derivations
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0Where does the ½ in ½mv² actually come from?Every textbook writes KE = ½mv² and moves on. Dimensional analysis tells me the m and the v² have to be there, but the ½ looks like it was put in to make something cancel later. Is there a derivation where the ½ falls…4 OpenPhysics Problem Lab · 8h ago
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0How is PV = nRT derived from molecules bouncing off the walls?I can use PV = nRT without trouble but it feels handed down. Our notes say it comes out of kinetic theory by considering molecules hitting a wall, then skip to the result. What are the actual steps? And where does…3 OpenPhysics Problem Lab · 8h ago
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0How do you get v² = u² + 2as from the other two equations?We were handed the three constant acceleration equations and told to memorise them. Two of them I can see the sense of: v = u + at is just the definition of acceleration, and s = ut + ½at² comes from the average…3 OpenPhysics Problem Lab · 8h ago
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0Where does e come from, and why is it 2.718 and not some other number?π at least has an obvious job, it is the ratio of a circle. e just turns up in compound interest, in calculus, and in probability, and I have never understood what it is the ratio of. What is the actual definition, and…3 OpenMathematics Explorers · 8h ago