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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. In this chapter we study kinematics of motion in one dimensionmotion 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

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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 Dimension

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 2. Reading Quizzes

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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 objects speed at that point. B. the objects average velocity at that point. C. the objects instantaneous velocity at that point. D. the objects acceleration at that point. E. the distance traveled by the object to that point.

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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 objects speed at that point. B. the objects average velocity at that point. C. the objects instantaneous velocity at that point. D. the objects acceleration at that point. E. the distance traveled by the object to that point.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The area under a velocity-versus- time graph of an object is A. the objects speed at that point. B. the objects 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.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The area under a velocity-versus- time graph of an object is A. the objects speed at that point. B. the objects 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.

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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.

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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.

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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. theres not enough information to determine which block wins the race.

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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. theres not enough information to determine which block wins the race.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 2. Basic Content and Examples

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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

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Interpreting position-versus-time graphs

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Interpreting position-versus-time graphs

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Instantaneous Velocity Average 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 v avg = Δ s/ Δ t reaches a constant or limiting value. That is, the instantaneous velocity at time t is the average velocity during a time interval Δ t centered on t, as Δt approaches zero.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically QUESTION:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Finding Position from Velocity If we know the initial position, s i, and the instantaneous velocity, v s, as a function of time, t, then the final position is given by Or, graphically;

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.7 The displacement during a drag race QUESTION:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.7 The displacement during a drag race

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.7 The displacement during a drag race

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.7 The displacement during a drag race

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Motion with Constant Acceleration

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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Problem-Solving Strategy: Kinematics with constant acceleration

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Problem-Solving Strategy: Kinematics with constant acceleration

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Problem-Solving Strategy: Kinematics with constant acceleration

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Problem-Solving Strategy: Kinematics with constant acceleration

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football QUESTION:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Motion on an Inclined Plane

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline QUESTION:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Interpreting graphical representations of motion

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Instantaneous Acceleration The instantaneous acceleration a s at a specific instant of time t is given by the derivative of the velocity

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Finding Velocity from the Acceleration If we know the initial velocity, v is, and the instantaneous acceleration, a s, as a function of time, t, then the final velocity is given by Or, graphically,

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.21 Finding velocity from acceleration QUESTION:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.21 Finding velocity from acceleration

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 2. Summary Slides

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 2. Clicker Questions

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which position-versus-time graph represents the motion shown in the motion diagram?

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which position-versus-time graph represents the motion shown in the motion diagram?

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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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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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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particles position at t i = 0 s is x i = –10 m.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particles position at t i = 0 s is x i = –10 m.

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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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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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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The ball rolls up the ramp, then back down. Which is the correct acceleration graph?

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The ball rolls up the ramp, then back down. Which is the correct acceleration graph?

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Rank in order, from largest to smallest, the accelerations a A – a C at points A – C. A) a A > a B > a C B) a A > a C > a B C) a B > a A > a C D) a C > a A > a B E) a C > a B > a A

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A) a A > a B > a C B) a A > a C > a B C) a B > a A > a C D) a C > a A > a B E) a C > a B > a A Rank in order, from largest to smallest, the accelerations a A – a C at points A – C.

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