Relativity .... Why C in...... E = M C 2?

"Relativity .... Why C in...... E = M C 2?"

Why v in KE = 1/2mv^2?

"Einstein s famous equation defines the equivalence of energy and mass,

Not equivalence, interchangeability. Energy moves at c, mass cannot.

"but why does the speed of light (squared) become involved in this relationship?"

It is called "dimensional analysis". One of our most powerful tools.

http://en.wikipedia.org/wiki/Dimensional_analysis

Kinetic Energy is the integral of momentum time derivative with respect to distance. But momentum involves velocities and in relativity velocity transformations have c squared in the relationship; it is involved under the integral sign but because its a constant it comes out from under the integral sign intact. That's the short answer if you want the actual derivation pick up any text in Modern Physics or Relativity.

The link below shows how c² gets into relativity calculations. It actually happened before Einstein's developed E = mc²