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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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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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