Final answer:
a) The final displacement of the cyclist is 20.8 km east. b) The average velocity of the cyclist is 18.38 km/h east. c) The initial position of the cyclist cannot be determined. d) The total distance traveled by the cyclist is 27.2 km.
Step-by-step explanation:
a) The final displacement of the cyclist can be determined by adding up the individual displacements in each direction. The displacement to the east is 8.0 km, the displacement to the west is -3.2 km (since it is in the opposite direction), and the final displacement to the east is 16.0 km. Therefore, the total displacement is 8.0 km + (-3.2 km) + 16.0 km = 20.8 km east.
b) Average velocity is defined as the total displacement divided by the total time taken. To calculate the average velocity, we first need to find the total time taken. The cyclist took 20 minutes to travel 8.0 km east, 8 minutes to travel 3.2 km west, and 40 minutes to travel 16.0 km east. Therefore, the total time taken is 20 minutes + 8 minutes + 40 minutes = 68 minutes. Converting this to hours, we get 68 minutes ÷ 60 = 1.13 hours. Now, we can calculate the average velocity by dividing the total displacement (20.8 km east) by the total time taken (1.13 hours). The average velocity is 20.8 km ÷ 1.13 hours = 18.38 km/h east.
c) The initial position of the cyclist is not given in the question, so we cannot determine it.
d) Total distance traveled by the cyclist can be determined by adding up the distances travelled in each direction. The distance traveled east is 8.0 km + 16.0 km = 24.0 km, and the distance traveled west is 3.2 km. Therefore, the total distance traveled by the cyclist is 24.0 km + 3.2 km = 27.2 km.