1. Starter Vocabulary Term What is distance? What is displacement? What is frame of reference? What is speed? What is velocity? What is acceleration? Definition The length between two points. The change in velocity with respect to time. How fast and object is moving or traveling in a certain direction. The distance an object travels in a specific time. reference point which serves as the origin for an object shortest distance from the initial to the final position

2. Graphing Day 11

3. Questions for Consideration What is a position-time graph? What is a velocity-time graph? How do features on one graph translate into features on the other?

4. What is a Graph? A graph is a visual representation of a relationship between two variables, x and y. A graph consists of two axes called the x (horizontal) and y (vertical) axes. These axes correspond to the variables we are relating. In physical science we will usually give the axes different names, such as Position vs. Time (PT) or Velocity vs. Time (VT). The point where the two axes intersect is called the origin. The origin is also identified as the point (0, 0).

5. Plotting Points on a Graph There are times when you are given a point and will need to find its location on a graph. This process is often referred to as plotting a point and uses the same skills as identifying the coordinates of a point on a graph. The process for plotting a point is shown using an example in the following slides.

6. Step One First, draw a line extending out from the x-axis at the x- coordinate of the point. In our example, this is at 200.

7. Step Two Then, draw a line extending out from the y-axis at the y- coordinate of the point. In our example, this is at 300.

8. Step Three The point where these two lines intersect is at the point we are plotting, (200, 300).

9. Position-Time Graphs Show an object’s position as a function of time. x-axis: time y-axis: position

10. Position-Time Graphs Imagine a ball rolling along a table, illuminated by a strobe light every second. You can plot the ball’s position as a function of time. 0 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s

11. Position-Time Graphs 1234567 8 910 1 2 3 4 5 6 7 8 9 time (s) position (cm)

12. Position-Time Graphs What are the characteristics of this graph? Straight line, upward slope What kind of motion created this graph? Constant speed 1234567 8 9 10 1 2 3 4 5 6 7 8 9 time (s) position (cm)

13. Position-Time Graphs Each type of motion has a characteristic shape on a P-T graph. Constant speed Zero speed (at rest) Accelerating (speeding up) Decelerating (slowing down)

14. Position-Time Graphs Constant speed is represented by a straight segment on the P-T graph. time (s) pos. (m) Constant speed in positive direction. time (s) pos. (m) Constant speed in negative direction.

15. Position-Time Graphs Constant speed is represented by a straight segment on the P-T graph. time (s) pos. (m) A horizontal segment means the object is at rest.

16. Position-Time Graphs Curved segments on the P-T graph mean the object’s speed is changing. time (s) pos. (m) Speeding up in positive direction. time (s) pos. (m) Speeding up in negative direction.

17. Position-Time Graphs Curved segments on the P-T graph mean the object’s speed is changing. time (s) pos. (m) Traveling in positive direction, but slowing down. time (s) pos. (m) Traveling in negative direction, but slowing down.

18. Position-Time Graphs The slope of a P-T graph is equal to the object’s velocity in that segment. time (s) position (m) 10203040 10 20 30 40 50 slope = change in y change in x slope = (30 m – 10 m) (30 s – 0 s) slope = (20 m) (30 s) slope = 0.67 m/s

19. Position-Time Graphs The following P-T graph corresponds to an object moving back and forth along a straight path. Can you describe its movement based on the graph? time (s) position (m) N S

20. Velocity-Time Graphs A velocity-time (V-T) graph shows an object’s velocity as a function of time. A horizontal line = constant velocity. A straight sloped line = constant acceleration. Acceleration = change in velocity over time. Positive slope = positive acceleration. Not necessarily speeding up! Negative slope = negative acceleration. Not necessarily slowing down!

21. Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. time (s) velocity (m/s) N S Object is moving at a constant velocity North.

22. Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. time (s) velocity (m/s) N S Object is moving at a constant velocity South.

23. Velocity-Time Graphs If an object isn’t moving, its velocity is zero. time (s) velocity (m/s) N S Object is at rest

24. Velocity-Time Graphs If the V-T line has a positive slope, the object is undergoing acceleration in positive direction. If v is positive also, object is speeding up. If v is negative, object is slowing down.

25. Velocity-Time Graphs V-T graph has positive slope. time (s) velocity (m/s) N S Positive velocity and positive acceleration: object is speeding up! time (s) velocity (m/s) N S Negative velocity and positive acceleration: object is slowing down.

26. Velocity-Time Graphs If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction. If v is positive, the object is slowing down. If v is negative also, the object is speeding up.

27. Velocity-Time Graphs V-T graph has negative slope. time (s) velocity (m/s) N S Positive velocity and negative acceleration: object is slowing down, time (s) velocity (m/s) N S Negative velocity and negative acceleration: object is speeding up! (in negative direction)

28. Explain-Graphs Directions: Draw and Label the following graph. Makes sure the graph is a good size and neat.

29. Elaborate-Practice Problem: Graphs Directions: Write the following terms/statements. Use these terms to match the intervals/slopes on the graph on the next slide. *Constant Speed *Accelerating *Decelerating *Constant/No Change/Stopped

31. Elaborate-Identifying Graphs Directions: Identify the graphs slope as positive, stationary (constant), changing, or accelerating. Graph 1= Graph 2= Graph 3= Graph 4=

32. Directions: What makes the two graphs different (hint look at the x-axis and y-axis).

33. Teacher Explanation: Graph How to calculate speed and velocity using a graph.

34. Practice Problems: KWFL Graph Problem: What is the velocity of the object at time 2 second?

35. Practice Problems: KWFL Graph Problem: What is the average velocity of the object from time 2 seconds to 3 seconds?

36. Practice problems: KWFL Graph Directions: Using the graph and a KWFL chart answer the following problem. Problem: What is the velocity of the object?

37. Practice problems: KWFL Graph Problem: What is the acceleration at 4 seconds?

38. Practice problems: KWFL Graph Problem: What is the acceleration at initial velocity 12m/s and final velocity 16m/s?

39. Sample Test Questions As a group complete the following 6 problems. These are sample problems you will see on your unit test and on your final exam for this class.

40. Sample Test Questions As a group complete the following 8 problems. These are sample problems you will see on your unit test and on your final exam for this class.

41. Exit Slip On a sticky note, using the word problem tell me what you know, what you want to know, the formula, solve the problem, and tell me what you learned. A car goes from 20 m/s to 30 m/s in 10 seconds. What is its acceleration?