A commuting student leaves home and drives to school at an average speed of 42.0 km/h. After 22.0 min he realizes that he has forgotten his homework and returns home to get it at the same average speed. It takes 8.0 min to find the report, after which the trip to school 42.0 km away to the east is resumed at the same speed as before.
What is the average speed for the entire trip ?
10.6 m/s
To find the average speed for the entire trip, we need to calculate the total distance traveled and the total time taken.
First, let's calculate the distance traveled when the student drives from home to school. The student drove for 22.0 minutes, which is equivalent to 22.0/60 = 0.367 hours. The average speed is 42.0 km/h, so the distance traveled is 42.0 km/h * 0.367 hours = 15.414 km.
Next, the student returns home to get the homework. This means the student traveled an additional distance of 15.414 km back home.
After finding the homework, it takes 8.0 minutes, or 8.0/60 = 0.133 hours, before the student resumes the trip to school.
Finally, the student travels the remaining distance from home to school, which is 42.0 km.
Now, let's calculate the total distance traveled for the entire trip. The student traveled 15.414 km to school, 15.414 km back home, and then another 42.0 km to school. Therefore, the total distance traveled is 15.414 km + 15.414 km + 42.0 km = 72.828 km.
To calculate the total time taken for the entire trip, we add the time taken for each segment. The student spent 0.367 hours going to school, 0.133 hours returning home, and an additional 0.367 hours to reach school. Therefore, the total time taken is 0.367 hours + 0.133 hours + 0.367 hours = 0.867 hours.
Now, we can calculate the average speed for the entire trip by dividing the total distance by the total time: average speed = total distance / total time = 72.828 km / 0.867 hours = 84.07 km/h.
So, the average speed for the entire trip is approximately 84.07 km/h.