1. Ch 5 – A Mathematical Model of Motion  Graphing Motion in One Dimension  Graphing Velocity in One Dimension  Acceleration  Free Fall

2. 5.1 Graphing Motion in One Dimension  Position-Time Graphs  Representing motion with graphs…  Pay attention to axes and units!  Always ask yourself 2 Q’s: What is the object’s motion? What does the slope represent?  Slope = rise / run, or m/s for d-t graphs, which is velocity!  Uniform (constant) motion can be identified by an unchanging slope.

3. 5.1 Graphing Motion in One Dimension (cont.)  Using an Equation to Find Out Where and When  Motion can also be represented by an algebraic equation: v =  d /  t (where  d = d 1 – d o ) v =  d /  t (where  d = d 1 – d o ) Recall that this is the equation for average velocity. You can rearrange this equation to find the position of an object with uniform motion: Recall that this is the equation for average velocity. You can rearrange this equation to find the position of an object with uniform motion: d 1 = d o + vt or d = d o + vt d 1 = d o + vt or d = d o + vt You now have two equations of motion that will allow you to solve where and when for describing the motion of an object traveling uniformly. You now have two equations of motion that will allow you to solve where and when for describing the motion of an object traveling uniformly.

5. 5.2 Graphing Velocity in One Dimension  Instantaneous Velocity  What if the motion is not uniform? (Changing)  The slope is changing so the velocity must be as well – acceleration.  Ask again: What is the object doing? What does the slope represent?  Must use a new technique for slope, but this time it is not constant; you are finding a velocity at a given time – instantaneous velocity!

6. 5.2 Graphing Velocity in One Dimension  Velocity–Time Graphs  Same two questions: What is the object doing? What does the slope represent?  Additionally, you can also find displacement on a V-T graph using a new technique: area under the curve.  The displacement for a given time interval is the area under the curve of a V-T graph. (pg.743)  This leads to a 3 rd Q: What does the area under the curve represent? Displacement

7. Chapter 5 Assignment:  AC+P 1 pp. 108-111  AC # 16,18,19,21  P’s # 27,28,29*,31,34,40 * Use Logger Pro for this problem. * Use Logger Pro for this problem.

8. 5.3 Acceleration  Determining Average Acceleration  Average acceleration is the rate of change of velocity during a time interval.  a =  v /  t (from chapter 3)  Example: A car starts from rest and after 3 seconds is traveling 60 mph. BMW? Porsche? Audi? What is the average acceleration in mph/sec? v =  v 1 – v 0 = 60 mph and  t = t 1 – t 0 = 3 seconds a =  v /  t = 60 mph / 3 sec = 20 mph / sec 20 mph / sec

9. 5.3 Acceleration (cont.)  Constant and Instantaneous Acceleration (again)  Ask again: what does the slope represent? What does the area under the curve represent?  Instantaneous acceleration for a non-constant graph would be done by calculating slope of the tangent! (ex. page 95)  Pay attention to the axes!

10. 5.3 Acceleration (cont.)  Positive and Negative Acceleration  Pay attention to the chosen coordinate system when working with diagrams and graphs. With equations the sign will take care of itself. (Fig 5-13)  Equations and Examples for Objects with Constant Acceleration  Velocity: v = v 0 + at  Displacement  d = d 0 + ½ (v + v 0 )t  d = d 0 + v 0 t + ½ at 2  Final velocity: v 2 = v 0 2 + 2a (d – d 0 )

11. Practice Problem #27 pg. 103

12. 5.4 Free Fall  Acceleration Due to Gravity  Galileo Galilei  Recognized that motion of falling objects could only be understood if the effects of air, water, or whatever medium the object was falling through, were ignored.  a = g = - 9.8 m/s 2 if upward is defined as a positive position change and downward as the negative.  For equations of accelerating objects in free fall, simply substitute ‘a’ with ‘g’ and use as you would with other physics problems.  e.g v = v 0 + gt

13. Practice Problem #31 pg. 106

14. Chapter 5 Assignments:  AC+P 1 pp. 108-111  AC # 16,18,19,21  P’s # 27,28,29*,31,34,40,41,42  AC+P 2 pp. 109-114  AC # 22, 26  P’s # 44, 45, 46, 47, 51, 57, 60*, 63a,b*, 67,69, 72* * = Use Logger Pro for these problems