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
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
representing the position in two dimensions
R3
magnitude & direction
R3,4
component representation
R4
directed line segment
R4
why we use three different representations
R4
Using graphs to describe the position of objects moving in one dimension
R5
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
Displacement in two dimensions
R7
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
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
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
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
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
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
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
Representing and interpreting acceleration in one dimension
R24,25
using directed line segments for velocity
R24
using a number line for velocity
R25
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
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
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
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
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
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
Conclusion
R36
why problem solving is so difficult
R36
how to simplify kinematics problems
R36
why understanding motion is so important
R36