1. Graphing and Relationships

2. Density of Lead

5. Making Graphs Use the whole page Title – meaningful!
Label Axis : velocity, time, distance
Units : m/s, seconds, meters
Scale – trial and error – you do not always have to start at zero!
Use a ruler – neatness counts

6. Independent variable – the variable you manipulate.
Graph on the horizontal or X axis.
Time is always graphed on X axis (except for some chemistry applications).
Dependent variable – the outcome, result.
Graph on the vertical or Y axis.
Dependent depends on the independent!
Graphs are used to show relationships between the independent and dependent variables!
Slopes mean something!

8. Best fit lines – draw a line or curve so that the data points “hover” around the line.
The data points Do Not have to be on the line.
The distance the data points are off the line shows the amount of error to the actual relationship.
Best fit lines represent the relationships between the independent and dependent variable. That is what we are looking for.
Averaging data does not show how well the data represents the experiment – it is just an average!

9. “Best Fit Lines”

10. Types Relationships:
Graphs show the relationship between the independent and dependent variables.
Direct
Quadratic
Inverse

11. x = independent variable m = slope = rise/run b = y intercept
Direct Relationship
Linear – Straight Line
y = mx + b
y = dependent variable
x = independent variable
m = slope = rise/run
b = y intercept DV IV

12. Quadratic Relationship Exponential – Parabola y = kx2
y = dependent variable
k = constant
x = independent variable DV IV

13. x = independent variable Inverse Square : y =
Inverse Relationship
Hyperbola
xy = k or y =
y = dependent variable
k = constant
x = independent variable
Inverse Square : y =
Note – NOT an indirect relationship! DV IV

14. What type of relationship does this graph show between distance and time?
Direct
Quadratic
Inverse
Indirect

15. What type of equation does this graph show between distance and time?
y = mx + b
y =
y = ax2 + bx + c

16. Solving for the units of a constant (k).
Use this to determine the constant from a graph.
Constant can be the slope or the k in y = kx2 or y = k/x.
Given units :
m = kg (mass = kg)
t = s (time = seconds)
d = m (distance = meters)

17. xxxx (velocity)
Xxxxx (acceleration)
Xxxx (Force)

18. F = k m Substitute units for everything but k Xxxx So
k has units of m/s2 and represents acceleration!

19. Vf2 = vi2 + 2aK
Numbers are not important to units
drop the “2”
k = m
k has units of meters and represents distance!

20. a = k F So k has units of 1/kg or the inverse of kg
K represents 1/mass or the inverse of mass!
To compare the slope to your data, just take the inverse of the mass given in the data!

21. x
So K has units of kg·m/s2
K represents Force!

22. Writing Formulas for Graphs
Write the formula for the relationship in terms of the variables, NOT x and y!

24. Computer gave the constant to be 3.79x106 Speed = k Radius2
Units of k =

25. Computer gives the constant to be 1.45x10-5 Height = k/Radius
Units of k = m2

26. Manipulating Equations
xxx

27. xxx

28. xxx

29. Dimensional Analysis
An equation is possibly correct only if both sides of the equation have the same units of measure.
Given :
Just comparing the Units!
Constants (numbers) do
NOT matter!

31. xxxx
Remember – the numbers
do not matter! They can
just “fly” away!
Yes, I know m + m = 2m
but remember the 2
does not matter!

34. Homework
Graphing