mathematical models chapter 2 by mr. leavings. and just what are we going to learn? construct a...
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And just what are we going to LEARN?
Construct a speed vs. distance graphUse graphs to make predictionsDetermine the slope of a line (gives you V!)Distinguish between speed and accelerationCalculate acceleration from a formulaCalculate acceleration from the slope of a speed vs. time graph
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?
Scientific Models
Scientific Model: a model that shows how each variable relates to
one another
3 Types:
Physical Models Conceptual Models Graphical Models
Conceptual Models
These types of models are descriptive. We use them to describe how something works.
Graphical Models
Graphical Models: use graphs to show the relationship between the variable on the x axis and the variable on the y axis.
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!
Predicting from Graphs
The purpose of making a graph is to organize your data into a model so that you can make predictions.
Position- a comparison from starting point, includes direction.
Distance- an interval of length without regard to direction.
Position and Distance
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.
Determining Speed
Acceleration = the rate of change in speed of an object
= change in speed
change in time
Acceleration
Acceleration
What units are acceleration in? Lets find out:
Acceleration= change in speed
change in time
Acceleration =
Meters/second___________
Second
Meters/Second2
Acceleration
∆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.
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