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NEETPhysicsMotion in One Dimension

A car covers half the total distance of a trip at a constant speed v₀ . The remaining half of the distance is covered in two equal time intervals with speeds v₁ and v₂ . The average speed for the entire trip is:

Options

  1. A2v₀(v₁ + v₂) 2v₀ + v₁ + v₂
  2. Bv₀(v₁ + v₂) v₀ + v₁ + v₂
  3. Cv₀ + v₁ + v₂ 3
  4. D3v₀v₁v₂ v₁v₂ + v₀v₂ + v₀v₁

Correct answer

A. 2v₀(v₁ + v₂) 2v₀ + v₁ + v₂

Step-by-step solution

Let the total distance of the trip be 2d . The first half of the distance ( d ) is covered at a speed v₀ . Time taken for the first half, t₁ = d v₀ . The second half of the distance ( d ) is covered in two equal time intervals, say t₀ each, with speeds v₁ and v₂ . Distance covered in this half = v₁ t₀ + v₂ t₀ = d t₀ = d v₁ + v₂ Total time taken for the second half, t₂ = 2t₀ = 2d v₁ + v₂ . Total time for the entire trip, T = t₁ + t₂ = d v₀ + 2d v₁ + v₂ T = d ( v₁ + v₂ + 2v₀ v₀(v₁ + v₂) ) Average speed for the entire

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