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The subject of the formula force equals mass times acceleration is force.
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Which of the following correctly shows the same formula with acceleration as the subject of the formula?
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A) Acceleration equals force divided by mass, B) Acceleration equals force times mass, or C) Acceleration equals mass divided by force.
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First, let’s recall that the subject of any equation is the quantity that’s on its own side of the equals sign.
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On the right-hand side of the equation, there are two quantities, mass and acceleration, multiplied together.
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On the left side of the equation, we only have one quantity, force.
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That’s why we can say that force is the subject of this equation.
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The question asks us to identify the same formula but with acceleration as the subject.
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In other words, we want to change the subject of the equation.
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To do this, we’re going to rearrange the equation so that we just have acceleration on its own side of the equals sign.
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Whenever we rearrange an equation, there are two really important rules we need to remember.
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Firstly, we can use any mathematical operations including addition, subtraction, multiplication, and division.
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Secondly, it’s really important to remember that any operation we use must be applied to both sides of the equation.
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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.
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For this question, we need to think of an operation or operations that will leave acceleration on its own side of the equation.
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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.
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In this equation, we can see that acceleration is being multiplied by mass.
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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.
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The opposite or inverse of multiplication is division, so the first thing we want to do is divide by mass.
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Remember that any operations we use must be applied to both sides of the equation.
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So, we’re going to divide both sides of the equation by mass.
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So, on the left-hand side of the equation, we have force divided by mass.
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And on the right-hand side of the equation, we have mass times acceleration all divided by mass.
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Note that because we divided both sides of the equation by the same thing, the equation is still balanced.
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Or in other words, it’s still true.
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This is just another way of expressing exactly the same relationship between force, mass, and acceleration.
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On the right-hand side of the equation, we have a fraction that can be simplified.
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Acceleration is being multiplied by mass and then divided by mass.
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If we start with acceleration and multiply it by some quantity, then divide the result by the same quantity.
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Then, we’re left with the original acceleration value because multiplying and dividing by the same number are inverse operations.
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This leaves us with just acceleration on one side of the equation, which means we’ve successfully made acceleration the subject of the formula.
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Usually, we’d write the subject of the formula on the left-hand side.
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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.
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And there is our answer.
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If we take the formula force equals mass times acceleration and make acceleration the subject, then we have acceleration equals force divided by mass.