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?
average speed=total distance/time
add the times go get total time
add the distances to get total distance
To find the average velocity for the 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, the displacement is given by:
displacement = average speed × time = (6.60 m/s) × (22 minutes) = 145.20 meters north
For the second part:
displacement = average speed × time = (5.40 m/s) × (36 minutes) = 194.40 meters north
For the third part:
displacement = average speed × time = (11.4 m/s) × (8 minutes) = 91.20 meters north
Now, let's calculate the total displacement for the entire trip:
total displacement = 145.20 meters + 194.40 meters + 91.20 meters = 430.80 meters north
Next, let's calculate the total time for the trip:
total time = 22 minutes + 36 minutes + 8 minutes = 66 minutes
Now, we can calculate the average velocity for the trip:
average velocity = total displacement / total time = 430.80 meters / 66 minutes
To convert the time from minutes to seconds, we multiply by 60:
average velocity = 430.80 meters / (66 minutes × 60 seconds/minute)
Simplifying:
average velocity = 430.80 meters / 3960 seconds
Calculating:
average velocity ≈ 0.1091 m/s north
Therefore, the average velocity for the trip is approximately 0.1091 m/s north.