If you are asked to make a the subject of the formula V=u+at, derived from the first equation of motion. Then you need to re-arrange the equation making a the primary subject.

In this article, I will explain how to make a the subject of the formula from the first equation of motion. Also, we will make u the subject of the formula and likewise make t the subject of the formula. Everything is really easy using the basic mathematical method.

## 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**

Finally, we arrive at **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.