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.
First, let's calculate the displacement for each part of the trip:
For the first part:
Time = 22 minutes = (22/60) hours = 0.367 hours
Velocity = 6.80 m/s (given)
Displacement = Velocity * Time = 6.80 m/s * 0.367 hours = 2.4976 meters
For the second part:
Time = 36 minutes = (36/60) hours = 0.6 hours
Velocity = 5.20 m/s (given)
Displacement = Velocity * Time = 5.20 m/s * 0.6 hours = 3.12 meters
For the third part:
Time = 8 minutes = (8/60) hours = 0.133 hours
Velocity = 12.6 m/s (given)
Displacement = Velocity * Time = 12.6 m/s * 0.133 hours = 1.6758 meters
Now, let's calculate the total displacement:
Total displacement = Displacement of the first part + Displacement of the second part + Displacement of the third part
Total displacement = 2.4976 meters + 3.12 meters + 1.6758 meters = 7.2934 meters
The total time for the entire trip is the sum of the times for each part:
Total time = 22 minutes + 36 minutes + 8 minutes = 66 minutes = (66/60) hours = 1.1 hours
Finally, let's calculate the average velocity:
Average velocity = Total displacement / Total time
Average velocity = 7.2934 meters / 1.1 hours = 6.63 m/s
Therefore, the average velocity for the entire trip (in the due north direction) is 6.63 m/s.