1. Mathematical Models Chapter 2
By Mr. Leavings

2. And just what are we going to LEARN?
Construct a speed vs. distance graph
Use graphs to make predictions
Determine the slope of a line (gives you V!)
Distinguish between speed and acceleration
Calculate acceleration from a formula
Calculate acceleration from the slope of a speed vs. time graph

3. Mathematical Models Why would you want to make a model?
To answer complicated questions it is easier to break down the problem into more manageable pieces.
Example from your reading: Building a train.
How powerful of a motor do we need?
How strong of brakes to stop the train?
How much fuel to travel the distance required?

4. Scientific Models 3 Types: Physical Models Conceptual Models
Scientific Model: a model that shows how each variable relates to one another
3 Types:
Physical Models
Conceptual Models
Graphical Models

5. Physical Models
We can look, touch, feel and take measurements from them
Often constructed in scale

6. Conceptual Models
These types of models are descriptive. We use them to describe how something works.

7. Graphical Models
Graphical Models: use graphs to show the relationship between the variable on the x axis and the variable on the y axis.

8. Graphical Models
Dependent Variable: the measurement that changes based on the independent variable. Also the data that we measure.
Independent Variable: the measurement that we change to determine its effect on the dependent variable.
Independent variable ALWAYS placed on the x axis!
Dependent Variable is ALWAYS placed on the y axis!

9. Predicting from Graphs
The purpose of making a graph is to organize your data into a model so that you can make predictions.

10. Cause and Effect
Strong Relationship
Weak Relationship

11. Cause and Effect
No Relationship
Inverse Relationship

12. Position and Distance
Position- a comparison from starting point, includes direction.
Distance- an interval of length without regard to direction.

13. Determining Speed
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.

15. Acceleration

16. Acceleration Acceleration = the rate of change in speed of an object
change in time

17. Acceleration What units are acceleration in? Lets find out:
Acceleration= change in speed
change in time
Meters/second
___________
Acceleration =
Second
Meters/Second2

18. Acceleration ∆V = Vf - Vi ∆V
Delta V (∆V) is the change in velocity of an object.
∆V = Vf - Vi
Where Vf stands for the final velocity and Vi stands for the initial velocity.

19. Acceleration
___∆V___ t
a = OR
__Vf - Vi __ t
a =

20. Manipulating the equation
Acceleration
Manipulating the equation
__Vf - Vi __ t
a =
then
__Vf - Vi __ a
t =
and
Vf =
Vi + at
Vi =
Vf - at