8.1 Velocity and Net Change

In this lesson, you will learn to use integration to find velocity or the position function and the net change of a function.

Lesson Objectives

Upon completion of the lesson, you will be able to:

• • Use integration to find the velocity if given acceleration or to find the position function given the velocity.

  • Calculate the net change of a function.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

• 1. YouTube video: Velocity and Acceleration

• 1. YouTube video: Definite Integrals as Net Change

• 1. YouTube video: Displacement and Total Distance Traveled

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

1. 12.5 Distance and Displacement [Pheng Kim Ving]

   1. Note: Read up to and including problems and solutions #4. 2.

2. Acceleration, Velocity and Position [Interactive Mathematics]

• 1. The Definition of the Definite Integral

  2. Note: Scroll down to the section titled Interpretations of the Definite Integral. Read that section only.

3. Section 5.4 Indefinite Integrals and Net Change Theorem - Week 2 Notes

• 1. Note: Read from pdf page 6 to the end of the pdf.

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

• 1. Integral and Net Change [Memphis Educational Computer Connectivity Alliance]

  2. Note: Do problem 1. At the bottom of the page, click on Problems and do the second problem listed.

  3. Applications of the Indefinite Integral [Interactive Mathematics]

  4. Note: Do examples 1 and 2 only.

Additional Resources

Below are additional resources that help reinforce the content for this module.

• 1. Distance, Velocity, and Acceleration [CliffNotes]

  2. YouTube video: Gravity and Vertical Motion Problems

• 1. YouTube video: Net Change as the Integral of a Rate