A person travels x distance with velocity v₁ and then x distance with velocity v₂ in the same direction. The average velocity of the person is v, then the relation between v, v₁ and v₂ will be.

Solution

Physics sir · 3 steps

Equal distances, not equal times, so add up the times first and never average the speeds directly.

1. Time for each part. The first x takes t₁ = x/v₁ and the second x takes t₂ = x/v₂. The motion is in one direction, so the total displacement is 2x.
2. Use the definition. Average velocity is total displacement divided by total time, so v = 2x/(t₁ + t₂).

   v = 2x/(x/v₁+x/v₂) ⇒ 2/v = 1/v₁+1/v₂

3. So. The distance x cancels, leaving 2/v = 1/v₁+1/v₂, which is option (d).

The idea to keep. Equal distances give the harmonic mean, v = 2v₁v₂/(v₁+v₂). Equal times give the plain average (v₁+v₂)/2. Check which one is equal before you average.

Answer from the NTA final answer key. Solution by PrepWiser.