35 Return to Table of ContentsAssess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:An archer wants to be able to shoot an arrow so that it hits the ground as far as possible from the point where she shoots it. The ground is level. The archer reasons that the arrow should be aimed almost horizontally so its velocity component along the horizontal is as great as possible and therefore will travel as far as possible in the horizontal direction. Critique her reasoning.Is she right?A. Ye s B. No, because this won't make the horizontal component of the velocity bigger. C. No, because even though this will make the horizontal component of the velocity bigger, it won't make the arrow go farther. In a clear, coherent paragraph-length response, explain your answer above.What's the point? While the rules for significant digits will not be directly tested on the AP Physics 1 Exam, you will be expected to use a reasonable number of significant digits in calculations on the free-response section. Significance is an indication of the quality of the measurement and the given variables dictate the significance of the answer. Points may be deducted for an unreasonable number of number of significant digits.Teacher's Edition | 36AP Physics 1 Workbook####### UNIT 2Dynamics####### MisconceptionsStudents have an instinct about forces as pushes or pulls because of physiological experience but often have difficulty conceptualizing forces as interactions. If students are thinking of forces as things in and of themselves or as properties of objects (which are two common misconceptions about forces), they usually have a difficult time using Newton's second and third laws appropriately. Students also tend to believe that forces are proportional to velocity instead of understanding that net force is proportional to acceleration.One approach to helping students envision forces as interactions is to ask them to explicitly identify the agent exerting the force and the object on which it is exerted when they work with a force (e., in a free-body diagram). Doing this will enable them to check that any force they think is present actually exists. If they cannot identify the agent, which has to be Earth, another object or another system, exerting the force, then they need to reconsider including that force in the analysis. Identifying the agent and object also enables students to check that forces they are analyzing are all acting on the same object. It also allows students to check that "action-reaction pairs" have the same two objects involved, just in opposite roles. For example, is object A the agent for one force and the object for the other? It is best to avoid using the common terminology of forces "acting" on objects. The verb acting reinforces the misconception that forces are independent. Try to always use the term exerted and ensure that students could complete the sentence: This interaction can be represented by a force exerted by (object 1) on (object 2), filling in the parentheses as appropriate for the mon challenges that students have regarding Newton's first law include the idea that forces are required for motion with constant velocity. When observing classroom demonstrations of accelerating objects, students often need help recognizing that the velocity of an object is changing as a result of the net force exerted on the object. It should be made clear to students that the net force determines an object's acceleration, not its velocity. It can be very helpful to discuss friction and air resistance with the students as you are making this point. They often know you have to push on the accelerator to keep a car going at constant velocity or keep shoving a box to keep it sliding at constant velocity, but they have not thought about the forces exerted on the car or box that they cannot see. Students might not always see the connection betweenReturn to Table of ContentsTeacher's Edition | 37AP Physics 1 WorkbookNewton's laws and kinematics, so it is important for them to recognize Newton's second law as "cause and effect." It is important to present Newton's second law in itsoperational form of a F m , as the commonly used F ma leads some students to believethat the product of mass and acceleration is a force. Scaffolding around the differences between individual forces and the net force is beneficial, as this often causes students difficulty. Students often believe that all forces are equal to mass times acceleration, which further reinforces the misconception that forces are properties of objects.Scenario Misconception2I, 2 Velocity is a force. 2 Forces are required for motion with constant velocity. 2 Inertia deals with the state of motion (at rest or in motion).2 All objects eventually stop moving when the force is removed. 2, 2, 2 Inertia is the force that keeps objects in motion.2, 2, 2, 2 Action-reaction forces are exerted on the same body. 2, 2 There is no connection between Newton's laws and kinematics. 2, 2, 2 The product of mass and acceleration, ma , is a force.2, 2 Friction can't be exerted in the direction of motion. 2, 2, 2 The normal force on an object is equal to the weight of the object by Newton's third law. 2 Equilibrium means that all forces on an object are equal.2, 2, 2, 2 Equilibrium is a consequence of Newton's third law. 2, 2, 2, 2, 2, 2, 2, 2, 2, 2Only animate things (people, animals) exert forces; passive objects (tables, floors) do not exert forces. 2 A force applied by a hand, for example, is still exerted on an object after the object leaves the hand.Return to Table of ContentsTeacher's Edition | 38AP Physics 1 Workbook####### SkillsThe design of the AP Physics 1 course and exam focuses on seven overarching practices that capture important aspects of the work of scientists. Science practices describe the skills and abilities that students should learn and demonstrate, integrated with content knowledge, to reach a goal or complete a learning activity. While the skills listed below are critical to student success, most of them are scaffolded skills necessary for students to be successful at the science practice listed with each skill.Science Practice Related Skill Prompt Heading Scenario 1 Acceleration vs. mass graph Using Representations 21 Create and use a free-body diagram. Using Representations 2, 2. 2, 2, 2, 2, 2, 2, 2, 21 Plot data on a graph. Using Representations 2, 2, 2, 2 1 Scale and label axis. Using Representations 2, 2, 2, 21 Velocity vs. time graph Using Representations 2, 2 1 Identify systems. Using Representations 2, 2, 2, 2, 2 1 Linearize a graph. Using Representations 21 Match shapes of graphs to relationship. Data Analysis 2 2 Identify an equation that can be used to analyze physical situation. Quantitative Analysis 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 2 Derive or calculate including annotations. Quantitative Analysis 2, 2, 2, 2, 2, 2, 22 Relate slope to a physical quantity. Data Analysis 2, 2 4 Design an experiment. Experimental Design 2, 2, 25 Describe how measurements would be analyzed. Data Analysis 2, 2, 2 5 Sketch a line of best fit. Data Analysis 2 5 Error analysis Data Analysis 26 Justify a claim with evidence. Argumentation 2, 2, 2, 2, 2, 2, 2, 2, 2 6 Use equations to support reasoning. Using Representations 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.Return to Table of ContentsTeacher's Edition | 39AP Physics 1 Workbook UNIT 2 Dynamics | |Return to Table of ContentsRelationship Between Force and Acceleration EK 3.B SP 1, 5Prepare So far, students have seen linear and quadratic relationships. This may be the first time that they will see a relationship that is inversely proportional. If your students struggle with determining the functional relationship between variables, consider with them the equation for average speed v d avg t , which can be rewritten dv t avg . For a constant distance, what happens to the speed and the time? If you increase the speed, the time decreases. If you want to increase the time, you have to decrease the speed. Give them some data to graph, see that it is not linear, and decide what they could graph to make it linear (vavg vs. 1 /t). The slope of that graph will be the constant distance traveled.Average Speed (m/s)Time to Travel Some Unknown Distance (seconds) 12 1 6 24 3 3 4 2 52 6 1 71 8Teacher's Edition | 40 Return to Table of ContentsTeach The idea of inverse relationships is powerful and later leads to both Ohm's law (V = IR) and v = f_._Now that your students know what they should graph to make the graph linear, have them create the graph. What is the magnitude of the force exerted on each box?Can they think of a way to recreate this data themselves, so that they have a constant net force with varying accelerations based on mass? (One idea is to use a fan cart that will provide a constant force, and the students can add masses to the cart. If a motion detector is set up in front of the cart, it can collect velocity vs. time data and the slope of that line will be the acceleration of the cart.)Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:Data has been collected about the net external force on an object as well as that object's acceleration while the net external force is being exerted on it. What data should be graphed to create a linear graph? What would be the physical meaning of the slope of the graph?What's the point? Functional relationships will be tested on the AP Physics 1 Exam. You need to be able to look at a graph and use the data presented as evidence for a claim of the relationship between the variables graphed.Teacher's Edition | 41AP Physics 1 Workbook Dynamics UNIT 2 | |Return to Table of ContentsForce and Acceleration EK 1.C SP 1, 5, 6Prepare This is a good demonstration for students to get a "feel" for how the speed changes under the influence of a constant force, and then what happens to the speed of the object once the force is removed. If you have access to low-friction carts and motion detectors, you could set up this experiment for students to try themselves. This worksheet can be their prediction sheet and then they can test their predictions in the lab. In this page, we introduce students to a new tool. The "Checklist" will be provided as a scaffolding tool to help students check their own writing. By the end of the course, students should be able to ask themselves these questions without being prompted!Teach If you have low-friction skateboards, you can have students pull a box on the skateboard (to simulate a student) with a spring scale to see for themselves that if they want to pull with a constant force, their speed and the speed of the skateboard will increase. Ask the students here,

"What is the relationship between your speed and the speed of the skateboard?" (They should be equal.) "Why are they equal?" This will help them understand that systems that are "attached" must have the same speed at any clock reading. This may help with misconceptions later about the common speed and acceleration of systems (i., objects connected by strings). Note that the sample graph provided in Part B suggests that the textbooks must be VERY massive. This is just to help students visualize that there is a relationship between net external force, mass, and acceleration. Students will explore the mathematical relationships in later scenarios.Teacher's Edition | 42Assess To further assess student understanding of the concepts addressed in this scenario, you may want to ask students the questions below:A box of mass m is pushed for 10 seconds with a force P across a horizontal floor with negligible friction. After 10 seconds, the person stops pushing. Sketch a velocity vs. time graph for the box. Sketch in a dotted vertical line at t = 10 _seconds. What is d

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