Constant Rate of Change and Linear Functions
For Exercise use the "Jane Walking" applet. Jane is walking from her home to work. Jane passes a mailbox when she is 25 feet from her house. Between the mailbox and a tree she walks at a constant speed, covering 40 feet in 8 seconds.
1. Watch Jane's movement as she walks.
a. Describe the quantities in this situation that are varying. What quantities in the situation do not vary (remain constant in the situation)?
b. As Jane's distance from home increases, how does her distance from work change?
c. After Jane passes the mailbox, how long does it take her to travel 20 feet? 10 feet? 5 feet? Explain your thinking.
d. Alter Jane passes the mailbox, how far does she travel in 2 seconds? 6 seconds? Explain your thinking.
e. Use the applet to help you answer the following questions.
i. How far will Jane travel during any 1-second time interval after passing the mailbox?
ii. How far will Jane travel in 2.8 seconds? 3.1 seconds? k seconds?
iii. Use your answers from pan (ii) to help you write a formula to define the varying value of Jane's change in distance from the mailbox, Δd, in terms of the varying value of the change in time, Δt, since she passed the mailbox.
f. Review your responses to parts (c) through (e). Describe what it means for an object to move at a constant speed. (Note: Say something more than "The speed doesn't change"- be descriptive and reference specific quantities.)
In Exercise we saw examples where as the values of two quantities x and y changed together, the change in one variable was always some constant m times as large as the change in the other variable. This fixed relationship that describes how x and y change together describes what it means for one quantity to change at a constant rate of change with respect to another quantity.