The kinetic formula are EK=1/2*m*v^2. But how do we find it?
Looks like you already found it!
What do you mean? (How you would find the kinetic energy in a particular problem will depend on the details of that problem.)
Maybe he/she meant to ask how the formula is derived.
The simplest derivation is to consider how much work is done to accelerate an object to velocity v. Lets say we use constant force to accelerate the object over some distance d.
F = ma -> a = F/m (From Newton's 2nd)
W = F*d (From definition of work.)
v² = 2*a*d (Let us know if you need help deriving this one, but you should have seen it.)
Putting it all together.
v² = 2*d*a = 2*d*(F/m) = 2*(d*F)/m = 2*W/m
W = (m*v²)/2
So the amount of work required to accelerate (or decelerate, for that matter) an object of mass m to velocity v is (1/2)*m*v². Hence the Kinetic Energy.
Anyone else want to guess what the OP's real question was?
I've always found that to be the real challenge of explaining physics to someone. Once you understand what it is that the person actually wants to know or doesn't understand, explaining it is easy.
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