A bus covers the first half of a certain distance with speed v₁ and the second half with a speed v₂. The average speed during the whole journey is:Select the correct answer from the code given below:

1. A

   v₁v₂/(v₁ + v₂)

   Option (a) claims the average speed is v₁v₂/(v₁ + v₂). This formula incorrectly mimics parallel resistance and fails dimensional analysis for speed.

2. B

   2v₁v₂/(v₁ + v₂)

   Option (b) claims the average speed is 2v₁v₂/(v₁ + v₂). This is the correct harmonic mean derived by dividing total distance by total time taken for two equal halves, making it the key.

3. C

   (v₁ + v₂)/2

   Option (C) claims the average speed is the arithmetic mean (v₁ + v₂)/2. This formula applies when equal time intervals are spent at each speed, not equal distances.

4. D

   √(v₁v₂)

   Option (d) claims the average speed is the geometric mean √(v₁v₂). This is a mathematical mean that does not correctly calculate physical average speed for equal distances.

Summary. Official key is (b) 2v₁v₂/(v₁ + v₂). When a journey is divided into two equal halves covered at different speeds, the average speed is found using the harmonic mean. Using the arithmetic mean is a common student error. Option (b) correctly derives this through total distance divided by total time.