1. Chapter 2
Mathematical Models

2. Model
Scientific Model: A method of representing the relationship between variables.
Physical Model: Ones that we can look at, touch, feel, and take measurements from.
Conceptual Model: A written description or diagram based on ideas that are used to describe how a process or object works.
Graphical Model: Shows the relationship between two variables on a graph so that the relationship can easily be seen and understood.

3. Graph
A visual representation making the interpretation and prediction of data easier.

4. Graph Parts Title Label Units Scale Data
Regional Sales Per Quarter
Title
Label
Units
Scale
Data
Key/Legend (if more than one data set is on the same graph)
Sales (x$10,000)
Time (Quarter Year)

5. Graphs (3) Independent Variable: The variable in an experiment that is
manipulated by the experimenter
and that causes changes in the
dependent variable in the
experiment; this variable is plotted on the x-axis of a graph.
y-axis for the independent variable
Dependent Variable: The variable in an experiment that changes in response to choices made by an experimenter; this is plotted on the y-axis of a graph
x-axis for the independent variable

8. Graph Relationships Strong relationship Weak relationship Trial 3
Inverse relationship
No relationship

9. Position
Position means where something is compared with where it started, including direction.
Position is not the same as distance.

10. Velocity A change in position over time.
In a straight line in one direction it is the same as speed with a direction.

11. Slope Rise Run Slope = Distance Time Slope = Slope = Speed
Distance (m)
Slope =
Rise
Run
Slope =
Distance
Time
Slope = Speed

12. Slope (2)
Instantaneous speed: The speed the speed of an object at a specific point in its journey.
The slope of the line at that point.
Average Speed: the total distance traveled divided by the total time

13. Acceleration
Acceleration is the rate of change in the velocity of an object.
Rate of change means the ratio of the amount of change divided by how much time it took to change.
Deceleration: When the acceleration is negative it is called deceleration.
Changing directions is also accelerating.

14. Acceleration (2)
What does it mean that an object accelerates at 9.8 m/s/s, or 9.8 m/s2?
Time (s)
Velocity
(m/s)
What would the velocity be at 9 seconds?

15. Acceleration (3)
What does it mean that an object accelerates at -4.0 m/s/s, or -4.0 m/s2?
Time (s)
Velocity
(m/s)
What would the velocity be at 9 seconds?
Is that even possible?

16. Acceleration (4)
What does it mean that an object accelerates at 8/5 m/s/s, or 8/5 m/s2?
Time (s)
/ / / / / / / /5
Velocity
(m/s)
What would the velocity be at 9 seconds?