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Kinematics in One Dimension
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.


Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Kinematics in One Dimension
                Topics:
                •    Uniform Motion
                •    Instantaneous Velocity
                •    Finding Position from Velocity
                •    Motion with Constant Acceleration
                •    Free Fall
                •    Motion on an Inclined Plane
                •    Instantaneous Acceleration


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




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




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




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




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




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




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




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 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.
Finding velocity from position graphically

QUESTION:




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




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




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




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




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




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




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

QUESTION:




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




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




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




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




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




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

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Velocity acceleration

  • 1. Kinematics in One Dimension 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. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 2. Kinematics in One Dimension Topics: • Uniform Motion • Instantaneous Velocity • Finding Position from Velocity • Motion with Constant Acceleration • Free Fall • Motion on an Inclined Plane • Instantaneous Acceleration Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 3. Reading Quizzes Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 4. 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.
  • 5. 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.
  • 6. Basic Content and Examples Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 7. 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.
  • 8. Skating with constant velocity Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 9. Skating with constant velocity Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 10. Skating with constant velocity Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 11. Skating with constant velocity Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 12. Skating with constant velocity Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 13. Tactics: Interpreting position-versus-time graphs Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 14. Tactics: Interpreting position-versus-time graphs Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 15. 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 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.
  • 16. Finding velocity from position graphically QUESTION: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 17. Finding velocity from position graphically Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 18. Finding velocity from position graphically Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 19. Finding velocity from position graphically Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 20. Finding velocity from position graphically Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 21. Finding velocity from position graphically Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 22. Tactics: Interpreting graphical representations of motion Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 23. 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.
  • 24. Finding velocity from acceleration QUESTION: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 25. Finding velocity from acceleration Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 26. Summary Slides Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 27. Important Concepts Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 28. Important Concepts Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
  • 29. Applications Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Editor's Notes

  1. Answer: C
  2. IG2.1