Lesson 3.1: Motion in Space

In this lesson, you will learn about motion in space in terms of position, trajectory, velocity, speed, and acceleration, and its applications with regard to straight-line motion, circular motion, two-dimensional motion in a gravitational field, and three-dimensional motion.

View all of the instructional videos, read the provided readings, and practice exercises/activities. These will help you master the objectives for this lesson. Pay attention to additional comments provided.

Lesson Objectives

Upon completion of lesson 3.1, you will be able to:

• Determine position, velocity, speed and acceleration

• Compare trajectories

• Model and solve applications

Lesson Content

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

1. They Might Be Giants – Speed and Velocity w/ Marty Beller [2:10]

   1. Source: ParticleMen from YouTube

1. Acceleration [2:12]

   1. Source: TutorVista from YouTube

1. Projectile Motion [6:45]

   1. Source: TutorVista from YouTube

   2. This video has long pauses in between.

1. Determining Velocity, Speed, and Acceleration Using a Vector Valued Function [9:17]

   1. Source: bullcleo1 from YouTube

1. Vector Functions: Position, Velocity, Acceleration Word Problem, Ex 1 [3:23]

   1. Source: patrickJMT from YouTube

1. Vector Functions – Part 2 Position from Velocity or Acceleration [5:20]

   1. Source: Jason Rose from YouTube

1. Projectile Motion Example Solving for Distance and Time – Engineering Dynamics [7:33]

   1. Source: structurefree from YouTube

Lesson Readings

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

1. Chapter 12: Vector-Valued Functions

   1. This document covers materials from lessons in both Module 2 and Module 3.

   2. Read slides 3-14 for this lesson.

   3. Read slides 15-42 for Lesson 2.3.

   4. Read slides 43- 66 for Lesson 3.1.

   5. Read slides 90-102 for Lesson 3.2.

   6. Read slides 67-89, 103-127 for Lesson 3.3.

2. 11.3 Motion in Space

3. Projectile Motion

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. 13.4 Motion in Space: Velocity and Acceleration

   1. Stewart Calculus

   2. Instructions: On the Homework Hints tab, click on Vector Functions and choose 13.4 Motion in Space: Velocity and Acceleration from the list.

   3. Acceleration, Velocity, Position Problems (2 examples with solutions)

Additional Resources

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

1. Unit 12 – Circular Motion: Lesson 3 – Accelerations

2. Application of Circular Motion

3. Projectile Motion (video)

   1. Source: Khan Academy

   2. Part 1 [9:08]

• 1. Part 2 [9:14]

• 1. Part 3 [9:04]

• 1. Part 4 [8:58]

• 1. Part 5 [9:33]

• 1. Part 6 [9:49]

• 1. Part 7 [10:35]

• 1. Part 8 [1:47]

• 1. Part 9 [8:22]

• 1. Part 10 [10:07]

Homework Assignment

Do Homework 3.1 on MyMathLab.

Show Your Work Assignment

Show Your Work assignment will be given via Assignment Tool on Laulima. Please check your email for Laulima announcement.

Lesson 3.2: Arc Length -->