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 23.7 minutes at an average speed of 6.31 m/s. During the second part, she rides for 25.0 minutes at an average speed of 4.12 m/s. Finally, during the third part, she rides for 14.6 minutes at an average speed of 15.7 m/s. (a) How far has the bicyclist traveled during the entire trip? (b) What is the average speed of the bicyclist for the trip?
To find the distance traveled during the entire trip, we need to calculate the distance for each part and then sum them up.
For the first part, we can use the formula:
Distance = Speed * Time
Distance1 = (6.31 m/s) * (23.7 minutes) * (60 seconds / 1 minute)
Distance1 = 8956.22 meters
For the second part:
Distance2 = (4.12 m/s) * (25.0 minutes) * (60 seconds / 1 minute)
Distance2 = 6180 meters
For the third part:
Distance3 = (15.7 m/s) * (14.6 minutes) * (60 seconds / 1 minute)
Distance3 = 13719.6 meters
Now, we can sum up the distances:
Total distance = Distance1 + Distance2 + Distance3
Total distance = 8956.22 + 6180 + 13719.6
Total distance = 28955.82 meters
Therefore, the bicyclist traveled a total distance of 28,955.82 meters during the entire trip.
To find the average speed, we need to calculate the total time taken for the entire trip and divide the total distance by the total time.
Total time = Time1 + Time2 + Time3
Total time = 23.7 minutes + 25.0 minutes + 14.6 minutes
Total time = 63.3 minutes
Now, we convert the total time to seconds:
Total seconds = Total time * (60 seconds / 1 minute)
Total seconds = 63.3 * 60
Total seconds = 3798 seconds
Average speed = Total distance / Total time
Average speed = 28955.82 meters / 3798 seconds
Average speed = 7.627 m/s
Therefore, the average speed of the bicyclist for the trip is 7.627 m/s.