Question

4. A bicyclist makes a trip that consists of three parts, each in the same direction (due north) along a straight road. During the first part, she rides for 22 minutes at an average speed of 7.2 m/s. During the second part, she rides for 36 minutes at an average speed of 5.1 m/s. Finally, during the third part, she rides for 8.0 minutes at an average speed of13.0 m/s. (a) Make an x vs time graph and plot the initial and the final position of the bicyclist for the each of the three time periods as a function of time. (b) Draw on the graph lines representing the average velocity of the bicyclist during each of the three time periods. (c) Calculate the average velocity of the bicyclist during each of the three time periods. (d) How far does the bicyclist travel during the entire trip? (e) What is her average velocity for the trip?

Answer 1

(a)

to make a graph, we need to find distance traveled in each interval

in t1 = 22 minutes = 1320 seconds, d = 7.2 * 1320 = 9504 m

in t2 = 36 minutes = 2160 seconds, d = 5.1 * 2160 = 11016 m

in t2 = 8 minutes = 480 seconds , d = 13 * 480 = 6240 m

Here is the graph

I assume the cyclist starts from x = 0 position

26760 20520 9504 22 58 66

where the time is in minutes

---------------------------------------------------------------

average velocity during first interval

v = 9504 / 1320 = 7.2 m/s

during second interval

v = 11016 / 2160 = 5.1 m/s

during third interval

v = 6240 / 480 = 13 m/s

---------------------------------------------------------

how far the bicyclist travels

d = 9504 + 11016 + 6240

d = 26760 m

-------------------------------

average velocity during entire trip

v = total distance / total time

v = 26760 / 3960

v = 6.7575 m/s