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NEETPhysicsMotion in One Dimension

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If a car travels between two cities covering the journey in two equal distance halves at speeds v₁ and v₂ (where v₁ v₂ ), its average speed is always less than if it had traveled at those same speeds for two equal time intervals. Reason (R): The average speed for a journey divided into two equal di

Options

  1. ABoth (A) and (R) are true and (R) is the correct explanation of (A)
  2. BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
  3. C(A) is true but (R) is false
  4. D(A) is false but (R) is true

Correct answer

C. (A) is true but (R) is false

Step-by-step solution

For a journey divided into two equal distance halves at speeds v₁ and v₂ , the average speed is the harmonic mean: v_ dist = 2v₁v₂ v₁ + v₂ . For a journey divided into two equal time intervals at speeds v₁ and v₂ , the average speed is the arithmetic mean: v_ time = v₁ + v₂ 2 . Mathematically, for any two distinct positive numbers, the harmonic mean is strictly less than the arithmetic mean ( v_ dist The Reason (R) states that the average speed for equal distance halves is the arithmetic mean, which is incorrect. I

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