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I know the title isn’t that specific but honestly, I can’t think of a specific title that isn’t the whole problem.

Anyways. Force is directly proportional to mass. Force is directly proportional to acceleration.

Therefore, $\frac{force}{mass*acceleration} = k$ Ans this is true.

But…… $$\frac{force}{mass} = constant_1$$ $$\frac{acceleration}{force} = constant_2$$ Multiplying these equation gives us: $$\frac{acceleration}{mass} = constant_3$$

And surely this isn’t true. Acceleration and mass are not directly proportional. Am I making a mistake?

Atul Anand
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    Given that $\text{force} = \text{mass} \times \text{acceleration}$, the equation $\frac{\text{force}}{\text{mass}} = \text{Constant}$ will be true if and only if $\text{acceleration}$ is constant. – user2661923 Oct 12 '21 at 07:01

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When you say two variables, $x$ and $y$, are directly proportional, this means that when $x$ experiences some change, $y$ experiences that same change times a constant. However, this constant is dependent on other variables that may not be identified.

Your claim that $\frac{force}{mass}=constant_1$ is dependent on the fact that any other variable is not modified. Specifically, the $constant_1$ is only known to be constant wrt variations in $force$ or $mass$. We cannot claim that $constant_1$ is independent of some other variable, say $acceleration$

In fact, we know that $constant_1$ is indeed also directly proportional to $acceleration$.

Alan Abraham
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