Problem: Kinematics #4

A train covers half the distance of its journey with a speed 20 m s^-1 and the other half with a speed of 40 m s^-1. The average speed of the train during the whole journey is
A. 25 m s^-1
B. 27 m s^-1
C. 30 m s^-1
D. 32 m s^-1
E. 35 m s^-1

Solution

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The answer is B.

Let the total distance travelled by the train be d and the time taken for it to complete the first half and second half of the journey be t₁ and t₂ respectively. The distance travelled each half-journey is d/2 and it is the product of their respective travelling velocity and time taken.

For the first half-journey,


For the second half-journey,


Combining the above two equations, we get



Now we have the relationship between t₁ and t₂, we can eliminate one of them from our calculations. For convenience, let us state the d in terms of t₂ and find the average speed, which is the total distance travelled divided by the total time taken.



Rounding off to the nearest integer, we have 27 m s^-1.

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Question source: Malaysia National Physics Competition 2007 (Secondary Level)