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Understanding Forces and Motion: Mathematical Models in Integrated Science

In this chapter, students explore the fundamental concepts of forces and motion through mathematical modeling. Key learning goals include constructing speed vs. distance graphs, predicting speed using scientific models, and calculating acceleration using various methods. Students will distinguish between linear and nonlinear graphs, analyze distance vs. time graphs, and calculate percent error between measurements and predictions. Through these activities, learners develop a deeper understanding of how to represent motion mathematically and the relationship between speed, distance, and time in scientific exploration.

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Understanding Forces and Motion: Mathematical Models in Integrated Science

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  1. Unit 1, Chapter 2 Integrated Science

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

  3. Chapter 2 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. • 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.

  4. accelerate acceleration average speed conceptual model deceleration dependent variable free fall graphical model gravity independent variable physical model scientific model Chapter 2 Vocabulary Terms

  5. 2.1 Scientific Models • What is a scientific model? • Physical model? • Conceptual model? • Graphical model?

  6. 2.1 How to make a graph • 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.

  7. 2.1 How to make a graph • Draw a smooth curve that shows the pattern of the points. Don’t simply connect the dots. Make a title for your graph.

  8. Key Question: Can you predict the speed of the car at any point on the ramp? 2.1 Using a Scientific Model to Predict Speed *Read text section 2.1 BEFORE Investigation 2.1

  9. 2.2 Position and Time • Position- a comparison from starting point, includes direction. • Distance- an interval of length without regard to direction.

  10. 2.2 Determining Slope • 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.

  11. Key Question: How do you model the motion of the car? 2.2 Position and Time *Read text section 2.2 BEFORE Investigation 2.2

  12. 2.3 Acceleration • Acceleration = the rate of change in speed of an object • =change in speed • change in time

  13. 2.3 Acceleration

  14. Key Question: How is the speed of the car changing? 2.3 Acceleration *Read text section 2.3 BEFORE Investigation 2.3

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