1. Graphing data

2. Objectives
Convert quantities from one unit to another using appropriate conversion factors.
Identify the independent and dependent variables in an experiment.
Evaluate and make inferences from data represented graphically, and communicate valid conclusions supported by the data.
Express and manipulate relationships among physical variables quantitatively using graphs.
Assessments for this objectives appear as follows:
First objective: slide 3; Second objective: slide 4; Third objective: slide 5 and slide 26; Fourth objective: slide 26

3. Assessment Which of the following unit conversions is correct? A. B.

4. Assessment
A marble was dropped from varying initial heights and its final speed measured.
Identify the independent and dependent variables in this experiment.

5. Assessment As the marble falls farther, its speed: decreases increases
remains constant

6. Physics terms conversion factor variable independent variable
model

7. Equations
speed:

8. Converting units
When solving physics problems, you may need to convert units to make them consistent.
Click on this unit conversion calculator on page 58.

9. Converting units
Here are some examples of conversion factors for length.

10. Converting units
To convert from one unit to another, multiply by the appropriate conversion factor.
Pick the conversion factor that lets you cancel the unit you don’t want, and end up with the unit you want.

11. Test your knowledge
Use the conversion factor shown at right to convert 12 inches to centimeters.

12. Test your knowledge
Use the conversion factor shown at right to convert 12 inches to centimeters.
Flipping the conversion factor upside down lets you cancel the unit you don’t want, and end up with the unit you want.

13. Displaying data
Data can be displayed in tables, graphs and charts. In this lesson you will use all three methods.

14. Data in tables Work with a partner to answer these questions:
How is temperature changing over time?
Predict the temperature at t = 50 seconds.

15. The same data in a graph
Work with a partner to answer these questions:
How is temperature changing over time?
Predict the temperature at t = 50 seconds.
temperature °C
Point out that the how the data is displayed can make it easier to recognize trends and make predictions.
time (s)

16. The same data in a graph
Work with a partner to answer these questions:
How is temperature changing over time?
Predict the temperature at t = 50 seconds.
temperature °C
It is decreasing.
It will be roughly 10°C
Point out that the how the data is displayed can make it easier to recognize trends and make predictions.
time (s)

17. About variables
An experimenter may choose to manipulate one variable (the independent variable) to determine how this will affect another variable (the dependent variable).

18. About variables
This experimenter chose to record speed over a certain time interval.

19. About variables
The independent variable is time and is plotted on the x-axis.
The dependent variable is speed and is plotted on the y-axis.
Dependent variable
Independent variable

20. Test your knowledge
Louise measures the air temperature at noon every day for an entire year. She wants to graph her findings.
Which is the independent variable and which is the dependent variable?
Independent variable: ______________
Dependent variable: _______________
Air Temperature
Day of the Year

21. Test your knowledge
Louise measures the air temperature at noon every day for an entire year. She wants to graph her findings.
Which is the independent variable and which is the dependent variable?
Independent variable: ______________
Dependent variable: _______________
day of the year
air temperature
Air Temperature
Day of the Year

22. Scales
It is important to read the scales on the x- and y-axes when interpreting a graph. Which of these graphs shows a greater change in energy?

23. Scales
It is important to read the scales on the x- and y-axes when interpreting a graph. Which of these graphs shows a greater change in energy?
They are the same.

24. Visualizing data
Plotting data can reveal mathematical relationships between variables. Equations can be found to fit the graphs and model the relationships.

25. Exploring the ideas
In Investigation 2B you will find the equations needed to fit a set of graphs.
Click the interactive simulation, page 61.

26. Test your knowledge The equation for speed is:
If you hold the distance d constant and graph speed vs. time, what kind of relationship will you get?
linear
parabolic
inverse

27. Test your knowledge The equation for speed is:
If you hold the distance d constant and graph speed vs. time, what kind of relationship will you get?
linear
parabolic
inverse

28. Visualizing data
Plotting data can reveal mathematical relationships between variables.
No relationship
between x and y

29. Assessment Which of the following unit conversions is correct? A. B.

30. Assessment Which of the following unit conversions is correct? A. B.
If this is a final answer, round to the correct number of significant figures.

31. Assessment
A marble was dropped from varying initial heights and its final speed measured.
Identify the independent and dependent variables in this experiment.

32. Assessment
A marble was dropped from varying initial heights and its final speed measured.
Identify the independent and dependent variables in this experiment.
dependent variable: speed (m/s)
independent variable: height (m)

33. Assessment As the marble falls farther, its speed: decreases increases
remains constant

34. Assessment As the marble falls farther, its speed: decreases increases
remains constant