This applet is intended as a follow up series of challenge questions to the relay runners in the previous applets. In this applet, the concreteness of individual runners and the track are removed, and we consider the feasibility of halving, double, and tripling average speeds.
1. Using the Orange controls with no constraints, explore different possibilities for speeds and laps that the Orange runner can make. How does this affect the average speed?
(Note: The orange dot on the x-axis controls the number of laps. The endpoint on the orange segment controls speed.)
Suppose Orange can run any number of laps at any speed to achieve each of the following average speeds. How could this be done? Use the toggle buttons to explore halving, doubling, and tripling the average speeds.
2. What are the restrictions on halving the average speed?
If Orange runs one lap, what speed would half the one-lap average?
If Orange runs half a lap, what speed would half the one-lap average?
If Orange runs less than half a lap, what speed would half the one-lap average?
Why is this!?
3. What are the restrictions on doubling the average speed?
If Orange runs 3 laps, could it double the one-lap average?
If Orange runs 2 laps, could it double the one-lap average?
If Orange runs 1 lap, could it double the one-lap average?
Why is this!?
4. What are the restrictions on tripling the average speed?
If Orange runs 3 laps, could it triple the one-lap average?
If Orange runs 2 laps, could it triple the one-lap average?
If Orange runs 1 lap, could it triple the one-lap average?
Why is this!?
What is the relationship between the factor you want to increase your speed and the minimum number of laps it would take to do so?