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: ax    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