Bob N

I was thinking the halfway point, but that leads me to another wrong answer. I can't see any other interesting points where that would happen

I'm doing this question for physics, and I'm a bit stuck.

The question is:

A hotel elevator ascends 200m with maximum speed of 5 m/s. Its acceleration and deceleration both have a magnitude of 1.0 m/s^2

a) How far does the elevator move while accelerating to full speed from rest?

b) How long does it take to make the complete trip from bottom to top?

Part a I did

Vf^2 = Vi^2 +2aΔx

25 = 0 + 2(1)Δx

25/2 = Δx = 12.5 m (and I got the answer right)

now part b

I tried a couple of ways, I tried separating the problem after 12.5 m, so

x(t) = (.5 a t^2) + Vit + Xi

200 = .5t^2 + 5t + 12.5

So quadratic is .5t^2 +5t -187.5 = 0

t = 15 s

I added 5 s on top of that, since that is the time to the 12.5 m, from

Vf = Vi + a t

5 = 0 + 1(t)

but 20 s is apparently the wrong answer.

I tried treating the whole problem as one part, like

200 = .5at^2 + Vit + Xi

200 = .5t^2 + 0 + 0

400 = t^2

t=20 s

what am I doing wrong?