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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
In this chapter we study kinematics of motion in one dimension—motion along a straight line. Runners, drag racers, and skiers are just a few examples of motion in one dimension.
Chapter Goal: To learn how to solve problems about motion in a straight line.
Chapter 2. Kinematics in One Dimension
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Topics:
• Uniform Motion• Instantaneous Velocity• Finding Position from Velocity• Motion with Constant Acceleration• Free Fall• Motion on an Inclined Plane• Instantaneous Acceleration
Chapter 2. Kinematics in One DimensionChapter 2. Kinematics in One Dimension
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 2. Reading QuizzesChapter 2. Reading Quizzes
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
The slope at a point on a position-versus-time graph of an object is
A. the object’s speed at that point.B. the object’s average velocity at that point.C. the object’s instantaneous velocity at that point.D. the object’s acceleration at that point.E. the distance traveled by the object to that point.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
The slope at a point on a position-versus-time graph of an object is
A. the object’s speed at that point.B. the object’s average velocity at that point.C. the object’s instantaneous velocity at that point.D. the object’s acceleration at that point.E. the distance traveled by the object to that point.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
The area under a velocity-versus-time graph of an object is
A. the object’s speed at that point.B. the object’s acceleration at that point.C. the distance traveled by the object.D. the displacement of the object.E. This topic was not covered in this chapter.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
The area under a velocity-versus-time graph of an object is
A. the object’s speed at that point.B. the object’s acceleration at that point.C. the distance traveled by the object.D. the displacement of the object.E. This topic was not covered in this chapter.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
At the turning point of an object,
A. the instantaneous velocity is zero.B. the acceleration is zero.C. both A and B are true.D. neither A nor B is true.E. This topic was not covered in this chapter.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
At the turning point of an object,
A. the instantaneous velocity is zero.B. the acceleration is zero.C. both A and B are true.D. neither A nor B is true.E. This topic was not covered in this chapter.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
A 1-pound block and a 100-pound block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance
A. the 1-pound block wins the race.B. the 100-pound block wins the race.C. the two blocks end in a tie.D. there’s not enough information to
determine which block wins the race.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
A 1-pound block and a 100-pound block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance
A. the 1-pound block wins the race.B. the 100-pound block wins the race.C. the two blocks end in a tie.D. there’s not enough information to
determine which block wins the race.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 2. Basic Content and ExamplesChapter 2. Basic Content and Examples
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Uniform Motion
Straight-line motion in which equal displacements occur during any successive equal-time intervals is called uniform motion. For one-dimensional motion, average velocity is given by
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.1 Skating with constant velocity
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EXAMPLE 2.1 Skating with constant velocity
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EXAMPLE 2.1 Skating with constant velocity
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EXAMPLE 2.1 Skating with constant velocity
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.1 Skating with constant velocity
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.1 Skating with constant velocity
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Tactics: Interpreting position-versus-time graphs
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Tactics: Interpreting position-versus-time graphs
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Instantaneous VelocityAverage velocity becomes a better and better approximation to the instantaneous velocity as the time interval over which the average is taken gets smaller and smaller.
As Δt continues to get smaller, the average velocity vavg = Δs/Δt reaches a constant or limiting value. That is, the instantaneous velocity at time t is the average velocity during a time interval Δt centered on t, as Δt approaches zero.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.4 Finding velocity from position graphically
QUESTION:
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EXAMPLE 2.4 Finding velocity from position graphically
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EXAMPLE 2.4 Finding velocity from position graphically
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.4 Finding velocity from position graphically
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.4 Finding velocity from position graphically
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.4 Finding velocity from position graphically
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Finding Position from VelocityIf we know the initial position, si, and the instantaneous velocity, vs, as a function of time, t, then the final position is given by
Or, graphically;
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EXAMPLE 2.7 The displacement during a drag race
QUESTION:
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EXAMPLE 2.7 The displacement during a drag race
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EXAMPLE 2.7 The displacement during a drag race
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EXAMPLE 2.7 The displacement during a drag race
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Motion with Constant Acceleration
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Problem-Solving Strategy: Kinematics with constant acceleration
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Problem-Solving Strategy: Kinematics with constant acceleration
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Problem-Solving Strategy: Kinematics with constant acceleration
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Problem-Solving Strategy: Kinematics with constant acceleration
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.14 Friday night football
QUESTION:
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EXAMPLE 2.14 Friday night football
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EXAMPLE 2.14 Friday night football
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EXAMPLE 2.14 Friday night football
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.14 Friday night football
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.14 Friday night football
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EXAMPLE 2.14 Friday night football
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Motion on an Inclined Plane
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EXAMPLE 2.17 Skiing down an incline
QUESTION:
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EXAMPLE 2.17 Skiing down an incline
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EXAMPLE 2.17 Skiing down an incline
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EXAMPLE 2.17 Skiing down an incline
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.17 Skiing down an incline
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Tactics: Interpreting graphical representations of motion
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Instantaneous Acceleration
The instantaneous acceleration as at a specific instant of time t is given by the derivative of the velocity
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Finding Velocity from the AccelerationIf we know the initial velocity, vis, and the instantaneous acceleration, as, as a function of time, t, then the final velocity is given by
Or, graphically,
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EXAMPLE 2.21 Finding velocity from acceleration
QUESTION:
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EXAMPLE 2.21 Finding velocity from acceleration
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Chapter 2. Summary SlidesChapter 2. Summary Slides
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General Principles
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General Principles
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Important Concepts
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Important Concepts
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Applications
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Applications
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Chapter 2. Clicker QuestionsChapter 2. Clicker Questions
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Which position-versus-time graph represents the motion shown in the motion diagram?
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Which position-versus-time graph represents the motion shown in the motion diagram?
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Which velocity-versus-time graph goes with the position-versus-time graph on the left?
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Which velocity-versus-time graph goes with the position-versus-time graph on the left?
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Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particle’s position at ti = 0 s is xi = –10 m.
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Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particle’s position at ti = 0 s is xi = –10 m.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Which velocity-versus-time graph or graphs goes with this acceleration-versus-time graph? The particle is initially moving to the right and eventually to the left.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Which velocity-versus-time graph or graphs goes with this acceleration-versus-time graph? The particle is initially moving to the right and eventually to the left.
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The ball rolls up the ramp, then back down. Which is the correct acceleration graph?
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The ball rolls up the ramp, then back down. Which is the correct acceleration graph?
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Rank in order, from largest to smallest, the accelerations a
A– a
C at
points A – C.
A) aA > a
B > a
C
B) aA > a
C > a
B
C) aB > a
A > a
C
D) a
C > a
A > a
B
E) aC > aB > aA
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
A) aA > a
B > a
C
B) aA > a
C > a
B
C) aB > a
A > a
C
D) a
C > a
A > a
B
E) aC > aB > aA
Rank in order, from largest to smallest, the accelerations a
A– a
C at
points A – C.