[AS level] Help with rearranging E=1/2mv^2

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alexmcfc43
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The question I'm attempting is 1 (c) (ii) on this paper: http://filestore.aqa.org.uk/subjects...2-QP-JUN14.PDF
And here's the markscheme: http://filestore.aqa.org.uk/subjects...W-MS-JUN14.PDF

I have worked out the change in energy and rearranged E=1/2mv^2 to v^2=E/O.5m however in the mark scheme it says that the equations should be rearranged to v^2=2xE/m. To me this doesn't make sense because the equation has a 1/2 in it and now it has be changed to 2 times the mass which to me doesnt make sense. I know this is long winded but can anyone tell me why the rearrangement is like this?
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benwolfy98
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(Original post by alexmcfc43)
the question i'm attempting is 1 (c) (ii) on this paper: http://filestore.aqa.org.uk/subjects...2-qp-jun14.pdf
and here's the markscheme: http://filestore.aqa.org.uk/subjects...w-ms-jun14.pdf

i have worked out the change in energy and rearranged e=1/2mv^2 to v^2=e/o.5m however in the mark scheme it says that the equations should be rearranged to v^2=2xe/m. To me this doesn't make sense because the equation has a 1/2 in it and now it has be changed to 2 times the mass which to me doesnt make sense. I know this is long winded but can anyone tell me why the rearrangement is like this?
e/(1/2m) = 2e/m as a/(b/c) =(ac)/b
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iMacJack
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(Original post by alexmcfc43)
The question I'm attempting is 1 (c) (ii) on this paper: http://filestore.aqa.org.uk/subjects...2-QP-JUN14.PDF
And here's the markscheme: http://filestore.aqa.org.uk/subjects...W-MS-JUN14.PDF

I have worked out the change in energy and rearranged E=1/2mv^2 to v^2=E/O.5m however in the mark scheme it says that the equations should be rearranged to v^2=2xE/m. To me this doesn't make sense because the equation has a 1/2 in it and now it has be changed to 2 times the mass which to me doesnt make sense. I know this is long winded but can anyone tell me why the rearrangement is like this?
forgetting about the symbols, you have 1/0.5 as a fraction right? how many halves go into 1? 2.
another way to think of it is v^2 = E divided by m/2
when you divide you flip the second fraction and multiply
v^2 = e * 2/m
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