# How Fast Does the Elevator Reach Its Top Speed?

• Lastone1
In summary, the problem involves determining the top speed of an elevator that travels 198 meters in 40 seconds, with 6 seconds of acceleration and 6 seconds of deceleration at a constant rate. The equations used are R=Ro+Vot+at²/2 and V²=Vo²+2aΔt, and the final answer is 5.82352 m/s. There may be some discrepancies with the given answer and further approaches can be explored.
Lastone1

## Homework Statement

A building have 198 meters, an elevator take 40 seconds to go all the way up, knowing that the elevator takes 6 secods to speed up and another 6 seconds to speed down and the aceleration is constant during this period. Determine the top speed of the elevator.

## Homework Equations

(1) R = Ro + Vot +at²/2
(2) V² = Vo² + 2aΔt

## The Attempt at a Solution

I tryed to R1 + R2 + R3 = 198

Now using (1) in R1 in this approach Ro is always zero, and in R1 Vo is also zero
R1 = 18a

For R2 we have aceleration zero but we have initial speed (the final speed of R1) so we have
R2 = 28V1

and R3 = R1 since same aceleration only in oposite direction.
R3 = 18a

for R2 I elaborated V1 using (2)

V1² = Vo² + 2aR1
V1² = 0 + 36a²
V1 = 6a

use that on the R2 formula:

R2 = 28xV1
R2 = 168a

Now going to the final formula:

I tryed to R1 + R2 + R3 = 198

18a + 168a + 18a = 198
a = 0.9705

now using the a on the first 6 secs of the aceleration.

V = at
V = 0.9705*6
V = 5,823529 m/s

The list is telling me the correct answer should be 6... where did I go wrong? The list answer may be wrong? Do you guys have another approach for this exercise? I would like to see it.

Thank you...

Last edited by a moderator:
You work looks fine, [strike]but your calculated value for a is off. I got a=0.99 m/s2[/strike]. Keep in mind sig figs as well.

EDIT: Never mind. I can't add.

Last edited:
I got the same answer too.

34v=198
v=5.82352

azizlwl said:
I got the same answer too.

34v=198
v=5.82352

How you got to 34v = 198??

It can be easily shown if you sketch the velocity vs time graph.

vt=s
vx6x1/2 +vx6x1/2 + 28xv= 198
34v=198

## 1. What is the study of mechanics?

Mechanics is the branch of physics that deals with the behavior of physical bodies when subjected to forces or displacements, and the subsequent motion that these bodies undergo.

## 2. What are the different types of mechanics?

There are three main types of mechanics: classical mechanics, quantum mechanics, and relativistic mechanics. Classical mechanics deals with the motion of macroscopic objects, quantum mechanics deals with the behavior of particles on a microscopic level, and relativistic mechanics explains the behavior of objects moving at high speeds.

## 3. What is the difference between statics and dynamics?

Statics is the branch of mechanics that deals with objects at rest or in a state of constant velocity, while dynamics deals with objects that are experiencing acceleration or are in motion.

## 4. How are forces described in mechanics?

In mechanics, forces are described using vectors, which have both magnitude and direction. This allows for a precise description of the effect of a force on an object.

## 5. What is Newton's first law of motion?

Newton's first law of motion, also known as the law of inertia, states that an object will remain at rest or in a state of uniform motion unless acted upon by an external force.