# Elevator Physics Question

1. Aug 31, 2008

### mossfan563

A certain elevator cab has a total run of 199 m and a maximum speed is 313 m/min, and it accelerates from rest and then back to rest at 1.10 m/s2. (b) How long does it take to make the nonstop 199 m run, starting and ending at rest?

How do I approach part B?

2. Aug 31, 2008

### Staff: Mentor

What have you done so far? How quickly does it reach maximum speed? What distance does that require?

3. Aug 31, 2008

### mossfan563

Well part A was how far does the cab move while accelerating to full speed from rest?
And the answer was 12.3698 m.
That's what I've done so far.

4. Aug 31, 2008

### Staff: Mentor

Good.

Treat the motion as having three stages: Accelerating to max speed; constant speed; decelerating to zero speed.

Figure out the distance and time associated with each stage of the motion.

5. Aug 31, 2008

### mossfan563

Well I technically have the distance and time for accelerating to max speed. I can't figure out the other two though. I tried the quadratic equation and it doesn't work.

6. Aug 31, 2008

### LowlyPion

What quadratic equation? You have 3 regions. There are the two - one at each end - getting to max speed and going back to 0, and you know the distances for both because they are symmetrically the same.

Since you know the distance for both, then you know what remains of the trip that you will account for with max speed. Knowing the distance and knowing the max speed then you can figure the time.

Time for the trip? Total time = Time to speed + time at max + time to slow to 0.

7. Aug 31, 2008

### mossfan563

Ok I understand that the time to speed and time to slow to 0 are pretty much the same. The time at max still is still confusing me. The remaining distance would be around 174.2.
I do know the max speed. I just don't know what formula to use.

8. Aug 31, 2008

### LowlyPion

V= x/t

9. Aug 31, 2008

### mossfan563

Ok I used this formula.
Here are the numbers I used.
Total distance = 199 m
Remaining distance = 174.2604 m
Time of speed up and slow down = 4.742.... s
Max speed = 5.21666666.... m/s

Using all these numbers I got an answer of 919.49 s.
Is this off? What am I doing wrong? Are my numbers wrong?

10. Aug 31, 2008

### LowlyPion

Going 174 m at 5 m/sec should be accomplished considerably quicker if you managed to slow up and down in only 9 seconds over 25 feet.