Chapter 2: Motion in One Dimension

1. Chapter 2:Motion in One Dimension

2. How to solve any physics problem: DUFAS Diagram or draw a picture Units and variables labeled Formulas written and ready to use Algebra shown with numbers and units Solution boxed with correct units and sig. figs.

3. There are three ways to describe motion. • Displacement • Velocity • Acceleration

4. Displacement and Velocity

5. First off, to describe motion, we must specify position.

6. But to specify position, we need to relate it to another known location You are here You want to be here

7. For motion in one dimension, it is convenient to use the x-axis. From this concept, we can create a number line.

8. 0 +

9. 0 -

10. Displacement • Displacement of an object - the change of position of the object • NOTE: displacement is not always equal to the distance traveled. 0

11. Displacement (x) • x = xf – xi • Where x = displacement xf = final position xi = initial position 0

12. Example What is the displacement if a car moves from an initial position of 10 m to a final position of 80 m? x =80 m – 10 m = 70 m

13. Example What is the displacement if a car moves from an initial position of 80 m to a final position of 20 m? x =20 m – 80 m = -60 m Note: the negative sign indicates the direction of displacement.

14. Distance and Displacement Every morning you drive 4 miles from home to NPHS and then come back home at night using the same route. What is the best statement describing your daily trip? (Assume you do not move far while at NPHS) • Your displacement is 0, distance traveled is 8 mi • Your displacement is 8 mi, distance traveled is 0 • Your displacement is 0, distance traveled is 0 • Your displacement is 8 mi, distance traveled is 8 mi

15. VELOCITY – change in displacement over time. • Average velocity :

16. Units for velocity • The SI unit for velocity is m/s; however, a velocity can be given in other units such as: • Km/sec or km/hr or mi/hr • When calculating the velocity, be sure all your units match. If they don’t, you need to convert.

17. Example: It takes 6.0 hours to drive to San Francisco from Newbury Park if driving at 65 mi/hr. How far is the trip? Newbury Park San Fransisco t = 6.0 hrs v = 65 mi/hrs Dx = ?

18. Example: The United States is 4,300 km wide. How long (in hours) would it take to drive across the country if someone were to drive at a steady 22 m/s the whole way? Dx = 4,300 km v = 22 m/s t = ?

19. Speed vs. Velocity • Speed is a SCALAR meaning it is only a number, direction doesn’t matter. • Speed = (total distance)/(time) • Velocity is a VECTOR meaning it has a number (magnitude) and direction. Direction matters. • Velocity = (displacement)/(time) • http://www.youtube.com/watch?v=GKQdkS0qG3g

20. Acceleration Acceleration – rate of change in velocity over time.

21. Units of Acceleration

22. Example: A car is initially coasting up hill at 8.5 m/s. 4.75 seconds later, the car is now rolling backwards at 2.6 m/s down the same hill. What is the car’s acceleration during this time period? + Vo - Vf Vo = 8.5 m/s t = 4.75 sec Vf = - 2.6 m/s

23. Another way to describe motion is to graph displacement and velocity as a function of time it

24. GLX Time! Plug motion sensor into one of the ports at the top (line the groove up) A position vs time graph should automatically open The “Play” button lets you start and stop data taking. There is no need to erase your graph. Just hit “Play” again to take more data and overwrite your old graph.

25. (1)Create this graph on your GLX using your motion sensor. (2) Describe your motion in your notes. In this case, displacement stays constant with time…there is no movement. Position (m) Time (s)

26. (1)Create this graph on your GLX using your motion sensor. (2) Describe your motion in your notes. Here the object has a low constant velocity in the beginning, and then it changes to a higher constant velocity. Position (m) Time (sec)

27. (1)Create this graph on your GLX using your motion sensor. (2) Describe your motion in your notes. This time the object travels away from the starting point at constant velocity, stops for some amount of time and then travels back to its starting point at constant velocity. Position (m) Time (s)

28. (1)Create this graph on your GLX using your motion sensor. (2) Describe your motion in your notes. Good luck on this one! Velocity is not constant. Velocity (slope) is increasing at a constant rate. Position (m) Time (s)

29. SPEED vs. VELOCITY • Both describe how fast the position is changing with respect to time. • Speed is a SCALAR quantity. It indicates an amount (magnitude), but not direction. • Velocity is a VECTOR quantity. It indicates both an amount (magnitude) and a direction.

30. SLOPE REVIEW

31. SLOPE REVIEW

32. SLOPE REVIEW

33. SLOPE REVIEW

34. SLOPE REVIEW

35. Position (m) Rise Run Time (s)

36. VELOCITY • Velocity is represented by the SLOPE of the curve on a displacement vs. time graph. • In this class, a positive (+) slope indicates a forward direction and a negative (-) slope indicates a backwards direction (return).

38. Use the position graph to answer the following: a. What is the object’s velocity from 10 – 15 seconds? 0 m/s (object is at rest) b. What is the object’s velocity from 15 – 25 seconds? = -4 m/s c. What is the object’s velocity from 0 – 40 seconds? = -1 m/s

39. Consider this trip… Position (m) Time (s)

40. INSTANTANEOUS VELOCITY How fast is the car going at this instant in time? Position (m) Time (s)

41. INSTANTANEOUS VELOCITY The slope of a curve at a given point, is equal to the slope of a tangent line at that point. Position (m) Time (s)

42. INSTANTANEOUS VELOCITY The slope of this line represents instantaneous velocity at the indicated point. Position (m) Time (s)

43. Describing Motion The x(t) graph describes a 1-D motion of a train. What must be true about this motion? • Speeds up all the time • Slows down all the time • Speeds up part of the time • Slows down part of the time • Speeds up & then slows down • Slows down & then speeds up Hint: What is the meaning of the slope of the x(t) graph?

44. Position vs. Time Graphs x A B t t1 The x(t) graph displays motions of two trains A and B on parallel tracks. Which statement is true? • At t1 both trains have the same velocity • At t1 both trains have the same speed • At t1 both trains have the same acceleration • Both trains have the same velocity sometime before t1 • The trains never have the same velocity

45. End Position Graphs

47. Motion can be described with a velocity vs. time graph.

48. Velocity vs. Time 1 constant acceleration Velocity (m/s) constant velocity Time (s)

49. Velocity vs. Time 2 + + velocity Velocity (m/s) 0 velocity 0 Time (s) - velocity -

50. The Slope of Velocity vs. Time Graphs Velocity (m/s) Rise =  v Run =  t Time (s)