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Algebra (Intermediate) - Subject of a Formula
 
Changing the Subject of a Formula | Special Situations
 

Changing the Subject of a Formula

v = u + at is a formula with v as the subject. Sometimes we want to change the subject. Another way of saying this is 'write t in terms of v, a, and u'.

In this case we are changing the subject to t.

We use the same rules as equations:

 

      v = u + at

 

(- u)

 
v – u = at

 

(divide by a )

 
v – u = t  
   a

 

 

Normally we put the subject on the left, so
       t = v – u
               a
 

 

 
 
  

Many formulae can be rearranged in this way using the rules of equations.

However there are two special situations, as described below.

 

Special Situations

1. When the new subject is inside a square root sign.

For example
  p = t squareroot_q02
   (divide by t)
 
p/t = squareroot_q02
   (square both sides)
 
 p2 = q
    
 
 t2
    
 
   q = p2
    
 
         t2
      

Note: we can remove the square root sign by making it the subject, then squaring both sides of the formula.

 
2. When the new subject is squared.

For example;

        y = p2 - 3
                  2

 (x2)
  
        2y = p2 – 3 (+3)  
  2y + 3 = p2 (square root)  
   
      p=  squareroot_2y2    

Note: we make the squared term the new subject, then square root.