Calculus: The Language of Change

Exercise Set 10.0
Velocity

by John Robeson

Exercise 1) 9.2.1 Again

Look up your solution to Exercise 9.2.1 or resolve it.  Be sure to include the features of stopping at stop signs and at Grandmother's house in your graph.  How do the speeds of 65 mph and 25 mph appear on your solution?  Be especially careful with the slope and shape of your graph.  We want to connect slope and speed and bend and acceleration later in the chapter and will ask you to refer to your solution.

Solution

Exercise 9.2.1 is repeated below.

Exercise 9.2.1 Again

Make a qualitative rough sketch of a graph of the distance traveled as a function of time on the following hypothetical trip:

(a)  You travel a total of 100 miles in 2 hours.

(b)  Most of the trip is on rural interstate highway at the 65 mph speed limit.  What qualitative feature or shape does the graph of distance vs. time have when speed is 65 mph?

(c)  You start from your house at rest, gradually increase your speed to 25 mph, slow down, and stop at a stop sign.

(d)  What shape is the graph of distance vs. time while you are stopped?

(e)  You speed up again to 25 mph, travel a while, and enter the interstate.  At the end of the trip, you exit, slow to 25 mph, stop at a stop sign, and proceed to your final destination.

(a)

(a)  You travel a total of 100 miles in 2 hours.