Acceleration, constant velocity, deceleration

In summary, you are looking for four equations to solve for the unknowns (initial acceleration, constant velocity, final deceleration, and duration of initial acceleration, duration of constant velocity motion, and duration of final deceleration).
  • #1
warsno
4
0

Homework Statement


A building is 320 meters tall. An elevator accelerates uniformly for 30 meters, travels at a constant rate for 260 meters, then decelerates uniformly for the last 30 meters. The total time is 90 seconds.
What is the velocity for the middle 260 meters?


Homework Equations


s=.5at^2, v=at, s=vt



The Attempt at a Solution

I tried 320m:290m=v(final)sec:3.5556 sec. This yields a ball park answer but I don't think it's right. I'd be very grateful for any help.
 
Physics news on Phys.org
  • #2
You have six unknowns: initial acceleration; constant velocity; final deceleration; the duration of the initial acceleration; the duration of the constant velocity motion; the duration of the final deceleration.

So you need six equations to find all the unknowns.

The problem directly describes, in words, four equations. You need to figure out what two additional equations and solve the system.

You may find a shortcut if you think about the physical significance of the fact that the lengths of the initial and final segments are equal, but that is not strictly necessary.
 
  • #3
I think that the initial acceleration and the deceleration are the same, ditto for the time for phase 1 and 3 so it seems to me that there are really 4 unknowns. I have tried 320= 2(.5a(90-t)^2))+(at)t in various forms but I always wind up with 2 unknowns and I can't find think of another equation. Am I barking up the wrong tree?
 
  • #4
You are right, the initial acceleration and the final deceleration are the same in magnitude, so only four unknowns.

There are: ##a##, the acceleration; ##v##, the constant velocity; ##t_1##, the duration of acceleration; ##t_2##, the duration of the uniform motion.

What equations do you have?
 
  • #5
Thank you for considering my problem. For the 1st segment, s=1/2at^2, 60=at^2, a=60/t^2. Then, v=at, v=(60/t^2)(t), v=60/t. For the 2nd segment, s=vt, 260=(60/t)(90-2t), 260=5400/t - 120t/t, 260= (5400/t-120), ...Whoops- I just saw my arithmetic error. Got it. Anyway, thank you again for your very kind assistance.
 
  • #6
It seem to me that you are using the same unknown "t" for both the first and the second segment.

Is this what you have spotted? Have you solved the problem?
 
  • #7
In the second segment (sentence 4 above), I didn't denote it very well, but what I used was 60/t to represent the constant velocity during the second segment and time being 90-2t (with t being the time during the first and 3rd segments). The mistake I made was adding 260+120 and getting 400. That will yield a believable answer for the constant velocity but won't check when you use it to confirm the distance of the first segment that would be produced by the derived acceleration and the calculated time of 14.2 seconds. Adding 260 + 120 and getting 380 makes everything check. In any case, I am grateful to you for taking the time to consider my question.
 
  • #8
Note that the problem is symmetric: equal time/duration for acceleration and deceleration. Hence you can reduce this to a "half-problem": the elevator accelerates for 30 meters, then rides uniformly for 130 meters, 45 seconds total. I think this should be much easier to solve.
 

1. What is acceleration?

Acceleration is the rate at which an object's velocity changes. It can be described as the change in velocity over a certain period of time. Acceleration can be positive, negative, or zero, depending on whether the object is speeding up, slowing down, or maintaining a constant velocity.

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time interval.

3. What is constant velocity?

Constant velocity is when an object's speed and direction do not change. This means that the object is moving in a straight line at a constant speed. An object can have a constant velocity even if its speed is zero, as long as its direction remains constant.

4. How does deceleration differ from acceleration?

Deceleration is the opposite of acceleration. It is the rate at which an object's velocity decreases, or slows down. While acceleration can be positive, negative, or zero, deceleration is always negative since it involves a decrease in velocity.

5. What causes deceleration?

Deceleration can be caused by various factors, such as friction, air resistance, or a decrease in the force propelling the object. For example, a car will decelerate when the brakes are applied, and a ball thrown into the air will decelerate due to the force of gravity acting against it.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Replies
3
Views
5K
  • Introductory Physics Homework Help
Replies
3
Views
765
  • Introductory Physics Homework Help
Replies
2
Views
836
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
2K
Back
Top