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# Derivation of physics formulae - is there resources for this somewhere?

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1. I understand that at University, you're expected to be able to derive physics formulae from first principles. I can kind of understand KE = 1/2 mv squared, as it's the integral of momentum with respect to velocity (when rearranged), but I don't quite understand why integration is chosen.

The same applies ad nauseum to any other formulae, whether it's Special Relativity/Lorentz Transformation or Universal Gravitation. As per title, is there any resources for this anywhere?
2. KE is integral of Force against distance.
3. (Original post by Rather_Cynical)
I can kind of understand why KE = 1/2 mv squared, as it's the integral of momentum with respect to velocity, but I don't quite understand why.
I'm happy to help, but you'll have to explain the above sentence to me...
4. I should clarify - the formula I saw was rearranged, which ended up being the integral of mv with respect to v between v and zero. I know the formula starts off with force and displacement

(Original post by Blank_Planet)
I'm happy to help, but you'll have to explain the above sentence to me...
That's an interesting blunder. I mean I can see how the mathematics is being manipulated (basic calculus) but I don't understand the reasoning behind the choice to integrate.
5. (Original post by Rather_Cynical)
I should clarify - the formula I saw was rearranged, which ended up being the integral of mv with respect to v between v and zero. I know the formula starts off with force and displacement

That's an interesting blunder. I mean I can see how the mathematics is being manipulated (basic calculus) but I don't understand the reasoning behind the choice to integrate.
Integration gives you the area under the curve.

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