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 6.60 m/s. During the second part, she rides for 36 minutes at an average speed of 5.40 m/s. Finally, during the third part, she rides for 8.0 minutes at an average speed of 11.4 m/s.

What is her average velocity for the trip?

Perform a vector addition to determine the magnitude and direction of the total displacement. Divide that by the total elapsed time for the average velocity. The average velocity has both magnitude and direction. They may want both.

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To find the average velocity for the trip, we need to calculate the total displacement and the total time taken by the bicyclist.

To calculate the total displacement, we can add up the individual displacements for each part of the trip. Since the bicyclist is moving only in one direction (due north), the displacements will have the same direction.

First, we calculate the displacement for each part of the trip using the formula:

displacement = average speed × time

For the first part of the trip:
displacement1 = 6.60 m/s × 22 minutes

Here, we need to convert minutes to seconds, so 22 minutes = 22 × 60 seconds.

displacement1 = 6.60 m/s × (22 × 60 seconds)

Next, we repeat the same steps for the second and third parts of the trip:

For the second part of the trip:
displacement2 = 5.40 m/s × 36 minutes = 5.40 m/s × (36 × 60 seconds)

For the third part of the trip:
displacement3 = 11.4 m/s × 8 minutes = 11.4 m/s × (8 × 60 seconds)

Now, we can calculate the total displacement by adding up the individual displacements:

total displacement = displacement1 + displacement2 + displacement3

After calculating the total displacement, we can find the average velocity by dividing the total displacement by the total time taken for the trip.

total time taken = time for the first part + time for the second part + time for the third part

Total time taken = 22 minutes + 36 minutes + 8 minutes

Again, we need to convert minutes to seconds, so:

Total time taken = (22 + 36 + 8) × 60 seconds

Finally, we can calculate the average velocity:

average velocity = total displacement / total time taken

Substitute the values calculated above to find the average velocity.