# Question Video: Changing the Subject of a Word Equation Physics

The subject of the formula force = mass × acceleration is force. Which of the following correctly shows the same formula with acceleration as the subject of the formula? [A] Acceleration = force/mass [B] Acceleration = force × mass [C] Acceleration = mass/force

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### Video Transcript

The subject of the formula force equals mass times acceleration is force. Which of the following correctly shows the same formula with acceleration as the subject of the formula? A) Acceleration equals force divided by mass, B) Acceleration equals force times mass, or C) Acceleration equals mass divided by force.

First, let’s recall that the subject of any equation is the quantity that’s on its own side of the equals sign. On the right-hand side of the equation, there are two quantities, mass and acceleration, multiplied together. On the left side of the equation, we only have one quantity, force. That’s why we can say that force is the subject of this equation. The question asks us to identify the same formula but with acceleration as the subject. In other words, we want to change the subject of the equation.

To do this, we’re going to rearrange the equation so that we just have acceleration on its own side of the equals sign. Whenever we rearrange an equation, there are two really important rules we need to remember. Firstly, we can use any mathematical operations including addition, subtraction, multiplication, and division.

Secondly, it’s really important to remember that any operation we use must be applied to both sides of the equation. So, if we multiply the left-hand side of the equation by something, then we also need to make sure that we multiply the right-hand side of the equation by the same thing.

For this question, we need to think of an operation or operations that will leave acceleration on its own side of the equation. To figure out what these operations might be, first we want to identify any operations which are being applied to acceleration in this equation and then try to undo them. In this equation, we can see that acceleration is being multiplied by mass.

So, to undo this, we want to do the opposite of multiplying by mass with the aim of getting rid of this from the right-hand side of the equation and just leaving acceleration on its own. The opposite or inverse of multiplication is division, so the first thing we want to do is divide by mass. Remember that any operations we use must be applied to both sides of the equation. So, we’re going to divide both sides of the equation by mass.

So, on the left-hand side of the equation, we have force divided by mass. And on the right-hand side of the equation, we have mass times acceleration all divided by mass. Note that because we divided both sides of the equation by the same thing, the equation is still balanced. Or in other words, it’s still true. This is just another way of expressing exactly the same relationship between force, mass, and acceleration.

On the right-hand side of the equation, we have a fraction that can be simplified. Acceleration is being multiplied by mass and then divided by mass. If we start with acceleration and multiply it by some quantity, then divide the result by the same quantity. Then, we’re left with the original acceleration value because multiplying and dividing by the same number are inverse operations. This leaves us with just acceleration on one side of the equation, which means we’ve successfully made acceleration the subject of the formula.

Usually, we’d write the subject of the formula on the left-hand side. So, all we need to do now is swap around the right-hand side and the left-hand side to give us acceleration equals force divided by mass. And there is our answer. If we take the formula force equals mass times acceleration and make acceleration the subject, then we have acceleration equals force divided by mass.