# Make a the Subject Of The Formula v = u + at

In this article I will make a the subject of the formula v = u + at, make u the subject of the formula v2 = u2 + 2as, and make t the subject of the formula m = t + 1/t-3. These questions fall under algebraic equation in mathematics and it takes some little skills to get the answer.

When solving questions involving subject of the formula, you must know your addition, subtraction, cross multiplication, how to square and take square root, and collecting like terms, and rearrangement of variables.

I will ensure I solved the above algebraic equation in a way that will be easy to understand and also you can ask any question if you are having any difficulty in the steps I used.

**Make a the subject of the formula v = u + at**

Firstly, locate where a is and then rearrange. In this case, you will make at to be alone on the right hand side and take u to the left hand side.

V = u + at

Then, subtract u from both sides

V – u = u – u + at

V – u = at

On the right hand side, a multiplies t and to make a stand alone, you have to divide the formula on the right and left hand side by t

(V – u) / t = at/t

(v – u) / t = a

You can then rearrange again to make a the subject of the formula

a= (v – u) / t

**Make u the subject of the formula v2 = u2 + 2as**

The first step to take is to make u2 stand alone on the right hand side, and to achieve that, subtract 2as from both sides

V2 – 2as = u2 + 2as – 2as

V2 – 2as = u2

It is u we are asked to make the subject of the formula and not u2, so the next thing to do is to remove power 2 on u. And to achieve that, we will find the square root of both sides

(v2 – 2as)^1/2 = u

Therefore, u = (v2 – 2as)^1/2

**Make t the subject of the equation m =t + 1/t-3**

To solve the above question, you will multiply both sides by t-3

M(t-3) = (t + 1)/(t-3)* (t-3)

M(t-3) = t + 1

Open the bracket on the left hand side

Mt – 3m = t + 1

Subtract t from both sides

Mt – t – 3m = t – t + 1

Mt – t – 3m = 1

Also add 3m to both sides

Mt – t -3m + 3m = 1 + 3m

Mt – t = 1 + 3m

Factorise the equation on left side

T(m-1) = 1 + 3m

Divide both sides by m-1

T(m-1)/(m-1) = (1+3m)/(m-1)

T=(1+3m) / (m-1)

So you make make t the subject of the equation.