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Question about fiding speed and distance 
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#1
Nov1113, 07:58 AM

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I had a test earlier today and one question was,
A 20kg object initially at rest is accelerated at constant power of 12.0w. After 9.0s it has moved 56.0m. Find its speed at t=6.0s and its position at that instant. I got v=6 and distance=36m are these values correct? 


#2
Nov1113, 08:26 AM

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But the "12.0 w" really has nothing to do with the problem and can be ignored. If an object accelerates from rest at constant acceleration, a [itex]m/s^2[/itex], then after time, t, it will have speed [itex]at[/itex] m/s and will have moved distance [itex](1/)at^2[/itex] m. 


#3
Nov1113, 08:56 AM

P: 17

P*t=W
12*9=108 therefore W=108joules W=F*displacement F=108/56 F=1.93N F=ma a=1.93/20 a=0.1 so at t=6 Pt=W 12*6=72joules W=72joules W=F*displacement displacement=72/(20*0.1) displacement=36m P=Fv v=12/(20*0.1) v=6 


#4
Nov1113, 08:57 AM

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Question about fiding speed and distance
Halls, it doesn't say constant acceleration. Constant power is what you might get from a car with a continuously variable transmission.



#5
Nov1113, 08:58 AM

P: 17

I am assuming the acceleration is constant. Is that right?



#6
Nov1113, 09:01 AM

P: 17

Have I gone wrong somewhere?



#7
Nov1113, 09:07 AM

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Me thinks...
P=Fv 12=20*x'*x'' 3/5x'=x" x(0)=0, x'(0)=0 http://www.wolframalpha.com/input/?i...%27%280%29%3D0 x=2(2/5)^{1/2}t^{3/2} pugging t=9 x=18(6/5)^1/2 whereas according to question it should be 56m??? Either the question, me or wolframalpha is incorrect... 


#8
Nov1113, 09:12 AM

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#9
Nov1113, 09:41 AM

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If we disregard x(9) value in question { http://www.wolframalpha.com/input/?i...3D0%2Cx%289%29 }
For x(6) we get 24/(5)^0.5 http://www.wolframalpha.com/input/?i...3D0%2Cx%286%29 


#11
Nov1113, 10:24 AM

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P=dW/dt P=d(∫F.dx)/dt P=F.dx/dt P=Fv If a is const. P=ma*(at) P=ma^{2}t Then Power is not constant as given in the question... 


#12
Nov1213, 04:52 AM

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I saw this question when it was in the other section, it looked fishy to me then and I just had a go at it. Unless I am missing something it does not have a solution.
The way the question is formulated you will as Enigman pointed out end up with a 2nd order ODE for the position; but then the constants are overdetermined. I wonder if this is a case of the teacher trying to add a red herring (constant power) without realizing that this implies that the accelaration can not be constant. 


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