Guided Practice 1.1: How do we measure velocity?

Overview

Our study of calculus begins with a basic building block for understanding change: the concept of average velocity. Two formulas for average velocity are introduced in the section and connected to the concept of the slope of a line. The concept of instantaneous velocity – central to an understanding of calculus – is introduced at the end.

Learning objectives

Basic objectives: Each student is responsible for gaining proficiency with each of these tasks prior to engaging in class discussions, through the use of the learning resources (below) and through the working of exercises (also below).

• Given a formula for the position of an object as a function of time, find the object’s position at a specific time.
• Calculate the average velocity of an object over a given time interval using the average velocity formula on page 2.
• Calculate the average velocity of an object over a given time interval using the average velocity formula on page 5.
• Explain the differences between the two average velocity formulas in this section.
• Explain the difference between average velocity and instantaneous velocity.

Advanced objectives: The following objectives are the subject of class discussion and further work; they should be mastered by each student during and following class discussions.

• Explain the meaning of a negative velocity.
• Interpret the average velocity of an object geometrically through the use of the graph of its position function.
• Use the second average velocity formula to find the average velocity of an object on an interval starting at time $t = a$ and ending at time $t = a + h$, where $a$ is given but $h$ is a variable. Express the answer in simplest form as a function of $h$.
• Given the average velocity of an object from time $t = a$ to time $t = a+h$, find its instantaneous velocity at the single moment $t = a$. (See Example 1.1 and Screencast 1.1.3.)

Learning resources

To gain proficiency in the learning objectives, use the following resources. You may include other resources if you wish, in addition to or in replacement of the following.

Textbook: In Active Calculus, read Section 1.1 pages 1–7. Make sure to read actively, working through examples and activities as you go.

Video: Watch the following videos at the MTH 201 YouTube playlist (http://bit.ly/GVSUCalculus).

• Using the average velocity formula (7:39)
• Alternative average velocity formula (11:07)
• Finding instantaneous velocity (14:03)

Activities

The following activity is to be done during and following your reading and viewing of the resources. Go to student.desmos.com and join using your name in the format Last, First. For example, I would enter my name as Ballif, Serge. Complete each part of the activity. Some of these problems will require you to work them out on paper before entering your answer. Practice producing high quality work so that your work is readable and meaningful. You will receive a mark of Pass if each item response shows a good-faith effort to be right and is submitted prior to the deadline.