You are an engineer in charge of designing a new generation of elevators for a p

Question

You are an engineer in charge of designing a new generation of elevators for a prospective upgrade to the Empire State Building. Before the state legislature votes on funding for the project, they would like you to epare a report on the benefits of u is the time it will take the elevator to go from the ground floor to the 102nd floor observatory. They are unlikely to approve the project unless the new elevators make the trip much faster than the old elevators If state law mandates that elevators cannot accelerate at greater than 3.90 m/s2 or travel faster than 13.8 m/s, what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor? Number

Explanation / Answer

lets solve the problem by breaking it in to two pieces.

1) Acceleration Phase,

we have
rate of change of velocity = accleration

dv/dt =a

which implies that
v = at
13.8 = 3.9 *t
t = 3.54 s

Total Acceleration time = 2 * 3.54 = 7.08 s

d for acceleration = 0.5*a*t^2
da = 0.5 * 3.9 * (7.08)2 = 97.75 m

2)the second one is the Constant Velocity Phase
we have
373 m - 97.75 m = 275.25 m
therefore

rate of change of distance = speed

dx/dt =v

which implies
x= d = v* t
275.75 = 13.8 * t
hence t = 19.94 s

Total Time = 19.94 + 7.08 = 27.03 s

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