1. Foundations of Physical Science
Unit 1: Forces and Motion

2. Chapter 2: Mathematical Models
2.1 Using a Scientific Model to Predict Speed
2.2 Position and Time
2.3 Acceleration

3. Learning Goals Construct a speed vs. distance graph.
Use a graph to make a prediction that can be quantitatively tested.
Calculate the percent error between a measurement and a prediction.
Create and analyze a distance vs. time graph.

4. Learning Goals (continued)
Determine the slope of a line.
Distinguish between linear and nonlinear graphs.
Distinguish between speed and acceleration.
Calculate acceleration from a formula.
Calculate acceleration from the slope of a speed vs. time graph.

5. Vocabulary accelerate acceleration average speed conceptual model
deceleration
dependent variable
free fall
graphical model
gravity
independent variable
physical model
scientific model

6. 2.1 Using a Scientific Model to Predict Speed

7. Can you predict the speed of the car at any point on the ramp?

8. Scientific Models
A model that shows how each variable from an experiment relates to another
Mental models
Physical models
Conceptual models
Graphical models

9. Making a Graphical Model
A graph shows a relationship between the variable on the x-axis and on the y-axis
Graphs use numbers and are considered “mathematical models”
Dependent variable (y-axis)
Independent variable (x-axis)

10. Making a Graphical Model
Decide what to put on the x and y axis.
Make a scale for each axis by counting boxes to fit your largest value.
Plot your points by finding the x value, and drawing a line up until you get to the right y value. Put a dot for each point.

11. Making a Graphical Model
Draw a smooth curve that shows the pattern of the points. Don’t simply connect the dots.
Make a title for your graph.

12. Reading a Graph
Graphs organize your data into a model you can use to make predictions

13. Cause and Effect Relationships
How does one variable effect another?
Graphs are a good way to see whether there is a connection or not

14. Cause and Effect Relationships
Strong
Weak
Inverse

15. 2.2 Position and Time

16. Position
Position (Displacement)- comparison from starting point, includes direction
Distance- interval of length without regard to direction
Position and Distance-not the same thing!

17. Determining Speed from the Slope of a Graph
Slope is the ratio of “rise” (vertical change) to the “run” (horizontal change) of a line.
The rise is determined by finding the height of the triangle shown.
The run is determined by finding the length along the base of the triangle

18. Speed
The slope of the position vs. time graph

19. Instantaneous and Average Speed
Does your speed stay exactly the same during a real trip?
Average Speed: total distance divided by the total time taken
(Initial velocity + Final velocity) 2
Instantaneous Speed: the speed you have at a specific point in your journey; use a position vs. time graph

21. 2.3 Acceleration

22. Acceleration The rate at which velocity/speed changes with time
Change: magnitude, direction or both
a = change of velocity/time interval

23. Force Causes Acceleration
To accelerate an object, it has to be pushed or pulled…a force is applied
Force can be:
Sudden
Steady (i.e. gravity)

24. Acceleration a = (Vf - Vi)/t Vf = Final Velocity Vi = Initial Velocity
t = time

25. Acceleration Slope of the speed-time graph = acceleration
> slope = > acceleration

26. Deceleration (Negative Acceleration)
< slope = < acceleration

27. No Acceleration (Constant Velocity)
Zero acceleration = straight line on the speed-time graph
constant speed = no acceleration

28. Acceleration

29. The Units of Acceleration
Usually done in metric units
Change in speed divided by change in time
5 Meters per second per second (m/s/s)
5 Meters per second squared (m/s2)
The speed is increasing by 5 m/s every second

30. Free Fall A state of fall under the influence of only gravity
Free from air resistance

31. Free Fall
The amount of acceleration is the same for all freely falling objects in the same vicinity
Freely falling objects gain speed at the rate of 9.8 m/s each second (9.8 m/s2)