Magnitude of acceleration

  • #1
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Homework Statement



A person is standing on an elevator initially at rest at the first floor of a high building. The elevator then begins to ascend to the sixth floor, which is a known distance h above the starting point. A plot of the acceleration as a function of time is shown in the figure above. The elevator undergoes an unknown constant acceleration of magnitude a for a given time interval T. Then the elevator moves at a constant velocity for a time interval 4T. Finally the elevator brakes with an acceleration of magnitude a, (the same magnitude as the initial acceleration), for a time interval T until stopping at the sixth floor.

Find a,the magnitude of the acceleration. Express your answers in terms of h and T as needed.



Homework Equations


[/B]
I thought this equation is the right one:
d=1/2*a*t^2
initial velocity is O


The Attempt at a Solution


[/B]
The question is somewhat obscure to me. Should I find an average magnitude?

a=h/(36*T^2) as h - six floors and there are 6 T - time intervals

or simply - the lift speeding up during T:

a=h/(6*T^2)

It looks simple but I am confused.
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement



A person is standing on an elevator initially at rest at the first floor of a high building. The elevator then begins to ascend to the sixth floor, which is a known distance h above the starting point. A plot of the acceleration as a function of time is shown in the figure above. The elevator undergoes an unknown constant acceleration of magnitude a for a given time interval T. Then the elevator moves at a constant velocity for a time interval 4T. Finally the elevator brakes with an acceleration of magnitude a, (the same magnitude as the initial acceleration), for a time interval T until stopping at the sixth floor.

Find a,the magnitude of the acceleration. Express your answers in terms of h and T as needed.



Homework Equations


[/B]
I thought this equation is the right one:
d=1/2*a*t^2
initial velocity is O


The Attempt at a Solution


[/B]
The question is somewhat obscure to me. Should I find an average magnitude?

a=h/(36*T^2) as h - six floors and there are 6 T - time intervals

or simply - the lift speeding up during T:

a=h/(6*T^2)

It looks simple but I am confused.

Is the "first floor" the American/Canadian version, meaning "ground floor", or is it the British version, meaning what a Canadian or American would call the second floor (with Brits calling the ground floor exactly that---the ground floor---floor zero)?
 
  • #3
andrewkirk
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Use the standard equations of motion under constant acceleration to write formulas for each of:
  1. speed at end of initial acceleration
  2. distance travelled during initial acceleration
  3. distance travelled in middle period of constant speed
  4. distance travelled during final deceleration
Each of those will be a formula that uses only a and T. Some of the formulas may need to use answers from earlier steps.
Then, setting the sum of 2 to 4 equal to h, you get an equation in which the only unknown is a. Then solve the equation.
 
  • #4
183
4
Use the standard equations of motion under constant acceleration to write formulas for each of:
  1. speed at end of initial acceleration
  2. distance travelled during initial acceleration
  3. distance travelled in middle period of constant speed
  4. distance travelled during final deceleration
Each of those will be a formula that uses only a and T. Some of the formulas may need to use answers from earlier steps.
Then, setting the sum of 2 to 4 equal to h, you get an equation in which the only unknown is a. Then solve the equation.

Great, I got it right at last. Many thanks. Dividing h by 6 was a bad idea. :(

Well, I have learnt British English but this can be American. :)
 
  • #5
andrewkirk
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Well, I have learnt British English but this can be American. :)
Actually it doesn't matter which it is, since the distance travelled is that between the first and sixth floors, which is the same (assuming all floors have the same height) regardless of whether 'first floor' means ground floor (American interpretation) or the floor above the ground floor (British interpretation). Either way it's five floors.

But then since h - the total distance travelled in metres - is taken as known, the number of floors travelled is irrelevant too.
 

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