A formula, like v = u + at is great if we want to know the value of v.

But what if we want to know the value of u? Or the value of a?

We can use algebraic manipulation to rearrange the formula so that it tells us about “u” instead of about “v”.

Algebraic manipulation is like a game with only one rule. The rule is that you can do any arithmetic you like to the equation, as long as you do the same arithmetic to both sides of the equation. So you can add 5 to both sides of the equation. Or you can divide both sides of the equation by 7.

Well our equation is v = u + at, and we want to get the “u” on its own.

So, if we subtract “at” from both sides, we get v – at = u. This is what we wanted! (although it’s probably nicer to write is as u = v – at)

If we want to get the a on its own we can do the following steps:

• v = u+at
• v-u = at
• (v-u)/t = a

So a = (v-u)/t

We have now learned how to change the subject of a formula (the subject was v and we changed the subject to u and then to a).

Example

Let’s practice some (maybe not all;)) of these with the teacher:

Exercise

Let’s practice the questions below:

The answers are below:

Extension Questions

Here are some harder questions so that you can challenge yourself to develop this skill further. In each of these you need to make x the subject of the equation:

Below are the answers:

Textbook Exercise

Now you can do questions 1 to 8 from exercise 2K on page 33 and then questions 11, 12 and 15 from exercise 2J on page 32:

The answers are below: