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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

1. v₁v₂ / (v₁ + v₂)
2. 2v₁v₂ / (v₁ + v₂)
3. (v₁² + v₂²) / (v₁ + v₂)
4. (v₁ + v₂) / 2

Correct answer: 2v₁v₂ / (v₁ + v₂)

Solution

The average speed is calculated as total distance divided by total time. Since the particle covers half the distance with speed v₁ and the other half with speed v₂, the total time is the sum of the times taken for each half. Solving this gives the average speed as 2v₁v₂ / (v₁ + v₂).

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