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Constants are generally added in functions to adjust for when magnitudes don't contain information necessary to the accuracy of the equation. Why is it that $v^2=cad$ instead of $v^2=ad$? What information is conveyed by the constant?

Qmechanic
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Striker
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    Related post by OP: http://physics.stackexchange.com/q/212679/2451 (only visible to 10k+ users) – Qmechanic Oct 15 '15 at 09:30
  • Related: http://physics.stackexchange.com/q/67432/2451 and links therein. – Qmechanic Oct 15 '15 at 09:37
  • No but, that question was different than this one. And once I realized it was a duplicate, I deleted it, but now it's back just to get downvoted more...? I don't understand. This is a separate question that I was not going to start over on the other post, and I think it's fair to ask since it is more general than what the related thread asked... – Striker Oct 15 '15 at 09:43
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    From the question as written, it's completely unclear what your question is since we don't know what $v^2,a$ and $d$ are. I suspect your question is why there's a constant even if $ad$ has already the correct units for $v^2$, but it is not clear at all. – ACuriousMind Oct 15 '15 at 10:48
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    Please specify what $v$,$c$,$a$ and $d$ are. – SchrodingersCat Oct 15 '15 at 10:57
  • Assuming the tags are correct, $v,,a,,d$ are velocity, acceleration & distance, no? I feel like there was a similar question just asked in the last 10 days, but can't seem to find it. – Kyle Kanos Oct 15 '15 at 11:49

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By purely dimensional analysis there is always an unknown (dimensionless) constant, as the dimensional analysis can only tell you if your units are correct. You can always multiply your equation by any number and it will still be dimensionally correct.

To look at it from the other direction, if I propose that kinetic energy is given by the equation $KE=mv^2$

Dimensionally this is correct, but clearly it is missing a factor of $1/2$ from the real equation and you cannot determine this by purely dimensional analysis. You either need to look at where the equation comes from or have some experimental data to determine what the correct constant is in any particular situation.

nivag
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