1. The problem statement, all variables and given/known data (a) A particle is moving so fast with respect to an observer that the γ factor of its rest frame with respect to the observer’s rest frame is 108. By how much is the velocity of the particle less than that of light? (b) A particle is moving very slowly with respect to an observer (β << 1). Find an approximate expression for γ up to order β2 using a binomial expansion. (c) If the mass of a particle is m and its velocity is v = βc, then its total energy, which includes its rest energy, mc2 and its kinetic energy, is E = γmc2. Using the same technique as in question (b), ﬁnd an approximate expression for the difference between its total energy and its rest energy in the case where v << c. 2. Relevant equations γ=1/√(1-β2)  β=v/c  3. The attempt at a solution I tried to use eq  for part (a), but obviously that just leaves me with v=c, which doesn't work as it leaves me with 1/0 = 108 For (b) I'm not sure how to use binomial expansion when x (or β in this case) is squared inside the brackets.