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A Mathematical Model of Motion

A Mathematical Model of Motion. Chapter 5. Position Time Graph. d(m). 60. 50. 40. D. 30. B. 20. C. A. 10. 1. 2. 3. 4. 5. 6. t(s). Describing Motion. Uniform Motion. Uniform Motion means that equal changes occur during successive time intervals. d(m). 60. 50. slope = Δy

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A Mathematical Model of Motion

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  1. A Mathematical Model of Motion Chapter 5

  2. Position Time Graph

  3. d(m) 60 50 40 D 30 B 20 C A 10 1 2 3 4 5 6 t(s) Describing Motion

  4. Uniform Motion Uniform Motion means that equal changes occur during successive time intervals.

  5. d(m) 60 50 slope = Δy Δx slope = rise run rise Δy 40 30 20 run Δx 10 1 2 3 4 5 6 t(s) Slope

  6. slope = Δy Δx v = Δd Δt v = d1 – d0 t1 – t0 Slope of Distance vs Time GraphVelocity

  7. v = d1 – d0 t1 – t0 v = d1 – d0 t1 d1 = d0 + v t1 assume: t0 = 0s

  8. v = 10m/s v = d1 – d0 t1 – t0 d0 = 20m d(m) 60 t1 = 10s 50 40 30 20 10 d1 = d0 + vt1 v = 50m – 20m 5s – 2s 1 2 3 4 5 6 t(s) d1 = 20m + (10m/s)(10s) d1 = 120m

  9. Physics 1-8 Practice Problems:1-12 Pages:85, 87, 89 Section Review Page: 89 Due: 9/24/02

  10. Problem 12 East West d0= -400 d0= 200 d =d0 + vt v = 12m/s v = -15m/s d = -400+ 12t d = 200+ -15t

  11. dtruck = dcar -400+ 12t =200+ -15t 27t =600 t =22s d = 200m+ (-15m/s)(22s) d = 130m

  12. Instantaneous Velocity

  13. v(m/s) Constant 60 50 Faster 40 Slower 30 20 10 1 2 3 4 5 6 t(s) Velocity vs Time Curve

  14. v(m/s) 60 Δd = vΔt 50 v = Δd Δt 40 30 { A = l x w 20 d = v x t 10 1 2 3 4 5 6 t(s) v vs t Area underneath the v vs. t curve is Distance.

  15. a = Δv = v1 –v0 Δt t1 – t0 Acceleration Acceleration is the rate of change of velocity. Acceleration is the slope of the velocity vs. time curve.

  16. Δv=1m/s Δt=8s Δv=5m/s Δt=1.5s

  17. a = Δv Δt a = Δv Δt a = 5m/s 1.5s a = 1m/s 8s a = 3.3m/s² a = 0.13m/s² Find Acceleration from the Graph!! At: t = 1s At: t = 10s

  18. Physics 1-8 Practice Probs:13-26 Pages:93,97,98 Section Review Page: 93 Due: 9/26/02

  19. Finding d from V vs t curve v d =1/2(v- v0)t d = v0t t v0 d =1/2(v- v0)t + v0t

  20. d =1/2(v-v0)t + v0t d =(1/2v)-(1/2v0)t + v0t d =(1/2v)+(1/2v0)t d =1/2(v+v0)t Add Initial Displacement - d0 d = d0 +1/2(v+v0)t

  21. v = v0 +at d = d0 +1/2(v + v0)t d = d0 +1/2(v0 +at + v0)t d = d0 +1/2v0t +1/2v0t+ 1/2at2 d = d0 +v0t +½at2

  22. v = v0 +at (v2+v02) 2a d = d0 + Combine: t = (v-v0)/a d = d0 +1/2(v+v0)t d = d0 +1/2(v+v0) (v-v0)/a v2 = v02 +2a(d-d0)

  23. *Basic Equations* v = v0 + at d = d0 +1/2(v+v0)t d = d0 +v0t +½at2 v2 = v02 +2a(d-d0)

  24. A motorcycle traveling at 16 m/s accelerates at a constant rate of 4.0 m/s2 over 50 m. What is its final velocity? Given: V0 = 16m/s a = 4m/s2 d = 50m v = ? v2 = v02 +2a(d-d0)

  25. 0 v = √656m2/s2 v2 = v02 +2a(d-d0) v2 = (16m/s)2 +2(4m/s2)(50m) v = 25.6m/s

  26. Physics 3-3 Page:112 Problems: 52,54,57 Due: 10/3/06

  27. Lab Results

  28. Physics 1-10 Practice Probs:27-30 Pages:103 Section Review Page: 103 Due: 9/27/02

  29. Falling Acceleration due to Gravity 9.8m/s² 32ft/s² a=g

  30. t=0s,d=0m,v=0m/s t=1s,d=4.9m,v=9.80m/s t=2s,d=19.6m,v=19.6m/s t=3s,d=44.1m,v=29.4m/s

  31. The Scream Ride at Six Flags falls freely for 31m(62m-205ft). How long does it drop and how fast is it going at the bottom? t = √2d/a Known: a = -g = 9.8m/s² d0 = 0m v0 = 0m/s d = 55m Find: t= ? v = ? Equation: d = d0 + v0t + ½at² d = ½at²

  32. t = √2(55m)/9.8m/s² t = 2.51s Equation: v = v0 + at v = at v = (2.51s)(9.8m/s²) v = 24.6m/s = 55mph

  33. Physics 3-4 Pages:112 Problems:66,67,70 Due: 10/10/06

  34. Going straight Up and Down • Slows down going up. • Stops at the top. • Speeds up going down. • Acceleration is constant.

  35. A ball is thrown up at a speed of 20m/s. How high does it go? How long does it take to go up and down? Use up as positive. Known: v0 = 20m/s a = g = -9.8m/s² d0 = 0m v = 0m/s Find: d = ? t =

  36. Eq: v2 = v02 +2a(d-d0) v02 -2a = d 0 = v02 +2a(d) v02 = -2a(d)

  37. (20m/s)2 -2(-9.8m/s2) = d d = 20.4m

  38. v = v0 + at v0 -a 20m/s -(-9.8m/s2) = t = t 0 = v0 + at v0 = -at 2.04s = t 4.08s = t The trip up!

  39. (20m/s)2 -2(-9.8m/s2) = d d = 20.4m

  40. Physics 1-12 Ques: 3-5 Pages:107-8 Ques: 15-19 Page:108 Due: 10/2/02

  41. Physics 1-13 Ques: 6-11 Pages:10 Ques:39-43 Page:111 Due: 10/3/02 Labs Report:10/3/02

  42. Physics 1-14 Ques:44-65 Page:111-114 Due: 10/7/02 Test: 10/8/02

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