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NEET PHYSICSMOTION IN A STRAIGHT LINEMedium

Question

A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is

A

v₁v₂ / (v₁ + v₂)

B

2v₁v₂ / (v₁ + v₂)

C

2v₁²v₂² / (v₁² + v₂²)

D

(v₁ + v₂) / 2

Step-by-Step Solution

Average speed is defined as the total path length travelled divided by the total time interval during which the motion has taken place .

  1. Identify Parameters: Let the total distance be dd. Distance covered in the first half = d/2d/2 with speed v1v_1.
  • Distance covered in the second half = d/2d/2 with speed v2v_2.
  1. Calculate Time Taken: Time for the first half, t1=DistanceSpeed=d/2v1=d2v1t_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{d/2}{v_1} = \frac{d}{2v_1}. Time for the second half, t2=d/2v2=d2v2t_2 = \frac{d/2}{v_2} = \frac{d}{2v_2}.
  • Total time, T=t1+t2=d2v1+d2v2=d2(1v1+1v2)=d2(v1+v2v1v2)T = t_1 + t_2 = \frac{d}{2v_1} + \frac{d}{2v_2} = \frac{d}{2} \left( \frac{1}{v_1} + \frac{1}{v_2} \right) = \frac{d}{2} \left( \frac{v_1 + v_2}{v_1 v_2} \right).
  1. Calculate Average Speed (vavgv_{avg}): vavg=Total DistanceTotal Timev_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} vavg=dd(v1+v2)2v1v2v_{avg} = \frac{d}{\frac{d(v_1 + v_2)}{2v_1 v_2}} vavg=2v1v2v1+v2v_{avg} = \frac{2v_1 v_2}{v_1 + v_2} This result represents the harmonic mean of the individual speeds when equal distances are covered.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOTION IN A STRAIGHT LINE. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMOTION IN A STRAIGHT LINEparticlecoversdistancedistanceaverage

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