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 6.80 m/s. During the second part, she rides for 36 minutes at an average speed of 5.20 m/s. Finally, during the third part, she rides for 8.0 minutes at an average speed of 12.6 m/s. What is her average velocity for the trip?
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To find the average velocity for the entire trip, we need to calculate the total displacement and divide it by the total time taken.
To start, we can find the displacement for each part of the trip by multiplying the average speed by the time traveled:
Displacement of first part = (average speed of first part) * (time of first part)
Displacement of first part = 6.80 m/s * 22 minutes = 149.60 meters
Displacement of second part = (average speed of second part) * (time of second part)
Displacement of second part = 5.20 m/s * 36 minutes = 187.20 meters
Displacement of third part = (average speed of third part) * (time of third part)
Displacement of third part = 12.6 m/s * 8.0 minutes = 100.80 meters
Next, we can calculate the total displacement by adding up the displacements from each part of the trip:
Total displacement = displacement of first part + displacement of second part + displacement of third part
Total displacement = 149.60 meters + 187.20 meters + 100.80 meters = 437.60 meters
Finally, we can calculate the average velocity by dividing the total displacement by the total time taken:
Average velocity = Total displacement / Total time
Total time = (time of first part) + (time of second part) + (time of third part)
Total time = 22 minutes + 36 minutes + 8.0 minutes = 66.0 minutes
To convert minutes to seconds, we can multiply by 60:
Total time = 66.0 minutes * 60 seconds/minute = 3960 seconds
Average velocity = 437.60 meters / 3960 seconds = 0.11 m/s
Therefore, the average velocity for the entire trip is 0.11 m/s.