What if the Odometer is Broken?

1. Write your name here:

2. Find the “Velocity and Position” applet on the website.

3. Make up a scenario about an object in motion and recording the speed of the object at various times. (For example, the numbers that you will see when you pull up the applet correspond to the following scenario: I was driving from Logan to California and it took me 12 hours. There was a terrible snowstorm covering all of Northern Utah, so I had to drive very slowly; when I looked at my odometer after the first hour, I was only going 25 mph!! It got better as I drove South, so I was able to drive faster as time went on. I recorded my current speed in miles per hour every hour after the beginning of my drive.)

Write your scenario here (2-5 sentences).

4. Generate some possible speeds at t=1,2,...,12, type them into the applet, and record them here. Note: Make sure your units are consistent! If you are recording speed every minute, the units of speed should be distance per minute (e.g. miles per minute, not miles per hour).

5. When you checked the speedometer at t=1 it was ______ ___________ per _____________. Suppose you drove that exact speed during the entire first interval (hour, minute, day, etc.). How far would you have gone in that first interval?

6. What is the area of the first rectangle? (The one with base from 0 to 1 and height given by point A.)

7. Discuss the following questions with your group and then write 1-2 paragraphs on the back of this sheet summarizing your discussion and answering: Why are the values from (5) and (6) the same? With this in mind, what does the total area of all the rectangles represent? Why would fitting a curve and computing the area under the curve be a more accurate representation? How do the area under the curve and the total area of the rectangles compare?