Question

To visit your favorite ice cream shop, you must travel 490 m west on Main Street and then 990 m south on Division Street. Suppose you take 46 s to complete the 490-m displacement and 72 s to complete the 990-m displacement.

a. What is the magnitude of your average velocity during this 118-second period of time?
b. What is the direction of your average velocity during this 118-second period of time?
c. What is your average speed during the trip?

Answer 1

a. The magnitude of the average velocity is 9.29 m/s. b. The direction of the average velocity is 63.43 degrees south of west. c. The average speed is 12.54 m/s.

Step-by-step explanation:

a. To calculate the magnitude of average velocity, we need to find the total displacement and divide it by the total time taken. In this case, the total displacement is 490 m west + 990 m south = sqrt((490^2) + (990^2)) = 1096.71 m. The total time taken is 46 s + 72 s = 118 s. So, the magnitude of average velocity is 1096.71 m / 118 s = 9.29 m/s.

b. The direction of average velocity can be found using trigonometry. The angle of the resultant displacement with the west direction can be calculated as inverse tangent of (990 m / 490 m) = 63.43 degrees. Therefore, the direction of average velocity is 63.43 degrees south of west.

c. Average speed is defined as the total distance traveled divided by the total time taken. In this case, the total distance traveled is 490 m + 990 m = 1480 m. The total time taken is 118 s. So, the average speed is 1480 m / 118 s = 12.54 m/s.