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A particle covers half of its total distance with speed v1 and the rest half distance

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

Options

(a) (v1v2)/(v1+v2)
(b) (2v1v2)/(v1+v2)
(c) (2v1²v2²)/(v1²+v2²)
(d) (v1+v2)/2

Correct Answer:

(2v1v2)/(v1+v2)

Explanation:

Let the tot. distance covered by the particles be 2s. Then
vₐᵥ = 2 s / (s/ v₁ + s/ v₂) = 2 v₁v₂ / v₁ + v₂

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