Final answer:
The girl's average velocity during the 30-minute time interval is 2.888888888888889 m/s
Step-by-step explanation:
To find the average velocity, we need to divide the total distance traveled by the total time taken. The girl runs 5.20 kilometers in 30.0 minutes, which is equivalent to 13 laps around the track. Therefore, the total distance traveled is 13 times the length of the track (13 * track length). The average velocity is the total distance traveled divided by the total time taken. We must convert the time from minutes to seconds, so we multiply the total time taken by 60. Finally, we divide the total distance by the total time to get the average velocity in meters per second.
Let's calculate:
Total distance = 13 * track length
Total time = 30.0 minutes * 60 = 1800 seconds
Average velocity = Total distance / Total time
Average velocity = (13 * track length) / 1800
Now, we can substitute the value of the track length given in the question:
Average velocity = (13 * 400) / 1800
Average velocity = 5200 / 1800
Average velocity = 2.888888888888889 m/s
Therefore, the average velocity of the girl during this 30.0 minute time interval is 2.888888888888889 m/s.