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The Model Shop:
Learning about Elementary Functions through Data
Selected Solutions and Hints

42 - They must have adjusted the time so that zero was launch, and the –33 point was beforehand. That means you can use that point to figure out the elevation of the field, but you shouldn't use it in figuring out the slope of the line.

#### 5: Chinese Trains

15 - The purpose of this question is make sure you note that the trip goes to the next day, and that it does not start at midnight. Using the table in the book, under time, it should be 36.23 – 14.42, or 21.81 hours. Or you can take the departure time, 14:25 (or 2:25 pm) and add 24 hours to get 14:25 the next day. Two hours earlier is 12:25 (for 22 hours duration). The train arrives at 12:14, which is 11 minutes earlier. So the elapsed time is 21 hours 49 minutes.

25 - 1463 km / 21.81 hours = 67 kph. Just make sure you divide in the right order!

This is the average speed. When you make a graph, you'll see that the speed is not constant.

#### 6: Hooke's Law

96 - Since we hung masses and saw how much stretch here was, the mass was independent, and the stretch was dependent. To set it up the other way, see how much mass you need to stretch some predetermined amount, for example, how much mass you need to stretch the string 5 cm, 10 cm, etc.

#### 38: Absolute Zero

938 - The intercepts are pretty close (and pretty close to the orthodox value for absolute zero, –273.15 degrees Celsius). But the slopes are way different. One reason is that the two groups must have had different amounts of gas in their canisters. The other (less important, and more confusing) reason is that the second group measured its pressure in pascals instead of kilopascals.

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