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
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.