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
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- 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