Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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:

t₁t₂ / (t₂ - t₁)

t₁t₂ / (t₂ + t₁)

t₁ - t₂

(t₁ + t₂) / 2

Step-by-Step Solution

Let the length of the escalator be $L$ .

Velocity of Preeti ( $v_p$ ): When walking on the stationary escalator, $v_p = \frac{L}{t_1}$ .
Velocity of the Escalator ( $v_e$ ): When standing on the moving escalator, $v_e = \frac{L}{t_2}$ .
Relative Velocity: When she walks on the moving escalator, her net velocity ( $v$ ) with respect to the ground is the sum of her walking speed and the escalator's speed (since both are in the same direction) . $v = v_p + v_e = \frac{L}{t_1} + \frac{L}{t_2}$ $v = L \left( \frac{1}{t_1} + \frac{1}{t_2} \right) = L \left( \frac{t_1 + t_2}{t_1 t_2} \right)$
Calculate Time ( $t$ ): The time taken to cover distance $L$ with velocity $v$ is: $t = \frac{L}{v} = \frac{L}{L \left( \frac{t_1 + t_2}{t_1 t_2} \right)}$ $t = \frac{t_1 t_2}{t_1 + t_2}$

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