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...the legislature wants to know the time it will take the elevator to go from the ground floor to the 102nd observatory in order to get funding approved.

If the state law mandates that elevators cannot accelerate at greater than 2.70m/s2 or travel faster than 16.3 m/s, what is the MINIMUM time in which an elevator can travel the 373 m from the ground floor to the observatory floor?

I understand that I will need to use Vf =Vi+at   and   x=Vit+1/2 at2, but I'm not sure how to work with the info given. I'm using x=373m, V=16.3 m/s, a=2.7 m/s2. I know there should be an initial acceleration no greater than 2.7, but I also know that there should be no acceleration once it gets up to the max speed of 16.3 m/s, so I'm not sure how to work that all in!

Explanation / Answer

v = 16.3 m/s, a = 2.7 m/s2. L = 373 m

acceleration stage: velocity from 0 to v, time = v/a, displacement = v2/(2a)

deceleration stage: velocity from v to 0, time = v/a, displacement = v2/(2a)

constant velocity stage, displacement = L - v2/(2a) - v2/(2a) = L - v2/a, time = (L - v2/a)/v

total time = v/a + v/a + (L - v2/a)/v = L/v + v/a = 28.9 s

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