(adsbygoogle = window.adsbygoogle || []).push({}); This is not homework. I'm reading a physics for laypeople book and I'm trying to wrap my head around something that other people obviously have little or no trouble understanding.

I understand what it means when someone says that a body's acceleration is directly proportional to the magnitude of the impressed force. It means that if you apply one more unit of force, you'll get one more unit of acceleration out of it. Double the force applied, double the resulting acceleration; triple the force, triple the acceleration.

What I don't understand is what to imagine when someone says that something is directly proportional to thesquareof something, or directly proportional to the squarerootof something. Is being "directlyproportional to the squareroot" of something the same as being "inverselyproportional to thesquare" of something?

1) Suppose we lived in a universe in which a body's acceleration was directly proportional to thesquareof the impressed force. What would that mean? Would it mean that if Idoubledthe impressed force, I'dquadruplethe resulting acceleration? Or would it mean that if I wanted todoublethe acceleration, I'd have toquadruplethe impressed force?

2) Likewise, say a body's acceleration was directly proportional to the squarerootof the impressed force. What would that mean?

3) Suppose thattriplingthe impressed force yielded6 timesthe acceleration, and thatquadruplingthe force yielded8 timesthe acceleration. What sort of proportional relationship would that be?

4) Suppose thatadding 1 unitof forceyielded 1 unitof acceleration, and thatadding 2 unitsof forceyielded 1.5 unitsof acceleration, and thatadding 3 unitsof forceyielded 1.8333... unitsof acceleration, and thatadding 4 unitsof forceyielded 2.08333... unitsof accceleration. What sort of proportional relationship would that be?

5) Suppose thatadding 1 unitof forceyielded 1 unitof acceleration, and thatadding 2 unitsof forceyielded 1.5 unitsof acceleration, but thatadding 3 unitsof forceyielded 1.75 unitsof acceleration, and thatadding 4 unitsof forceyielded 1.875 unitsof acceleration. What sort of proportional relationship would that be?

Thanks in advance for your help...

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# Basic question about basic concept: proportionality

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