Notesale: Turn your study into money

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Rearranging equations
Rule 1
Whatever you do to 1 side of the equation you must also do to the other
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i
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in the following equation if you wish to make A the subject then B must be subtracted from both
sides of the equation
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A–B=C
A - (B + B) = C + B
A=C+B
Rule 3
If the term you want is multiplied by another expression then you should divide both sides of the
equation by that expression
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e
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g
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E
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make m the subject when p = m/v
pv = mv/v
pv = m: so; m = pv
Rule 4
If you currently have the square of a term that you wish to make a target then you should take the
square root of both sides
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e
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Example 1
Ek = 1/2mv2 or Ek = m(v2)/2
Rearrange to make v the subject:
m(v2)/2 = Ek

Firstly reverse the equation:

Next multiply both sides by 2 to remove it: 2m(v2)/2 = 2Ek gives m(v2) =2Ek
Next divide both sides by m to remove it:

m(v2)/m = 2Ek/m gives v2 = 2Ek/m

Next square root both sides to find v:

v = √2Ek/m

Example 2
a = v – u/t
Rearrange to make v the subject:
Firstly reverse the equation:

v – u/t = a

Next multiply both sides by t gives: (v – ut)/t = at
Next add u to both sides:

gives v – u = at

v – u + u = at + u gives v= at + u

Remember that you must also apply same principle to the units so ensure all values used are
expressed in same units
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g
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3 x 105 J kg-1 / 1
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3 J



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