Author Topic: [PHYSICS] Numerical : Work Power Energy  (Read 2026 times)

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Offline Aaruni Kaushik

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[PHYSICS] Numerical : Work Power Energy
« on: March 07, 2014, 12:54:29 pm »
A particle moves along a straight line. A force acts on the particle which produces a constant power. It starts with initial velocity 3 m/s and after moving a distance 252 m its velocity is 6 m/s. Find the time taken.
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Offline Aaruni Kaushik

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Re: [PHYSICS] Numerical : Work Power Energy
« Reply #1 on: March 08, 2014, 08:57:38 pm »
P = W/t = FxS/t = m x s x a /t

Now, P1 = P2 (since P is constant, given in question)

=> m x a1 x s /t = m x a2 x s /t

or a1 = a2

i.e., acceleration is constant.

=> equations of motion may be applied.

so,

2as = v^2 - u^2

i.e., 504a = 36 - 9

or a = 27/504.

v = u + at

v - u = at

t = (v - u) / a
  =  3 x 507 / 27 = 56s
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Offline Aaruni Kaushik

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Re: [PHYSICS] Numerical : Work Power Energy
« Reply #2 on: March 08, 2014, 08:58:04 pm »
can someone verify? because the answer provided is 54, and this is the only solution I can arrive at.
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Is God willing to prevent evil, but not able? Then he is not omnipotent. ; Is he able, but not willing? Then he is malevolent. ; Is he both able and willing? Then whence cometh evil? ; Is he neither able nor willing? Then why call him God?

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Offline Aaruni Kaushik

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Re: [PHYSICS] Numerical : Work Power Energy
« Reply #3 on: March 08, 2014, 09:07:13 pm »

P = \frac{W}{t} = \frac {F*s}{t} = \frac{m*a*s}{t}


now,
P_1 = P_2 \\

\Rightarrow \frac{m*a_1*s}{t} = \frac{m*a_2*s*}{t} \\

or \\

a_1 = a_2

i.e., acceleration is constant

=> equations of motion may be applied.

so,

2*a*s = v^2 - u^2 \\

504a = 36 -9 \\

a = \frac{27}{504} \\

v = u + at \\

v - u = at \\

t = \frac{v -u }{a} = \frac{3 * 507}{27} = 56.33

just the same thing as above, but with tex
« Last Edit: March 08, 2014, 09:23:32 pm by Aaruni Kaushik »
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Is God willing to prevent evil, but not able? Then he is not omnipotent. ; Is he able, but not willing? Then he is malevolent. ; Is he both able and willing? Then whence cometh evil? ; Is he neither able nor willing? Then why call him God?

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Offline karan

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Re: [PHYSICS] Numerical : Work Power Energy
« Reply #4 on: March 08, 2014, 11:07:32 pm »
What you did looks correct. Assuming the calculations are completely correct(which seems to be the case here) I think you have arrived at the correct solution.
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Offline Aaruni Kaushik

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Re: [PHYSICS] Numerical : Work Power Energy
« Reply #5 on: March 08, 2014, 11:08:32 pm »
but the guy who asked this question is positive that the answer is 54.
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Offline karan

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Re: [PHYSICS] Numerical : Work Power Energy
« Reply #6 on: March 08, 2014, 11:16:24 pm »
I doubt if there is any other method to do this. I'm also certain you have done it the right way.
As the person who asked you has said he's sure, I think you ask him to prove it. Else, if he has got it from book/question bank I am certain something is wrong.


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Offline Aaruni Kaushik

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Re: [PHYSICS] Numerical : Work Power Energy
« Reply #7 on: March 08, 2014, 11:18:15 pm »
"Ok look. P=dW/dt = F . dx/dt = F . v

So stop thinking acceleration is constant or F . d is constant.

Yes. So a=dv/dt

So v.dv/dt = constant

=k

=>vdv=kdt

Integrating both sides

V^2/2 = kt + c

At t =0, v=3. So c= 9/2

So it becomes v^2 = 2kt + 9

I think its alright upto here

But after this i've tried various approaches but it vain"

That's what he has to say.
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"It is a miracle that curiosity survives formal education" - Albert Einstein

Is God willing to prevent evil, but not able? Then he is not omnipotent. ; Is he able, but not willing? Then he is malevolent. ; Is he both able and willing? Then whence cometh evil? ; Is he neither able nor willing? Then why call him God?

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Offline karan

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Re: [PHYSICS] Numerical : Work Power Energy
« Reply #8 on: March 08, 2014, 11:30:35 pm »
"So stop thinking acceleration is constant or F . d is constant."

What does this mean?
It's pretty clear from the wording of the question that the power constant thingy is for for constant "a". I feel differentiating it like this is unnecessarily making the whole thing complex.

I still think what you did is right.

Anyways check this:
http://physics.stackexchange.com/questions/78426/what-does-power-really-mean

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