1. Position vs. clock time data give us a function y = .01 t^2 - 40 t + 100, where t is time in seconds and y is position in cm..

• Make a table for y vs. t, using t = 0, 100, 200, 300, 400.
• For each time interval calculate the average rate at which position changes.
• Plot average rate of position change vs. midpoint clock time and sketch a straight line through your graph points.
• Your graph will show v vs. t. Find the slope and v-intercept of your straight line.
• What is the equation of your linear function? Give the function in slope-intercept form, using v and t as your variables.
• According to Bubba what should be the equation of your straight line?

2. Cooter figured out that when his car rolled off its blocks and coasted down the hillside in his unmowed from yard, its velocity function was v = -.27 t + 12.8. According to Bubba what will be the position vs. clock time function corresponding to the velocity function? If you think need the information to answer the question, you should know that Cooter's car was at position y = 12 with respect to the coon dog under his front porch.

3. The temperature of a bolled possum just brought out of the pressure cooker in Cooter's very warm kitchen is given by T = 95 + 130 * 2^(-.7 t), where t is clock time in hours and T is temperature in Fahrenheit.

• Evaluate the temperature at t = 0, .5, 1, 1.5 and 2 and construct a graph of T vs. t.
• Find the average rate at which temperature changes during each interval.
• Plot average rate of temperature change vs. midpoint clock time and sketch a straight line through your graph points. How well do the graph points match the straight line?
• If we call the rate of temperature change R, then you just plotted a graph of R vs. t. Label the graph as such.
• Determine the slope-intercept form of your linear equation.
• How well does your linear equation match the actual rate of temperature change?
• This function isn't quadratic. Do you think the rate function is really supposed to be linear?

4. If y = a t^2 + b t + c, then suppose that t = t1 and t = t1 + `dt are two clock times.

• What is the difference between the first clock time and the second? What therefore is the time interval between these two clock times?
• What are the values of y at t = t1 and at t = t1 + `dt?
• By how much does y change between these two clock times?
• At what average rate does y change between these two clock times?

• What is the clock time midway between the two given clock times?

• What is the velocity function corresponding to the given position function?

• What is the value of the velocity function at the midway clock time?