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 particle travels between two points with speeds v₁ and v₂ ( v₁ v₂ ) for two equal time intervals, its average speed is strictly greater than if it travels with the same speeds for two equal distances. Reason (R): The arithmetic mean of two distinct positive numbers is always greater than their
Options
- ABoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
- BBoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
- CAssertion (A) is true but Reason (R) is false
- DAssertion (A) is false but Reason (R) is true
Correct answer
B. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
Step-by-step solution
For a particle travelling with speeds v₁ and v₂ for two equal time intervals, the average speed is the arithmetic mean (AM): v_ avg, time = v₁ + v₂ 2 For a particle travelling with the same speeds for two equal distances, the average speed is the harmonic mean (HM): v_ avg, dist = 2v₁v₂ v₁ + v₂ By the mathematical property of positive distinct numbers, the arithmetic mean is strictly greater than the harmonic mean (AM > HM). Therefore, v_ avg, time > v_ avg, dist . Both Assertion (A) and Reason (R) are true, and Re