Chapter 2 Mathematical Models

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.

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

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)

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

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

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

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

Slope Rise Run Slope = Distance Time Slope = Slope = Speed Distance (m) 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 Slope = Rise Run Slope = Distance Time Slope = Speed

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

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.

Acceleration (2) What does it mean that an object accelerates at 9.8 m/s/s, or 9.8 m/s2? 0 1 2 3 4 5 6 7 8 Time (s) 0 9.8 19.6 29.4 39.2 49.0 58.8 68.6 78.4 Velocity (m/s) What would the velocity be at 9 seconds?

Acceleration (3) What does it mean that an object accelerates at -4.0 m/s/s, or -4.0 m/s2? 0 1 2 3 4 5 6 7 8 Time (s) 32 28 24 20 16 12 8 4 0 Velocity (m/s) What would the velocity be at 9 seconds? Is that even possible?

Acceleration (4) What does it mean that an object accelerates at 8/5 m/s/s, or 8/5 m/s2? 0 1 2 3 4 5 6 7 8 Time (s) 0 8/5 16/5 24/5 32/5 40/5 48/5 56/5 62/5 Velocity (m/s) What would the velocity be at 9 seconds?