Calculus, 8th Edition,stewart; page 34 problem 16

Question

Jason leaves Detroit at 2:00 PM and drives at a constant speed west along I-94. He passes Ann Arbor, 40 mi from Detroit, at 2:50 PM.

(a) Express the distance traveled in terms of the time elapsed.

(b) Draw the graph of the equation in part (a).

(c) What is the slope of this line? What does it represent?

Answer 1

Step:1

(a)

Jason drives  miles in  minutes with constant speed.

Find the constant speed.

Speed is defined as the distance traveled to the time elapsed.

Speed ,  where  is distance and  is time.

Speed of the Jason is .

mi/min.

 mi/hr.

 mi/hr.

Step:2

Total Distance travelled by Jason :

The total distance traveled =  constant speed  time.

The distance traveled in terms of the time elapsed  miles.

Step:3

(b)

Graph :

Graph the function .

axis : Time  in hours.

axis : Distance  in miles.

Step:4

(c)

The distance as a function of time is  miles.

Compare the equation with slope-intercept form of lines .

Slope is .

The slope  represents increasing in distance by  miles for every  hour increase in time .

Solution:

(a) The distance traveled in terms of time .

(b) Graph of the function .

(c) The slope  represents increasing in distance by  miles for every  hour increase in time .