1. Chapter 2 Section 2:1 Page 39

2. Chapter 2 One Dimensional Motion To simplify the concept of motion, we will first consider motion that takes place in one direction. One example is the motion of a commuter train on a straight track. To measure motion, you must choose a frame of reference. A frame of reference is a system for specifying the precise location of objects in space and time.

3. Choose frame of reference 01234567-2-3-4-5-6-7-8-9

4. Chapter 2 Displacement  x = x f – x i displacement = final position – initial position Displacement is a change in position. Displacement is not always equal to the distance traveled. The SI unit of displacement is the meter, m.

5. Chapter 2 Positive and Negative Displacements Section 1 Displacement and Velocity

6. Chapter 2 Average Velocity Average velocity is the total displacement divided by the time interval during which the displacement occurred. In SI, the unit of velocity is meters per second, abbreviated as m/s. Average velocity = change in position change in time displacement time interval = v avg = ∆x ∆t = x f –x i t f - t i

7. Chapter 2 Velocity and Speed Velocity describes motion with both a direction and a numerical value (a magnitude). Average speed is equal to the total distance traveled divided by the time interval. Speed has no direction, only magnitude. distance traveled time interval average speed =

8. Assignments Practice A page 44: 1,3,4,5 Given: Asked: Formula: Substitute: Answer with units

9. Interpreting Velocity Graphically v avg = ∆x ∆t x f –x i t f - t i = rise run slope = = change in vertical coordinates change in horizontal coord Time (s) Displacement (m)

10. Chapter 2 Interpreting Velocity Graphically, continued The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph. The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path.

11. Velocity from Graph Velocity not Constant Time (s ) Displacement (m)

12. Assignments Practice A Page 44: 1,3,4,5 Section Review Page 47 Problems 1, 3, 4, 6

13. Acceleration and Motion Acceleration is the change in velocity divided by the time it takes for the change to occur. Acceleration has a magnitude and a direction. If an object speeds up, the acceleration is in the direction that the object is moving. If an object slows down, the acceleration is opposite to the direction that the object is moving.

14. Acceleration Equations Average Acceleration (m/s 2 ) = ∆ v ∆t a avg = Change in velocity (m/s) time (s) v f -_v i t f - t i = f denotes final I denotes initial (starting) v f final velocity v i initial velocity t f final time t i initial time ∆t is always +

15. Practice B page 49 1-3 Given: Asked: Formula: Substitute: Do the math: Answer: ∆ v ∆t a = v f -_v i t f - t i =

16. Assignment Practice A Page 44: 1,3.4.5 Section Review Page 47 Problems 1, 3-6 Practice B Page 49 Problems 1-3

17. Practice B page 49: 1 Given: Asked: Formula: Substitute: Do the math: Answer: ∆ v ∆t a = v f -_v i t f - t i =

18. Practice B page 49: 2 Given: Asked: Formula: Substitute: Do the math: Answer: ∆ v ∆t a = v f -_v i t f - t i =

19. Practice B page 49: 3 Given: Asked: Formula: Substitute: Do the math: Answer: ∆ v ∆t a = v f -_v i t f - t i =

20. Acceleration Direction and Magnitude Page 50

21. Chapter 2 Changes in Velocity, continued Consider a train moving to the right, so that the displacement and the velocity are positive. The slope of the velocity-time graph is the acceleration. –When the velocity in the positive direction is increasing, the acceleration is positive, as at A. –When the velocity is constant, there is no acceleration, as at B. –When the velocity in the positive direction is decreasing, the acceleration is negative, as at C.

22. Positive Acceleration An airliner starts at rest and then reaches a speed (velocity) of 80 m/s in 20 s. What is its acceleration? a = v f -_v i t f - t i a = 80 m/s -_0 m/s 20s - 0s 80 m/s 20s a = 4 m/s 2

23. Negative Acceleration A skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2s. What is her acceleration? a = v f -_v i t f - t i a = 0 m/s -_3 m/s 2s - 0s - 3 m/s 2s a =- 1.5 m/s 2

24. Chapter 2 Velocity and Acceleration (P51)

25. Displacement with constant acceleration v avg = ∆x ∆t v avg = v f + v i 2 ∆x ∆t v f + v i 2 ∆x = ½(v f +v i ) ∆t =

26. Practice C page 53, 1-4 Given: Asked: Formula: ∆x = ½(v f +v i ) ∆t Substitute: Do the math: Answer:

27. Assignments Practice A Page 44: 1,3.4.5 Section Review Page 47 Problems 1, 3-6 Practice B Page 49 Problems 1-3 Practice C page 53, 1-4

28. Velocity with constant acceleration Final Velocity (p54) ∆ v ∆t a = v f -_v i ∆t = a ∆t = v f - v i v f = v i + a ∆t

29. Velocity with constant acceleration Displacement from acceleration and initial velocity (p54) ∆x = ½(v f + v i ) ∆t derived previously ∆x = ½(v i + a ∆t + v i ) ∆t ∆x = ½(2v i + a ∆t) ∆t ∆x = v i ∆t + 1/2a ∆t 2 v f = v i + a ∆t derived previously

30. Practice D page 55, 1-4 Given: Asked: Formula: ∆x = v i ∆t + 1/2a ∆t 2 Substitute: Do the math: Answer: v f = v i + a ∆t

31. Assignments Practice A Page 44: 1,3.4.5 Section Review Page 47 Problems 1, 3-6 Practice B Page 49 Problems 1-3 Practice C page 53, 1-4 Practice D page 55, 1-4

32. Final Velocity from V i and ∆x (P56) ∆x = ½(v f +v i ) ∆t Derived Previously 2 ∆x = (v f +v i ) ∆t = ∆t _2 ∆x_ (v f +v i ) v f = v i + a ∆t Derived Previously v f = v i + a _2 ∆x_ (v f +v i )

33. Derivation (cont) v f = v i + a _2 ∆x_ (v f +v i ) v f - v i = a _2 ∆x_ (v f +v i ) (v f - v i )(v f +v i ) = a 2 ∆x v f 2 - v i 2 = 2a∆x v f 2 = 2a ∆x +v i 2

34. Assignments Practice A Page 44: 1,3.4.5 Section Review Page 47 Problems 1, 3-6 Practice B Page 49 Problems 1-3 Practice C page 53, 1-4 Practice D page 55, 1-4 Practice E page 57-58 (2a,b,c, 3,a,b,4,5)

35. Sample E page 57-58 (2-5) Given Asked Formula Substitute Do the math, do the math also on the units Answer – compare units (dimensional analysis)

36. Schedule Tuesday 9/4 Page 44 Wednesday 9/5 Page 47 Thursday 9/6 Page49 Friday 9/7 Page 53 Monday 9/10 Page 55 Tuesday 9/11 Page 57-58 Wednesday 9/12 Section Review P59:4-6 Thursday 9/13 Falling Objects (P64&65) Friday 9/14 Problems P64:1,3 P65:4,5,6 Monday 9/17 Lab Tuesday 9/18 Chapter Review Wednesday 9/19 Chapter 2 Test

37. Equations for Constantly Accelerated Straight-Line Motion

38. Assignments Practice A Page 44: 1,3.4.5 Section Review Page 47 Problems 1, 3-6 Practice B Page 49 Problems 1-3 Practice C page 53, 1-4 Practice D page 55, 1-4 Sample E page 57-58 (2-5) Section Review P 59: 4-6

39. Page 59 Problem 5

40. Free Fall (p61) Free fall- a situation in which the only force on the object is the force of gravity. The force of gravity produces a constant acceleration. g g=-9.81 m/s 2 Free fall can be up – see page 61

41. Assignments Practice A Page 44: 1,3.4.5 Section Review Page 47 Problems 1, 3-6 Practice B Page 49 Problems 1-3 Practice C page 53, 1-4 Practice D page 55, 1-4 Sample E page 57-58 (2-5) Section Review P 59: 4-6 Sample F page 64: 1,3 Section Review page 65: 4-6 Chapter Review page 68- :3,8,17,22,31,37,46

42. Problem Solving Given: Asked: Formula: Substitute Answer with Units