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A person travelling in a straight line moves with a constant velocity v₁ for certain distance 'x' and with a constant velocity v₂ for next equal distance. The average velocity v is given by the relation

1. v = √(v₁v₂)
2. 1/v = 1/2 (1/v₁ + 1/v₂)
3. v = 2/(1/v₁ + 1/v₂)
4. v = v₁v₂ / (v₁ + v₂)

Correct answer: 1/v = 1/2 (1/v₁ + 1/v₂)

Solution

Since the two distances are equal, the total distance is 2x while the total time is x/v₁ + x/v₂. Dividing total distance by total time gives 1/v = 1/2(1/v₁ + 1/v₂).

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