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http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Physics (9702)/9702_w13_qp_11.pdf
Question 8. Why cant we just add up the speeds and divide them by 2? :|
Short answer, because the time taken with each speed is different.
Let's do the math behind this - suppose the distance traveled with both speeds is denoted by "s".
Suppose the time taken at 600 kmph = t(1).
Then, since Speed = Distance/Time, we can write
600 = s/t(1)
So that
t(1) = s/600
Similarly, let's do the same for the other speed. The distance traveled is still "s", the speed = 400 kmph, and the time taken to traverse this distance = t(2). So:
400 = s/t(2)
So that
t(2) = s/400
The average speed is the total distance traveled dividing by the time taken (the average velocity is different - it is equal to total displacement divided by time taken).
= (Total Distance traveled)/(Time taken to cover that distance).
Since the plane travels a distance "s" in one direction and returns the same distance "s", the total distance traveled = s+s = 2s.
The time taken = t(1) + t(2) = s/400 + s/600 = 3s/1200 + 2s/1200 = 5s/1200 = s/240
Therefore, the average speed = 2s/(s/240) = 480 kmph = C.
Hope this helped!
Good Luck for all your exams!