2 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
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 another3 Types:Physical ModelsConceptual ModelsGraphical Models
5 Physical ModelsWe can look, touch, feel and take measurements from themOften constructed in scale
6 Conceptual ModelsThese types of models are descriptive. We use them to describe how something works.
7 Graphical ModelsGraphical Models: use graphs to show the relationship between the variable on the x axis and the variable on the y axis.
8 Graphical ModelsDependent 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 EffectStrong RelationshipWeak Relationship
11 Cause and EffectNo RelationshipInverse Relationship
12 Position and DistancePosition- a comparison from starting point, includes direction.Distance- an interval of length without regard to direction.
13 Determining SpeedSlope 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.