1. Warm-Up Pick up: A Giancoli book Far back left cabinet 1 of each paper at the front 3 Equation Sheets 1 Kinematics Multiple Choice 1 Kinematics Free Response I will be absent Friday

2. Kinematics: 1-D

3. Today’s Problems Giancoli, Chapter 2 5, 7, 9, 10, 11, 14, 17, 26, 37, 38, 39, 41, 44, 49, 51, 52, 53, 56

4. Kinematics Study of motion 1-Dimensional Horizontal (x) or Vertical (y) 2-Dimensional Horizontal and Vertical simultaneously Next time

5. Linear Motion: Review Distance Length of the path travelled Displacement Overall change in position Displacement   Distance

6. Linear Motion: Review Speed Based on distance Velocity Based on displacement What happens if you travel in a complete circle? Velocity = 0

7. Linear Motion: Velocity Remember: v = x t Where v is velocity x is displacement t is time Unit m/s

8. Linear Motion Example (#5, pg. 42) You are driving home from school steadily at 65 mph for 130 miles. It then begins to rain and you slow to 55 mph. You arrive home after driving 3 hours and 20 minutes. a. How far is you hometown from school? 203 miles b. What was your average speed? 62 mi/h

9. Linear Motion Practice #7 #9 #10 #11

10. Linear Motion Check #7 a. 4.29 m/s b. 0 #9 2.7 min #10 4.43 h 881 km/h #11 55 km/h 0

11. Linear Motion: Acceleration a = Δv = v f – v i t t Where a is acceleration v f is final velocity v i is initial velocity t is time Unit m/s 2 or m/s/s

12. Acceleration Practice #14. Ans: 5.2 s

13. Kinematics: 1-D 3 equations: v = v o + at x = x o + v o t + ½at 2 v 2 = v o 2 + 2a(x - x o ) With constant acceleration Like gravity

14. Equation 1 v = v o + at Where v is velocity v o is initial velocity a is acceleration t is time

15. Equation 1 Derivation a = Δv = v f – v i t t

16. Equation 2 x = x o + v o t + ½at 2 Where x is displacement x o is initial position v o is initial velocity t is time a is acceleration

17. Equation 3 v 2 = v o 2 + 2a(x - x o ) Where v is velocity v o is initial velocity a is acceleration x is displacement x o is initial position

18. Kinematics Summary EquationMissing Variable v = v o + atx x = x o + v o t + ½at 2 v v 2 = v o 2 + 2a(x - x o )t

19. Kinematics Example #26 Ans: a = -3.9 x 10 2 m/s 2, a = 40 g

20. Kinematics Example #37 Ans: t = 1.5 s

21. Kinematics Practice #38 #41

22. Kinematics Check #38 h = 13m #41 5.22 s

23. Kinematics Example #44 Ans: a. +/- 12.8 m/s, b. t = 0.735 s, 3.35 s, c. Up and down

24. Kinematics Practice #49

25. Kinematics Check #49 a. 5.33 s b. 40.2 m/s c. 89.7 m

26. Kinematics and Graphs Let’s examine a Velocity vs. Time graph:

27. Graphs: Important Aspects Labels Title Axes Measurements and units Slope Slope = Δy Δx Δx Area (under the curve)

28. Velocity vs. Time: Slope Slope = Δy = v = m/s = acceleration Δx t s

29. Velocity vs. Time: Area Area = ½ b h = (m/s) s = m = displacement

30. Slope and Area These will be very useful throughout the year Slope Vertical. Horizontal Divide the units Area Base times height Multiply the units

31. Acceleration vs Time AREASLOPE m/s 2 * s = m/sm/s 2 / s = m/s 3 VelocityNot Useful

32. Velocity vs Time AREASLOPE m/s * s = mm/s / s = m/s 2 Displacement Acceleration

33. Displacement vs Time AREASLOPE m * s = m*sm / s = m/s Not Useful Velocity

34. Slope and Area Summary GraphAreaSlope Acceleration (m/s 2 ) vs Time (s)Velocity (m/s)Not Useful (m/s 3 ) Velocity (m/s) vs Time (s)Displacement (m)Acceleration (m/s 2 ) Displacement (m) vs Time (s)Not Useful (m*s)Velocity (m/s) These are definitely not the only cases Ex. Force vs. displacement

35. Instantaneous vs. Average Displacement vs Time (x vs t) graph Average velocity v = Δx t x’s and t’s from graph Instantaneous velocity Velocity at one particular time Line tangent to that time

36. Graphing Example #39

37. Graphing Example #51

38. Graphing Practice #52 #53 #56

39. Graphing Check #52 a. t = 0 to 17 s b. t = 28 s c. t = 38 s d. Both directions #53 a. t = 50 s b. t = 90 s to 107 s c. t = 0 to 20 s, and t = 90 to 107 s d. t = 75 s #56 a. 1700 m b. 500 m