This section covers the following concepts: Average velocity. Slope of a secant line. Instantaneous velocity.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at our next class meeting. Important new vocabulary words are indicated in italics.
- Given the position function, find the position of the object at a specific time.
- Compute the average velocity of an object on a specific time interval, using the first average velocity formula.
- Compute the average velocity of an object on a specific time interval, using the second average velocity formula.
- Explain the difference between the first and the second average velocity formulas.
- State the units of the average velocity of an object.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Explain the graphical interpretation of the average velocity.
- Explain the difference between instantaneous velocity and average velocity.
- 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 \(t=a\).
To prepare for class
As you follow the instructions listed below (in particular when watching a video), you should take notes for yourself, just as you would in a lecture. In particular, you should immediately make yourself a list of things you didn't quite understand. When you are done, you should go over this list yourself again and see if some of the points have become clear to you - and if not, you should write a detailed & clear feedback message to your teacher (for example in your Q&A forum if your class uses one).
Read the Introduction in Section 1.1 and Do the Preview Activity (which your teacher might require you to do on WeBWorK).
Watch the following video about the average velocity formula:
Review the preview activity you have completed previously and verify that you have calculated an average velocity.
Watch the following video about the alternative average velocity formula:
Watch the following video about finding the instantaneous velocity:
Do some experimentation with the following interactive applet (make sure to follow the instructions listed at the bottom of the page, under "Explore"): Average and Instantaneous Rate of Change
The following instructions will apply always and will not mentioned in the future:
- Finish any in-class activities you might not have finished during class.
- Start working on the problems on the WeBWorK assignment your teacher has assigned for this section.