A proton is accelerated from rest through a potential difference of 500MV. Classical mechanics indicates that quadrupling the potential difference would double the speed. Were a classical analysis valid, what speed would result from a 2000MV potential difference?
The Attempt at a Solution
We were first asked to find the original speed of the proton going through 500MV which is 0.76c Since 2000MV = 4*500MV and 4V means v is doubled, why can't I just double 0.76c to get the new speed for the proton accelerated through the 2000MV?