After cruising at 75 mph down I-80 for 15 minutes on a roach trip, you hit traffic and travel at 15m/s for 15 minutes for the rest of trip. your average speed is 24.26 m/s.
What if you were traveling at each speed for the same distance instead of time? What would your average speed be there?
To find the average speed when traveling at each speed for the same distance instead of time, we need to calculate the total distance covered and the total time taken for each segment of the trip.
Let's first determine the distance covered during the first segment of the trip. We were traveling at 75 mph (which can be converted to meters per second) for 15 minutes.
1 mile = 1609.34 meters
1 hour = 3600 seconds
Distance covered during the first segment:
Distance = Speed * Time
Convert speed from mph to m/s:
75 mph = 75 * 1609.34 meters / 3600 seconds ≈ 33.53 m/s
Time in the first segment = 15 minutes = 15 * 60 seconds = 900 seconds
Distance in the first segment = 33.53 m/s * 900 seconds = 30,174 meters
Now, let's calculate the distance covered during the second segment of the trip. We were traveling at 15 m/s for 15 minutes.
Distance in the second segment = Speed * Time
Time in the second segment = 15 minutes = 15 * 60 seconds = 900 seconds
Distance in the second segment = 15 m/s * 900 seconds = 13,500 meters
Now, let's calculate the total distance covered during the entire trip.
Total distance = Distance in the first segment + Distance in the second segment
Total distance = 30,174 meters + 13,500 meters = 43,674 meters
Now, let's calculate the total time taken during the entire trip.
Total time = Time in the first segment + Time in the second segment
Total time = 900 seconds + 900 seconds = 1800 seconds
Finally, let's calculate the average speed for the entire trip.
Average speed = Total distance / Total time
Average speed = 43,674 meters / 1800 seconds ≈ 24.26 m/s
So, the average speed when traveling at each speed for the same distance is approximately 24.26 m/s.