Below are several different scenarios. Take distance units to be “feet” and time units to be “minutes.” Assume Dave’s path to Gould Hall is along a straight line which is 2400 feet long.

Question

I. Dave leaves Padelford Hall and walks at a constant spend until he reaches Gould Hall 10 minutes later. On a sheet of paper, sketch a graph of this situation and use your graph to answer the following questions:

a. Which axis did you use to describe time, and which axis did you use to describe distance traveled?

b. Explain your choices for part a.

II. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the halfway point. Then he gets confused and stops for 1 minute. He then continues on to Gould Hall at the same constant speed he had when he originally left Padelford Hall. On a sheet of paper, sketch a graph of this situation and use your graph to answer the following questions:

c. Compare and contrast the slope of the graph from before the 1-minute pause to the graph after the pause. What are the similarities and/or differences?

d. What does the graph look like during the 1-minute of Dave's confusion?

III. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the half-way point. Then he gets confused and stops for 1 minute to figure out where he is. Dave then continues on to Gould Hall at twice the constant speed he had when he originally left Padelford Hall. On a sheet of paper, sketch a graph of this situation and use your graph to answer the following questions:

e. Compare and contrast the graph from before the 1-minute pause to the graph after the pause. What are the similarities and/or differences?

f. Using all three sketches, in which scenario does Dave reach Gould Hall fastest? How do you know?

g. Using all three scenarios, represent each scenario as an algebraic function.

Answer 1

put time on the x axis, distance on the vertical, the y axis

slope of the line = speed, feet per minute

if he stops, that part of the line's graph is a flat horizontal line segment

reaching the destination in 10 minutes is faster than reaching the midway point in 6 minutes, with or without a 1 minute pause