1. The problem statement, all variables and given/known data The full problem can be seen here - however, I only need help with one part: http://puu.sh/biN9W/ee2a7bf393.png [Broken] I'm not sure how to find the velocity of a particle when accelerated to the point that it exceeds or approaches the speed of light when the classical equations are used. I'd really appreciate if someone could help me with it. 2. Relevant equations K = (γ-1)mc^2 P = γmv Mass of electron: .511MeV/c^2 or 9.11*10^-31kg 3. The attempt at a solution I've got 5+ pages of scratch work scribble but I've tried many things. I've tried just using classical equations, which nets a velocity greater than the speed of light, so that can't work. I've tried finding the value of gamma from K = (γ-1)mc^2 and using that value of γ to find a velocity, but that didn't give me the correct answer either. An explanation or tips would really be appreciated. Also, another problem that I've been having a lot of trouble with can be seen here http://puu.sh/biNDy/4bdaa9d2b3.png [Broken]. This one really racks my brain. For this one, I've had two thoughts: 1. The velocity needed to travel the distance in a certain time and 2. The velocity needed to dilate time to a specific number and it's this that kills me. I feel like, as #1 changes, #2 also changes. I've tried making two equations - one setting v equal to the distance of the planet divided by time, and another one setting time equal to the time dilation equation (ΔT/sqrt(1-u^2/c^2)) Any tips for this one would also be appreciated!