Question

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

Answer 1

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