STATEMENT OF PROBLEM

1. A bicyclist travels .5 mile. Obtain a data set consisting of (at least) 25 (time in sec, distance in ft) pairs of observations. (Or you can use the data set below.)

Input := 

data = {{0, 0}, {6., 7.}, {12., 28.}, {18., 61.}, 
{24., 102.}, {30., 148.}, {36., 195.},  {42., 241.}, 
{48., 285.}, {54., 327.}, {60., 370.}, {66., 419.}, 
{72., 479.}, {78., 557.},  {84., 658.}, {90., 787.}, 
{96., 947.}, {102., 1137.}, {108., 1353.}, {114., 1590.}, 
{120., 1835.}, {126., 2075.}, {132., 2295.}, 
{138., 2476.}, {144., 2599.}, {150., 2644.}};

2. Plot every 8th data point. What was the average speed of the bicycle in each interval? Connect the data points with line segments. What is the slope of each segment?

3. Plot every 4th, every other, and every data point, and answer the same questions.

4. Let the line segments that connect the data points be our `distance function'. What would our distance function look like if we took a data point every foot? every inch? if we had an electronic recording device that took observations continuously?

5. What happens to the length of the line segments as we take measurements more frequently? What does the slope of the line segments tell us? If we have continuous observations, what slope (the slope of what line) would give us the same information?

6. Estimate when the velocity ( in ft/sec and mi/hr) is greatest in this one-half mile cycling trip.

7. How would you decide how many observations to take?

8. In some research or industrial settings, observations may be very expensive or dangerous to obtain. Crash testing of automobiles and `weatherbeater' airplanes sent to obtain data about hurricanes are two examples. In these situations, additional factors play a role in determining the number of observations to obtain. Discuss some appropriate issues using these examples and/or some of your own.