Question

A bicyclist rides on a North-South trail from her home to work. She starts at home and rides due North for 22 minutes with a velocity of 7.2 m/s. She gets tired, so she slows down and rides for 36 minutes due North with a velocity of 5.1 m/s. Suddenly, she realizes that she missed her destination, frantically turns around, and rides due South for 8.0 minutes with a velocity of 10.1 m/s before reaching work.

a. What is her average velocity (magnitude and direction) between her home and work?

b. What is her average speed between her home and work?

c. Sketch a position (m) versus time (s) graph of her trip from her home to work. Consider her home to be the origin. Be sure to label both axes and scale them appropriately.

Answer 1

let

t1 = 22 minutes, v1 = 7.2 m/s
t2 = 36 min, v2 = 5.1 m/s
t3 = 8 min, v3 = 10.1 m/s

a)
average velocity = total displacement/time taken

= (v1*t1 + v2*t2 - v3*t3)/(t1+t2+t3)

= (7.2*22 + 5.1*36 - 10.1*8)/(22 + 36 + 8)

= 3.96 m/s (towards north)

b) average speed = total distance travelled/time taken

= (v1*t1 + v2*t2 + v3*t3)/(t1+t2+t3)

= (7.2*22 + 5.1*36 + 10.1*8)/(22 + 36 + 8)

= 6.41 m/s

c)