Question

Find the potential difference required to accelerate protons from rest to 10% of the speed of light. (at this point, relativistic effects start to become significant.)

Answer 1

I don't know much about the potential difference but I certainly can calculate the energy of the proton from rest to 10% of the speed of light.

Special relativity tells us that "the energy needed to accelerate a particle (with mass) grow super-quadratically when the speed is close to c, and is ∞ when it is c."

Expressed the theory in equation is as follows:

ENERGY  = rest mass × speed of light squared / (1−(“percent of speed of light”)squared )  = mc2/(1-("percent of speed of light")2)

Just plug-in the values and you can now have the answer what you are looking for!