Motion in One Dimension

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Motion in One Dimension

  1. 1. Motion in One Dimension Paul A. Tipler • Gene Mosca Physics for Scientists and Engineers, Fifth Edition W. H. Freeman & Company, 2004 Chapter 2: Motion in One Dimension
  2. 9. Motion in One Dimension <ul><li>Displacement and Average Velocity </li></ul><ul><li>Instantaneous Velocity </li></ul><ul><li>Acceleration (Average & Instantaneous) </li></ul><ul><li>Motion With Constant Acceleration </li></ul><ul><ul><li>Free Fall </li></ul></ul><ul><li>Velocity & Displacement By Integration </li></ul>
  3. 11. Usain Bolt to decide on double bid at last minute Posted Tue Jul 22, 2008 9:44am AEST http://www.abc.net.au/news/stories/2008/07/22/2310466.htm?site=olympics/2008 Athletics: Lightning Bolt breaks 100m record Usain Bolt, of Jamaica, kneels by the timing board showing his new world record of 9.72 seconds in the 100m at the Reebok Grand Prix athletics meet on Sunday. Photo by AP. Otago DAily Times http://www.odt.co.nz/sport/athletics/8073/athletics-lightning-bolt-breaks-100m-record
  4. 12. http://www.telegraph.co.uk/sport/othersports/olympics/2570560/Usain-Bolt-smashes-100-metres-field-in-Beijing-Olympics-final---Olympics.html Usain Bolt smashes 100 metres field and world record in Beijing Olympics final Usain Bolt of Jamaica became the first man in history to run under 9.7 sec for the 100 metres and he did it easing down. By Mark Reason in Beijing Last Updated: 12:01AM BST 17 Aug 2008 Streets ahead: Usain Bolt of Jamaica demolishes the 100m field in the Bird's Nest stadium to become the fastest man on the planet Photo: AP http:// www.telegraph.co.uk / telegraph /multimedia/archive/00791/sofast117ap_791625c. jpg
  5. 13. http:// www.telegraph.co.uk /sport/ othersports / olympics /2594750/Beijing-Hall- of - fame - pain - and - shame.html Usain Bolt smashed the world records in the 100m, 200m and men's 4x100 relay in unique style Picture: Getty Images http://www.telegraph.co.uk/telegraph/multimedia/archive/00794/usainboltGETTY_794021i.jpg
  6. 14. arXiv.org  >  physics  > arXiv:0809.0209v2 Physics > Popular Physics <ul><li>Velocity dispersions in a cluster of stars: How fast could Usain Bolt have run? </li></ul><ul><li>H. K. Eriksen ,  J . R. Kristiansen ,  O . Langangen ,  I . K. Wehus </li></ul><ul><li>(Submitted on 1 Sep 2008 ( v1 ), last revised 2 Sep 2008 (this version, v2)) </li></ul><ul><li>Since that very memorable day at the Beijing 2008 Olympics, a big question on every sports commentator's mind has been “What would the 100 meter dash world record have been, had Usain Bolt not celebrated at the end of his race?“ </li></ul><ul><li>Glen Mills, Bolt's coach suggested at a recent press conference that the time could have been 9.52 seconds or better. We revisit this question by measuring Bolt's position as a function of time using footage of the run, and then extrapolate into the last two seconds based on two different assumptions. </li></ul><ul><li>First, we conservatively assume that Bolt could have maintained Richard Thompson's, the runner-up, acceleration during the end of the race. </li></ul><ul><li>Second, based on the race development prior to the celebration, we assume that he could also have kept an acceleration of 0.5 m/s 2 higher than Thompson. </li></ul><ul><li>In these two cases, we find that the new world record would have been 9.61 ± 0.04 and 9.55 ± 0.04 seconds, respectively, where the uncertainties denote 95% statistical errors. </li></ul>
  7. 15. Displacement and Average Velocity
  8. 16. Frame of reference
  9. 17. Displacement
  10. 18. Displacement
  11. 19. Positive displacement
  12. 20. Negative displacement
  13. 21. Average velocity
  14. 22. Graph x vs. t Geometric Interpretation of v av
  15. 23. Geometric Interpretation of v av
  16. 24. Graph x vs. t Geometric Interpretation of v av
  17. 25. Example 2.1 [Tipler]
  18. 26. Example 2.2 [Tipler]
  19. 27. Example 2.3 [Tipler]
  20. 28. Instantaneous Velocity
  21. 29. Graph x vs. t Geometric Interpretation of v
  22. 32. Obtaining velocity from x vs. t graphs
  23. 33. Obtaining velocity from x vs. t graphs
  24. 34. Obtaining velocity from x vs. t graphs
  25. 35. Obtaining velocity from x vs. t graphs
  26. 36. Example 2.1 [Young-Freedman]
  27. 37. Obtaining velocity from x vs. t graphs
  28. 38. Obtaining velocity from x vs. t graphs
  29. 39. Example 2.5 [Tipler]
  30. 40. Example 2.6 [Tipler]
  31. 41. Evalúe su comprensión. Gráfica x vs. t
  32. 42. Relative velocity
  33. 43. <ul><li>Displacement & Average Velocity </li></ul><ul><li>Instantaneous Velocity </li></ul><ul><li>Problems </li></ul><ul><ul><li>Tipler </li></ul></ul><ul><ul><li>Young -Freedman </li></ul></ul><ul><ul><li>Selected Problems </li></ul></ul>
  34. 44. Acceleration (Average & Instantaneous)
  35. 45. Average acceleration
  36. 46. Average acceleration
  37. 47. Example 2.7 [Tipler]
  38. 48. Example 2.2 [Young-Freedman]
  39. 49. Instantaneous acceleration
  40. 50. Obtaining acceleration from v vs. t graphs
  41. 52. Obtaining acceleration from v vs. t graphs
  42. 53. Obtaining acceleration from v vs. t graphs
  43. 54. Obtaining acceleration from x vs. t graphs
  44. 55. Obtaining acceleration from x vs. t graphs
  45. 56. <ul><li>Acceleration (Average & Instantaneous) </li></ul><ul><li>Problems </li></ul><ul><ul><li>Tipler </li></ul></ul><ul><ul><li>Young -Freedman </li></ul></ul><ul><ul><li>Selected Problems </li></ul></ul>
  46. 57. Motion With Constant Acceleration
  47. 58. Motion with constant acceleration
  48. 66. Example 2.10 / 2.11 [Tipler]
  49. 67. Example 2.12 [Tipler]
  50. 68. Stanford Linear Accelerator
  51. 69. Large Hadron Collider
  52. 70. Example 2.17 / 2.18 [Tipler]
  53. 71. Example 2.4 [Young-Freedman]
  54. 72. Example 2.15 / 2.16[Tipler]
  55. 73. Example 2.15 / 2.16 [Tipler]
  56. 74. Example 2.5 [Young-Freedman]
  57. 75. <ul><li>Motion With Constant Acceleration </li></ul><ul><li>Problems </li></ul><ul><ul><li>Tipler </li></ul></ul><ul><ul><li>Young -Freedman </li></ul></ul><ul><ul><li>Selected Problems </li></ul></ul>
  58. 76. Free Fall
  59. 77. Free fall
  60. 79. Object in free fall <ul><li>MichaelMaggs , 20 October 2007 </li></ul><ul><li>Image:Falling ball.jpg </li></ul><ul><li>From Wikipedia, the free encyclopedia </li></ul><ul><ul><li>http:// en.wikipedia.org / wiki / Image:Falling_ball.jpg </li></ul></ul><ul><ul><li>An initially-stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. </li></ul></ul><ul><ul><li>This image, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 1/20th of a second the ball drops one unit of distance (here, a unit is about 12 mm); by 2/20ths it has dropped at total of 4 units; by 3/20ths, 9 units and so on. </li></ul></ul><ul><ul><li>To take the picture, the ball - about the size of a tennis ball - was suspended by a short length of black thread and was released as the shutter was opened and the flash triggered. The shutter remained open for the whole of the half-second period, during which time the flash fired multiple times to capture the ball at 1/20 second intervals. </li></ul></ul>
  61. 81. Example 2.6 [Young-Freedman]
  62. 82. Example 2.9 [Tipler]
  63. 83. Example 2.9 [Tipler]
  64. 84. Example 2.7 [Young-Freedman]
  65. 85. Example 2.7 [Young-Freedman]
  66. 87. <ul><li>Free Fall </li></ul><ul><li>Problems </li></ul><ul><ul><li>Tipler </li></ul></ul><ul><ul><li>Young -Freedman </li></ul></ul><ul><ul><li>Selected Problems </li></ul></ul>
  67. 88. Velocity and Position by Integration
  68. 97. Example 2.19 [Tipler]
  69. 98. Example 2.19 [Tipler]
  70. 100. Position by integration
  71. 101. Example 2.9 [Young-Freedman]
  72. 102. <ul><li>Integration </li></ul><ul><li>Problems </li></ul><ul><ul><li>Tipler </li></ul></ul><ul><ul><li>Young -Freedman </li></ul></ul><ul><ul><li>Selected Problems </li></ul></ul>

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