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?

Seperating is the way to go.

 

You need to split it into 3 parts.

 

How long does it take to accelerate?

How long does it take to travel Xm at the top speed?

How long does it take to decelerate?

 

And add all 3 together. I've not given you X because I guess that's a a place you're likely to make a mistake and therefore something you should think about.

And pay attention to the sign of the acceleration term for part 3.

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