1. The problem statement, all variables and given/known data (a) A spaceship at rest in a certain reference frame S is given a speed increment of 0.50c. Relative to its new frame, it is then given a further 0.50c increment.This process is continued until its speed with respect to its original frame S exceeds 0.999c. How many increments does this process require? (b) The job of the Stanford Linear Accelerator Center (SLAC) in the United States is to accelerate electrons to very high energies, to crash these electrons into things and then to see what happens. The acceleration is accomplished with a 3.2 km long linear accelerator (linac) which is capable of accelerating electrons such that each electron will have energy of 50 GeV at the exit point of the accelerator.i. Assuming that the electrons accelerate constantly down the linac, what is the speed of the electron after going 1 m down the accelerator? ii. When the electrons exit the linear accelerator, magnets are used to curve the electron beams. Construction plans indicate that the radius of the curvature is 280 m. By considering the momentum of these now relativistic electrons, what is the minimum magnetic ﬁeld required to curve the electron beams? 2. Relevant equations v = (v' + u)/(1 + uv/c2) where v is velocity measured by stationary observer v' velocity measured by moving observer and u is the relative velocity between s and s' in this case 0.5c Etotal = ϒ mo c2\ vf = √(2 a Δx) where a is acceleration and Δx is distance covered when starting from 0 velocity 3. The attempt at a solution ok for the first part my attempt was just to write down the velocities after three increments and soon realized it was too tedious is there some kind of geometric progression that the velocities after increments follow. not putting my working here because it just pure math mess. for part b) i used the fact that the final energy is related to its final velocity by vfinal =√(1 - mo2c4/Etotal2) c is there anything wrong with the equation on top because when i plug in i get 0.followed by 10 9s. assuming that was correct although i highly doubted it i continued and calculated the acceleration in the accelerator by the above equation in relevant equations. then i calculated velocity at 1m to get 0.017c which is completely off can someone help me what is wrong with my working if you dont understand my working please ask me i will gladly make it clearer to you thanks for your help!