# Change of Subject of Formula

In previous topic of this chapter we have learnt about the subject in a formula. We know that a formula has both known and unknown quantities in it and the unknown quantity that we need to find using the hints and values of known quantities in the given question is said to be the subject of the formula.

Under this topic we will learn to change the subject of the formula. A formula can be given in any form but to change the subject we have to identify the known and unknown quantities given in the question. In some cases, the formula we know can directly be applied in order to get the value of the unknown quantity but in some cases we need to change the subject of the formula and then find the unknown quantity using the hints and known values. To change the subject of the formula, all we need to apply are simple mathematical operators such as addition, subtraction, division and multiplication.

Let us take an example to understand the concept in a better way.

1. We all know the following newton’s equation of motion;

v = u + at

where v = final velocity of the particle

u = initial velocity of the particle

a = acceleration of the particle

t = time taken by the particle to accelerate

here final velocity of the particle, i.e., is the subject of the formula.

Suppose we want to change the subject to ‘t’, then:

Step I: subtract ‘u’ from both sides of the equation.

v – u = u + at – u

⟹ v – u = at

Step II: Divide both sides of the equation by ‘a’:

$$\frac{v– u}{a}$$ = at/t

⟹ $$\frac{v– u}{a}$$ = t

Above equation is the required equation in which the subject is ‘t’.

In this way subject of an equation can be changed from one form to another.

Let’s have a look on another example of changing subject of formula:

2. considering another equation of newton’s equation of motion:

s = ut + ½ at2

where   s = displacement of the particle

u = initial velocity of the particle

a = acceleration of the particle

t = time taken by the particle to cover the displacement.

In this equation, the displacement of the particle ‘s’ is the subject of the formula.

Now, if we want to change the subject of the formula from ‘s’ to ‘u’, one should the following steps:

Step I: Subtracting ½ at2 from both sides of the equation, we get

s – ½ at2 = ut

Step II: dividing both sides of the equation by ‘t’, we get

$$\frac{s - \frac{1}{2}at^{2}}{t}$$ = ut/t

⟹ s/t – ½ at = u

hence the above equation is the equation having ‘u’ as the subject of the formula.

Similarly, subject of the formula can be changed by using simple mathematical operations.