Calculus I, Pre-Lab 2: Average Velocity & Slope of Tangent Line

Name:

The Pre-lab is intended to encourage you to prepare for the Lab, so answer these questions in your own words.

  1. A common example of secant and tangent lines can be found in the relationship between distance traveled and velocity. Suppose you travel from Eau Claire to Arizona (a total distance of 1350 miles), by driving to the Minneapolis airport and then flying to Phoenix. If you leave Eau Claire at 2pm (CST) and arrive in Arizona at 7pm (CST) (an elapsed time of 5 hours) then your average velocity for the entire trip was . To prepare for this lab, think more about the relationship between average velocities and distance traveled. For example, can you use the above average velocity of to compute the following (circle one option):
    a) How much time did the trip from Eau Claire to the airport (90 miles) take? (Yes or No)
    b) How much time did the total 1350-mile trip take? (Yes or No)
    c) What was your velocity at some particular time during the trip? (Yes or No)
    d) Why did you go to Arizona? (Yes or No)
  2. Given the following table of times and distances,

A / B / C / D / E / F / G
Time / 2:00 PM / 3:00 PM / 3:30 PM / 4:30 PM / 5:00 PM / 6:00 PM / 7:00 PM
Distance
traveled / 0 miles / 63 miles / 90 miles / 90 miles / 215miles / 780miles / 1350miles


Sketch a possible graph of the distance traveled vs. time. (Label axes with units & all points A through G.)

Compute the requested elapsed times and average velocities.

Elapsed time / Average Velocity
Between A and E / 3 hours
Between C and D
Between D and E
Between C and E
Between D and G
  1. Work out 5(a) page 50. Since this is an odd problem, the four answers are in the back of the book. Include enough work to show that you know where the answers come from.
  1. Read pages 46-49 in Stewart and carefully answer the following in your own words…be specific.

a)What is the procedure that you use to compute the average velocity using the correspondence or distance traveled as a function of time?

b)Sketch the secant line between points A and E on the graph from #2. How is the average velocity related to the secant line?

c)What are the units for the slope of the secant line?

d)Sketch a tangent line at the 4:45pm to the graph from #2. What are the units for the slope of the tangent line?

e)Why do we care about the slope of a tangent line to the graph in #2? What does the slope represent physically?

f)What if you wanted an accurate estimate of the slope of the tangent line? Explain how you would determine it.