# 1: Motion

Activities & Reader (ISBN 0-7872-3927-5, 190 pages)

How to Use This Book *xi*

Acknowledgments *xiii*

### Activities

- 1 - Looking Ahead
*1* - 2 - Communicating the Position of an Object
*3* - 2A - Communicating the Position of an Object (Alternative Version)
*7* - 3 - Describing Position
*9* - 4 - Using Graphs of Position vs. Time
*15* - 5 - Generating Sketches of Position vs. Time
*19* - 6 - Translating Graphs of Position vs. Time
*23* - 7 - Describing Displacement
*27* - 8 - Describing Velocity
*31* - 9 - Using Graphs of Velocity vs. Time
*35* - 10 - Generating Sketches of Velocity vs. Time
*39* - 11 - Translating Graphs of Velocity vs. Time
*43* - 12 - Relating Strobe Diagrams to Plots of Position vs. Time and Velocity vs. Time
*47* - 13 - Finding and Comparing Velocities
*53* - 14 - Relating Graphs of Position vs. Time and Velocity vs. Time
*57* - 15 - More Relating Graphs of Position vs. Time and Velocity vs. Time
*61* - 16 - Solving Constant-Velocity Problems Using Different Methods
*65* - 17 - Solving Constant-Velocity Problems
*69* - 18 - Recognizing Accelerated Motion
*73* - 19 - Describing Changes in Velocity
*75* - 20 - Recognizing Graphs of Acceleration vs. Time
*81* - 21 - Generating Sketches of Acceleration vs. Time
*85* - 22 - Translating Graphs of Acceleration vs. Time
*87* - 23 - Calculating Average Acceleration
*89* - 24 - Relating Strobe Diagrams to Graphs of Acceleration vs. Time
*93* - 25 - Relating Graphs and Kinematic Functions
*97* - 26 - Relating Kinematic Quantities with Kinematic Functions
*101* - 27 - Relating Graphs of Position, Velocity, and Acceleration vs. Time
*105* - 28 - Comparing Graphs of Velocity vs. Time and Displacement vs. Time
*109* - 29 - Translating Between Different Representations of Accelerated Motion
*111* - 30 - Graphical Representations of Motion: Reflection and Integration
*115* - 31 - Evaluating Procedures for Solving Kinematics Problems
*119* - 32 - Executing Procedures for Solving Kinematics Problems
*125* - 33 - Generating Procedures for Solving Kinematics Problems
*127* - 34 - Solving Constant-Acceleration Problems
*129* - 35 - Summarizing and Structuring Kinematics Ideas
*133*

### Reader: Chapter 1—Describing Motion *R1*

- 1.0 Introduction
*R1*- six terms used to describe motion
*R1*

- six terms used to describe motion
- 1.1 Position
*R1-5*- Describing the position of an object
*R1-4*- definition of the term
*origin**R1* - units of position: meter (m), kilometer (km), and centimeter (cm)
*R2* - three representations for position
*R2*- magnitude & direction representation
*R2* - component representation
*R3* - directed line segment representation
*R3*

- magnitude & direction representation
- representing the position in two dimensions
*R3*- magnitude & direction
*R3,4* - component representation
*R4* - directed line segment
*R4*

- magnitude & direction
- why we use three different representations
*R4*

- definition of the term
- Using graphs to describe the position of objects moving in one dimension
*R5*

- Describing the position of an object
- 1.2 Displacement
*R6,7*- Introduction
*R6* - Displacement in one dimension
*R6,7*- symbol for displacement: "delta-
*x*"*R6* - definition of displacement
*R6* - an example of displacement in all three representations
*R6,7*

- symbol for displacement: "delta-
- Displacement in two dimensions
*R7*

- Introduction
- 1.3 Velocity
*R8-18*- Introduction
*R8,9*- difference between speed and velocity
*R8* - how we recognize when something has a velocity
*R8* - definition of average velocity (in one dimension)
*R8* - definition of velocity (or instantaneous velocity)
*R9* - definition of speed
*R9*

- difference between speed and velocity
- Representing velocity (in two dimensions)
*R9-11*- using all three representations for velocity
*R10* - how to estimate the components of velocity using a directed line segment
*R11*

- using all three representations for velocity
- Representing velocity at different times (in one dimension)
*R12* - Relationships between graphs of position and velocity
*R12-15*- constant, positive velocity
*R13* - constant, negative velocity
*R13* - changing velocity
*R14* - meaning of the area below velocity vs. time
*R14* - graphs of position vs. time
*R15* - meaning of the slope of position vs. time
*R15*

- constant, positive velocity
- Using algebra to relate position and velocity
*R16,17*- equation for displacement when velocity is constant
*R17* - equation for position vs. time when velocity is constant
*R17*

- equation for displacement when velocity is constant
- Avoiding pitfalls when working with velocity concepts
*R18,19*- definition of average speed
*R18* - why the average speed for a trip is not the average of the speeds during the trip
*R18* - why the average speed for a trip is not the magnitude of the average velocity
*R18,19*

- definition of average speed

- Introduction
- 1.4 Acceleration
*R19-33*- Introduction
*R19-21*- how the term
*acceleration*is used in physics compared to how the term is used in everyday language*R19* - four examples of motion:
*R19-21*- a car moving at constant velocity
*R19* - a car with changing speed but constant direction
*R20* - a car with constant speed but changing direction
*R20* - a thrown ball has changing speed and direction
*R21*

- a car moving at constant velocity

- how the term
- Defining acceleration for straight-line motion (motion in one dimension)
*R21-24*- symbol for acceleration:
*a*_{x}*R21* - definition of average acceleration
*R21* - why "negative acceleration" does
__not__mean "slowing down"*R22,23* - definition of acceleration (or instantaneous acceleration)
*R24*

- symbol for acceleration:
- Representing and interpreting acceleration in one dimension
*R24,25*- using directed line segments for velocity
*R24* - using a number line for velocity
*R25*

- using directed line segments for velocity
- Relationships between graphs of acceleration, velocity, and position (vs. time)
*R26-28*- calculations of the slopes of tangent lines
*R26* - verification that the slope of position vs. time is the velocity
*R26,27* - meaning of the slope of velocity vs. time
*R27* - meaning of the area below acceleration vs. time
*R28*

- calculations of the slopes of tangent lines
- Deriving the kinematic equations for constant acceleration
*R28-33*- acceleration = 0
*R29*- how to find the displacement using a velocity graph
*R29* - equation for the position at time
*t**R29*

- how to find the displacement using a velocity graph
- acceleration <> 0
*R30-33*- how to find velocity using an acceleration graph
*R30* - equation for the velocity at time
*t**R30* - how to find position using a velocity graph
*R31* - equation for the position at time
*t*for constant acceleration*R31* - equation for the squared velocity after displacement "delta-
*x*"*R31* - how to use graphs to solve problems
*R32,33*

- how to find velocity using an acceleration graph

- acceleration = 0

- Introduction
- 1.5 Kinematics
*R34-36*- Introduction
*R34* - Definitions
*R34*- position
*R34* - displacement
*R34* - average velocity
*R34* - velocity
*R34* - speed
*R34* - average speed
*R34* - average acceleration
*R34* - acceleration
*R34*

- position
- Relationships between graphs of motion quantities
*R35*- meaning of the slope of position vs. time
*R35* - meaning of the slope of velocity vs. time
*R35* - meaning of the area below velocity vs. time
*R35* - meaning of the area below acceleration vs. time
*R35* - diagrammatic representation of these relationships
*R35*

- meaning of the slope of position vs. time
- Derived equations relating the motion quantities (for constant acceleration)
*R35*- equation for the velocity at time
*t**R35* - equation for the position at time
*t**R35* - equation for the squared velocity after displacement "delta-
*x*"*R35* - definitions of symbols used in these derived equations
*R35*

- equation for the velocity at time
- Conclusion
*R36*- why problem solving is so difficult
*R36* - how to simplify kinematics problems
*R36* - why understanding motion is so important
*R36*

- why problem solving is so difficult

- Introduction

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