1. Enduring Understanding: A small number of known values and a basic understanding of the patterns involved in motion may reveal a wide variety of kinematic information.

2. Essential Question: How may we symbolically represent kinematic information? What may be gained by doing this?
Essential Question: How do units of measurement affect kinematic understanding?

3. Graphing Basics
A car is driving at an average speed of 30 mph for 2.5 hours.
We may represent this trip symbolically. The goal is to give the potential audience thorough, concise, useful information.

4. Distance for car averaging 30 mph
We will put the information in a clearly labeled chart. Make sure the correct units of measurement are included.
We will put the information in a clearly labeled chart. Make sure the correct units of measurement are included.
Distance for car averaging 30 mph
Time (hours)
Distance (miles)
0.5
1.0
1.5
2.0
2.5

5. Distance for car averaging 30 mph
Fill in the distances for each of the 30 minute intervals.
Distance for car averaging 30 mph
Time (hours)
Distance (miles)
0.5 15
1.0 30
1.5 45
2.0 60
2.5 75

6. To get the full picture of this car trip, what else might you want to know?
What kind of car is it?
Where are you?
Where are you going?

7. Graphs will need to have a valid scale on the vertical and horizontal axis.

8. Both axes must be labeled with units indicated.

9. Graphs symbolically show the relationship between at least two variables. What are the variables in our example?
Distance and Time
Distance is dependent on time. Time is independent of distance.
Explain this statement.
We say that distance is a function of time.

10. We will follow the custom of putting the dependant variable on the vertical axis and the independent variable on the horizontal axis.
It is customary to title graphs as the vertical variable vs the horizontal variable.
For this class, graphs must have a title that follows this custom.

12. Data points are added.

13. Along with a trendline.

14. The slope of a line indicates the change in the vertical variable with respect to the horizontal variable.
In our example, distance vs time.
The slope of a line is often referred to as rise over run. The change in the vertical over the change in the horizontal.
This is useful for calculating the slope.

15. Any two points on the line may be used to find the slope.
Using the first two data points, determine the rise over run.
Δ is a symbol that indicates a change.
So rise over run may be symbolized as
Δ vertical / Δ horizontal

16. Sometimes, this is symbolized as
Δy / Δx or
(y2 – y1)/(x2 – x1)
In our case, we have Δd/Δt
Using the first two data points,
(15 miles – 0 miles)/(0.5 hours – 0.0 hours)
30 miles / hour

17. For a line, the same slope will be found by using any two data points .
Show two examples of this.
How are the units important?
What does the slope of the line represent?
speed
Give an equation for the line.

18. The general equation for a line
y = mx + b
m is the slope
b is the y intercept
For our example
d = 30t
Or d = vt
Look familiar?

19. What kinematic information is revealed by this graph?

20. Trendline is a general term that also applies to curves.
Consider this graph.
What will the trendline look like?

21. So far all of the data points have been on the trendline.
This will not always be the case.
A best fit trendline can be used.

22. Add a best fit trendline to this graph.

23. Find the slope and equation of the trendline.
y = 3x
Why is this particular graph useless for gaining kinematic information?