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Comprehensive Analysis of Graphs in Motion Physics

Explore the relationship between velocity, acceleration, displacement, and time intervals in a physics graph analysis. Understand key concepts and calculations with detailed examples.

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Comprehensive Analysis of Graphs in Motion Physics

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  1. page 41 #49 and #54

  2. } } a. c. c. d. b. c. a. The greatest velocity is at 48 seconds. b. Velocity is constant from 90 seconds to 108 seconds. c. Acceleration is constant from 0 to 38 seconds and 65 to 83 seconds. The acceleration is zero from 90 to 108 seconds (see b.). d. Greatest acceleration (Greatest Slope) is from 65 to 83 seconds. page 41 #49

  3. 17 17 16 16 12 13 14 4 15 7 8 9 10 11 15 3 4 1 2 3 4 5 6 1 2 5 5 page 41 #54 On a v vs t graph, the area under the curve is the displacement x. For this graph, EACH BLOCK REPRESENTS 10M/S IN 10 SECONDS X = VT X = 10(10) X = 100m EACH BLOCK REPRESENTS 100m From 0 to 60 seconds ( 1 minute) there are ≈ 17 Blocks ∴ 1700 m From 60 to 120 seconds ( second minute) there are ≈ 5 Blocks ∴ 500 m

  4. Page 41 # 50,51

  5. Page 41 # 50 On an x vs t graph, the instantaneous velocity is tangent to the curve at each point. For a time interval v = Δx / Δt for the triangle formed. a. v(10) = Δx = 3 - 0 Δt 10 - 0 v(10) = 0.3 m/s b. v(30) = Δx = 22 - 8 Δt 35 - 25 v(30) = 1.4 m/s

  6. Page 41 # 50 On an x vs t graph, the instantaneous velocity is tangent to the curve at each point. For a time interval v = Δx / Δt for the triangle formed. c. v between t = 0 and t =5 Δx 1.5 - 0 = 0.3 m/s Δt 5 - 0 d. v between t = 25 and t = 30 Δx 16 - 9 = 1.4 m/s Δt 30 - 25 e. v between t = 40 and t =50 Δx 10 - 19.5 = - .95 m/s Δt 50 - 40

  7. Page 41 # 51 a. Velocity Constant t = 0 to t = 18 seconds constant rate of change b. Velocity Greatest t = 27 seconds slope greatest c. Velocity Zero t = 38 seconds slope = 0 flat line d. Positive direction 0 to 38 seconds Negative direction 38 to 50 seconds

  8. Page 41 52, 53

  9. Page 41 52 b. x = v t v = 44 + 37 t = 27 - 16 = 11 x = 40.5(11) = 445.5m 2 a. second gear a = Δv a = 24 - 14 a = 2.5 m/s2 Δt 8 - 4 fourth gear a = Δv a = 44 - 37 a = 0.64 m/s2 Δt 27 - 16

  10. Page 41 53 first gear a = Δv a = 14-0 a = 4 m/s2 Δt 4 - 0 second gear a = Δv a = 24 - 14 a = 2.5 m/s2 Δt 8 - 4 third gear a = Δv a = 37 - 24 a = 3 m/s2 Δt 14 - 9 fourth gear a = Δv a = 44 - 37 a = 0.64 m/s2 Δt 27 - 16 fifth gear a = Δv a = 52 - 44 a = 0.35 m/s2 Δt 50 - 27 first four gears a = Δv a = 44 - 0 a = 1.6 m/s2 Δt 27 - 0

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