Einstein's formula is E=mc^2; but the formula for kinetic energy is 1/2 mv^2; why the difference?

You have to use both of them [

]

The Total enenergy E of a free particle with mass m and speed v is, *at non relativistic speeds*:

E = mc

^{2} + 1/2 mv

^{2}because it's the sum of "rest energy" (the first term) and kinetic energy (the second).

But that equation is not much used because it's "half relativistic and half not" since it uses E = mc

^{2} which is usually used only in SR, since in newtonian mechanics is a constant term and it's omitted, while the term 1/2 mv

^{2} is the kinetic energy only at low speeds.

If you use this one, you are always correct, in newtonian mechanics as well as in SR, even with zero-mass particles:

E

^{2} = (mc

^{2})

^{2} + (cp)

^{2}p is the particle's momentum.

for zero-mass particles: p = h[tex]\nu[/tex]/c ; [tex]\nu[/tex] = particle's frequency

for non zero-mass particles: p = mv/sqrt[1 - (v/c)

^{2}] ; v = particle's velocity.