--- tags: mth201, dailyprep --- # Daily Prep 10A -- MTH 201-04 ## Overview With Module 10 we change gears to study the last big concept of this course. We're going to study the question of, **If we know how fast an object is moving, how far does it travel on a given time interval?** This is sort of the opposite of the question we started the course with in August --- *Given the position of a moving object, how fast is it moving?* --- and we'll answer it by building a new tool that is related to, but quite different from the derivative. We start that process here by going back to basic geometry. ## 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. - Given the graph of a moving object's velocity, estimate the distance it traveled over a time interval using a rectangle sum. - Define the term *antiderivative* and identify an antiderivative of a given function. **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. - Given the graph of a moving object's velocity (which varies over time), estimate the distance it traveled over a time interval using a rectangle sum. - Use an antiderivative to compute the distance traveled by an object, given a formula for its velocity. ## Resources for learning **Reading:** In the _Active Calculus_ text, [read Section 4.1](https://activecalculus.org/single/sec-4-1-velocity-distance.html). **Video:** Watch these at the GVSUMath YouTube playlist: - Screencast 4.1.1 -- Quick Review: Determining distance traveled from velocity (3:37) https://www.youtube.com/watch?v=bTJuR2f-FSs&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=75 - Screencast 4.1.2 -- Estimating distance traveled using a velocity graph (5:54) https://www.youtube.com/watch?v=xwS-v8MLli4&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=76 - Screencast 4.1.4 -- Finding distance traveled with antiderivatives (8:22) https://www.youtube.com/watch?v=mAul5vTAJSA&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=78 You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below. ## Exercises The exercises are on Desmos. Go to [student.desmos.com](http://student.desmos.com) and you should see the Daily Prep for Module 10A. ## Submission and grading **Submitting your work:** Just work through the activities; your work is saved as you go. **How this is graded:** Daily Prep assignments are graded on the basis of *completeness and effort*: If your submission has **all parts completed** (no blank entries, even if left blank accidentally) and **a good-faith effort to provide a correct solution or explanation is given** (no responses of "I don't know" or "I didn't understand") and **the work is submitted on time**, it gets a "check". Otherwise it gets an "x". If you are stuck on an item, you're expected to ask questions and give your best effort.