Question

A cyclist rides 8.0 km east for 20 minutes, then he turns and heads west for 8 minutes and 3.2 km. Finally he rides east for 16 km, which takes 40 minutes. (a) What is the final displacement of the cyclist? (b) What is his average velocity?

Answer 1

1) The final displacement of cyclist is 20.8 km.

2) The average velocity of cyclist is 18.35 m/h

Step-by-step explanation:

The path traced by the cyclist is as shown in the attached figure

from the attached figure we can see

1) Initial distance covered = 8.0 km east therefore OA = 8.0 km

2) When the cyclist turns and travels 3.2 km west thus AB = 3.2 km

3) From B the cyclist turns and travels 16 km east thus BC = 16.0 km

As we can see that the total displacement is OC = OA- AB + BC = 8.0-3.2+16 = 20.8 km

Thus the final displacement is 20.8 km.

Part b)

By definition of average velocity we have

`v_(avg)=(Total\cdot Displacement)/(Total\cdot Time)=(20.8)/(20+8+40)=0.305km/min=18.35km/hr`