How did we arrive that kinetic energy $KE = \frac{1}2 mv^2 $?

Asked Sep 28 '16 at 13:55

Active Sep 28 '16 at 14:18

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There are proofs mathematically how we get kinematics formulae. But i can't understand the proof for kinetic energy equation. I know we can proof $KE$ equation from work energy theorem but what I learned was that we arrived from that change in $KE = W$. So I want proof for $KE = \frac{1}2 mv^2$ from other ways rather than work energy theorem.

Edit:

In kinematics acceleration makes sense when we say acceleration = rate of change of velocity . Which we can arrive mathematically as $a = \frac{v_f - v_i} t$ but i am curious to find how did we $KE = ??$ mathematically?

edited Sep 28 '16 at 14:18

asked Sep 28 '16 at 13:55

Fawad

4

Possible duplicate of Why does kinetic energy increase quadratically, not linearly, with speed? – ACuriousMind Sep 28 '16 at 13:58
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@ACuriousMind I know it increases how , but i want to know how we arrive to that formula mathematically? – Fawad Sep 28 '16 at 14:00
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The other question asks "why" too, and I think the answers there should certainly answer your question - read them. If you still have a question, you might modify this one to be a bit more specific. – ACuriousMind Sep 28 '16 at 14:02
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The question is senseless. You want to prove what you have defined. KE is defined this way so theorem you wrote down will have the the best form for verbal interpretation. – Ice-Nine Sep 28 '16 at 16:24

How did we arrive that kinetic energy $KE = \frac{1}2 mv^2 $?

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