Preeti reached the metro station and found that the escalator was not working. She walked up the stationaryescalator 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 up on the moving escalator will be

Concept:

Velocity is defined as the rate of change of displacement.

\(Velocity=\frac{Displacement}{Time}\)

When two bodies move in opposite direction then their relative speed is sum of their speeds whereas if they are moving in same direction then their relative speed is difference of their speeds.

Calculation:

Velocity of girl w.r.t. elevator = \(\rm\frac{d}{t_1}=v_{ge}\)

Velocity of elevator w.r.t. ground v_eG = \(\rm\frac{d}{t_2}\) then

velocity of girl w.r.t. ground

\(\rm\vec{v}_{gG} \ = \ \vec{v}_{ge} + \vec{v}_{eG}\)

i.e, V_gG = V_ge + V_eG

i.e, VgG = V_ge + V_eG

_{\(\frac{d}{t}=\frac{d}{t_1}+\frac{d}{t_2}\)}

_{\(\frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2}\)}

\(t=\frac{t_1t_2}{(t_1 \ + \ t_2)} \)