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NEET PHYSICSMOTION IN A STRAIGHT LINEMedium

Question

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk upon the moving escalator will be:

A

t₁t₂ / (t₂ - t₁)

B

t₁t₂ / (t₂ + t₁)

C

t₁ - t₂

D

(t₁ + t₂) / 2

Step-by-Step Solution

Let the length of the escalator be LL.

  1. Velocity of Preeti (vpv_p): When walking on the stationary escalator, vp=Lt1v_p = \frac{L}{t_1}.
  2. Velocity of the Escalator (vev_e): When standing on the moving escalator, ve=Lt2v_e = \frac{L}{t_2}.
  3. Relative Velocity: When she walks on the moving escalator, her net velocity (vv) with respect to the ground is the sum of her walking speed and the escalator's speed (since both are in the same direction) . v=vp+ve=Lt1+Lt2v = v_p + v_e = \frac{L}{t_1} + \frac{L}{t_2} v=L(1t1+1t2)=L(t1+t2t1t2)v = L \left( \frac{1}{t_1} + \frac{1}{t_2} \right) = L \left( \frac{t_1 + t_2}{t_1 t_2} \right)
  4. Calculate Time (tt): The time taken to cover distance LL with velocity vv is: t=Lv=LL(t1+t2t1t2)t = \frac{L}{v} = \frac{L}{L \left( \frac{t_1 + t_2}{t_1 t_2} \right)} t=t1t2t1+t2t = \frac{t_1 t_2}{t_1 + t_2}

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 LINEpreetireachedstationescalatorworking

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