Problem+2.5+Theo's+speed

R.A. Block E September 1, 2009 Big idea: Observation and description of changes in the world around us are the first steps to learning and finding patterns around us.

Essential Question: What are some situations that we can describe as variable?


 * __Problem 2.5__**


 * A. What was Theo’s fastest recorded speed, and when did it occur?**


 * B. What was Theo’s slowest recorded speed, and when did it occur?**


 * C. Describe the changes in Theo’s speed during the race.**


 * D. The graph only shows Theo’s speed at 10-minute intervals; it does not tell us what happened between 10-minute marks. The paths below show five possibilities of how Theo’s speed may have changed during the first 10 minutes. Explain in writing what each connecting path would tell about Theo’s speed.**

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Problem 2.5 He steadily increased and decreased for 30 minutes. Then he stopped, and jumped back up to 15 were he once again steadily increased and decreased. From there he steadily increased to 20, and dropped to a stop at 100 minutes.
 * 1) Theo’s fastest recorded speed was 20 miles per hour, it occurred at 90 minutes.
 * 2) Theo’s slowest recorded speed was 0 miles per hour, it occurred at 0 minutes, 40 minutes, and 100 minutes.
 * 3) The patterns and changes in Theo’s speed during the race were:

The possibilities for each one are: 1. 1- Theo steadily increased in speed 2- Theo accelerates quickly at first and then his speed steadies out. 3- Theo first increases speeds quite slowly, then increases faster. 4- Theo isn’t moving and then steadily increases his speed. 5- Theo is increasing in speed very fast and then stops.


 * Problem 2.5 follow up**


 * 1) **Would it be possible for the path below to represent Theo’s progress between 10-minute marks? Why or why not?**




 * 1) **During which 10-minute period(s) of the race did Theo’s speed change the most?**

Problem 2.5 follow up
 * 1) It would not be possible because he would have to increases his speed from 0 to 15 miles per hour extremely fast in only an instant.
 * 2) Theo’s speed changes the most within a 10-minute period from 90-100 minutes (the last 10 minutes) because it goes from 20 miles per hour to o miles per hour.


 * **Time**
 * (minutes)** || **Speed**
 * (miles per hour)** ||
 * **0** || **0** ||
 * **10** || **15** ||
 * **20** || **17.5** ||
 * **30** || **15** ||
 * **40** || **0** ||
 * **50** || **15** ||
 * **60** || **17.5** ||
 * **70** || **15** ||
 * **80** || **17.5** ||
 * **90** || **20** ||
 * **100** || **0** ||