Daily Prep 1A -- MTH 201-04

--- tags: mth201, dailyprep --- # Daily Prep 1A -- MTH 201-04 ## Overview If an object is moving but at a continuously changing speed, how do you tell how fast it’s going at a single moment in time? This simple question launches our study of calculus this semester. We will approach it by looking at the concept of **average velocity**, using a connection to the slope of a line. Then we’ll introduce the concept of **instantaneous velocity** and how to measure it. To conclude, we'll generalize the idea of "velocity" to the **rate of change** in a quantity. ## Learning objectives **Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. + Compute the average velocity of a moving object on an interval using either of the average velocity formulas. + Explain the differences between average velocity and instantaneous velocity. **Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. + Find the instantanous velocity of a moving object through a sequence of average velocities. + Find the average rate of change in a function on an interval. + Find the instantaneous rate of change in a quantity through a sequence of average rates of change. ## Resources for learning **Reading:** Read through [Section 1.1](https://activecalculus.org/single/sec-1-1-vel.html) of the _Active Calculus_ text. **Video:** Watch the following videos and take notes. The total running time is 32:45. - Using the average formula (7:38) https://www.youtube.com/watch?v=6HPe7iwr88k - Alternative average velocity formula (11:06) https://www.youtube.com/watch?v=O_Z9osv6VGk - Finding instantaneous velocity (14:03) https://www.youtube.com/watch?v=j8kJubOTkME ## Exercises The exercises for this Daily Prep are packaged as a **Desmos activity**. To access it, go to student.desmos.com and log in with your Desmos account. If you have successfully joined the Desmos class roster as part of the *Tools Assignment*, you will see "Daily Prep 1A" available in a list. Click the link to begin, and continue through the end. Your work is saved as you enter it, so there is nothing to "submit" at the end. ## Submission and grading  A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.