You drive in a straight line at 24 m/s for 8 miles, then at 30 m/s for another 8 miles. (a) how does your average speed sav compare with 27.0 m/s (the midpoint of 24 m/s and 30 m/s)?
1) sav < 27.0 m/s
2) sav = 27.0 m/s
3) sav > 27.0 m/s.
explain conceptually.
(b) verify your response to part (a) by calculating the average speed of this trip exactly

Part A.) The midpoint between the two speeds is just an estimate of the exact average speed. This is not exactly 27 m/s because although they have the same distance, they differ in speed. So, the answer is more or less, but not equal to, 27 m/s.

Part B.) The average speed is the total amount of distance traveled per total time.

Convert miles to meters: 1 mile = 1,609.34 meters
8 miles* 1,609.34 m/1 mile = 12,874.72 m

Average Speed = (12,874.72 m + 12,874.72 m)/[(12,874.72 m/24 m/s)+ (12,874.72 m/30 m/s)]
Average speed = 26.67 m/s

The center is basically the heart of it