Take the tour ×  As Wikipedia says:  [...] the kinetic energy of
a non-rotating object of mass $m$ traveling at a speed $v$ is
$mv^2/2$.  Why does this not increase linearly with speed? Why
does it take so much more energy to go from 1 m/s to 2 m/s than
it does to go from 0 m/s to 1 m/s?  My intuition is wrong here,
please help it out!  share|improve this question It doesn't
increase exponentially (a^x); it increases quadratically (x^2).
Can you correct the title? –  nibot Nov 11 '10 at 0:09 What I
found most counter-intuitive about this is that kinetic energy
is a coordinate-dependent quantity. In a different inertial
frame, the object will have a different kinetic energy. This
contradicts the intuitive notion that kinetic energy should be
independent of the coordinate system. –  nibot Nov 11 '10 at
0:12 Did you mean quadratically ($v^2$)? Exponentially means
something different ($~\exp(v)$). I believe there is derivation
in every standard high school level textbook ($dE = F dx = m a
dx = m \frac{dv}{dt} dx