A commuting student leaves home and drives to school at an average speed of 41.0 km/h. After 24.0 min she realizes that she has forgotten her homework and returns home to get it at the same average speed. It takes 9.0 min to find the report, after which the trip to school 41.0 km away to the east is resumed at the same speed as before.
What is the average speed for the entire trip ? What is the average velocity for the entire trip?
To find the average speed for the entire trip, we need to calculate the total distance traveled divided by the total time taken.
Let's break down the trip:
1. Driving from home to school:
- Distance: 41.0 km
- Time: 24.0 minutes
2. Returning home to get the homework:
- Distance: 41.0 km
- Time: 24.0 minutes
3. Finding the report at home:
- Time: 9.0 minutes
4. Resuming the trip from home to school:
- Distance: 41.0 km
- Time: 24.0 minutes
To find the total distance traveled, we add up the distances:
Total distance = 41.0 km + 41.0 km = 82.0 km
To find the total time taken, we add up the times:
Total time = 24.0 min + 24.0 min + 9.0 min + 24.0 min = 81.0 min
To convert the total time to hours:
Total time = 81.0 min * (1 hour / 60 min) = 1.35 hours
Now, we can calculate the average speed:
Average speed = Total distance / Total time
Average speed = 82.0 km / 1.35 hours ≈ 60.7 km/h
Therefore, the average speed for the entire trip is approximately 60.7 km/h.
Average velocity takes into account the direction of motion. Since the student drives to the east and then returns home to the west, the total displacement is 0. Displacement is the change in position, regardless of the distance traveled. In this case, the student ended up back at her starting point. Therefore, the average velocity for the entire trip is 0 km/h.
To summarize:
- Average speed for the entire trip: approximately 60.7 km/h
- Average velocity for the entire trip: 0 km/h