A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is: MCQ with Answer and Explanation

Question

A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is:

A. 2(v1 * v2) / (v1 + v2)

B. (v1 + v2) / 2

C. (v1 * v2) / (v1 + v2)

D. (v1^2 + v2^2) / (v1 + v2)

Answer: Option A

Solution (By JKSSB Mock Tests)

When equal distances are covered with different speeds v1 and v2, the average speed is not the arithmetic mean, but the harmonic mean of the two speeds. Total distance = 2x. Total time = (x/v1) + (x/v2). Average speed = Total Distance / Total Time = 2x / [x(1/v1 + 1/v2)] = 2v1v2 / (v1 + v2).

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