Shanghai Tower

Calculus Level 1

The Shanghai Tower has an architectural height of 632 meters, and is equipped with the world's fastest elevator which can travel at 18 18 m/s! If we assume that it travels at it's maximum speed, then it would take just under 36 seconds to reach the top. However, this assumption is unrealistic, as the elevator needs time to increase its velocity, i.e. accelerate.

If the acceleration of the elevator is given by the following graph:

Which of the following is the best graph to illustrate the velocity of the elevator?

A B C D

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9 solutions

Ayush Shukla
Jan 31, 2014

As long as acceleration is positive and constant, velocity will increase. When the acceleration becomes zero that does not indicate that elevator has stopped moving but rather it indicates now it is moving with constant velocity. When the acceleration becomes constant and negative it implies that retarding force is applied in the elevator and it's speed will decrease linearly. This complete scenario is best described in Figure (d). Answer = Option (d)

Albert Xu
Jan 29, 2014

This is just a note about this problem and the other problems relating too the Shanghai Tower that you have posted. It appears as if the pictures you posted are all of the Jin Mao Building, not the Shanghai Tower. Solution: We start off with a positive acceleration and B and D are the only graphs that go up. At the end we have a negative acceleration, so we slow down. The answer is D.

since the acceleration is constant during 1 to 3 sec, therefore the graph must be linearly increasing and vice versa during last 3 second... the only solution can be D

Ashish Ranjan - 7 years, 4 months ago
Pablo Del Corral
Jun 17, 2014

It's completely pointless the graphic A, because it can't reach a negative velocity, so it had to be D

Shailesh Hegde
Mar 9, 2014

step by step accelaration

Uday Rajapur
Feb 28, 2014

For 0 to 3 Sec constant Acceleration, 3 to 6 sec Constant Velocity, and 6 to 9 sec Deceleration. Hence Graph D

Robert Fritz
Feb 7, 2014

It's kind of simple actually. Think of it like this. If there was a hole that went through the earth and out the other side, and a person jumped in without any of the actual things but gravity acting on home like heat, and air resistance, the person would fall and increase his speed until he passed the earth's core. Since he is now on the other side, gravity will now act against him and cause him to slow down to exactly the opposite opening. If he fails to grab the edges then he just continues to repeat the process of technically falling back and forth. Like how Galileo observed a ball roll up and down an inclined plane. After understanding this, it just comes down to whether you know how to read a graph.

Darn, I guess I need to look over my answers. Home =him

Robert Fritz - 7 years, 4 months ago

Ooohhkaaaayyy xD But I think it's a bit simpler if you just look at the acceleration. At 0, the velocity is constant. If it's positive, it speeds up. If it's negative, it slows down. But I like your logic, too, bro :D

Daryl Yara - 7 years, 1 month ago

Del t(0) al t(3) la aceleración es positiva y constante, luego la velocidad aumenta linealmente. Del t(3) al t(6) la aceleración es cero, luego la velocidad se mantendrá constante. Del t(6) al t(9) la aceleración es negativa y constante, luego la velocidad disminuirá linealmente.

Sadia Kaukab
Jan 31, 2014

as we know velocity means rate of change per second and rate of change shows that it increases first then it moves at constant after that it moves at decreasing rate

when acceleration is +ve then final velocity is more than that of the initial.and when acceleration is -ve final velocity is less than initial.when accleration is 0, the velocity is uniform

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