In einstein's theory of special relativity the mass of an object moving with velocity v is m = m0 1 − v2/c2 where m0 is the mass of the object when at rest and c is the speed of light. the kinetic energy of the object is the difference between its total energy and its energy at rest: k = mc2 − m0c2. (a) show that when v is very small compared with c, this expression for k agrees with classical newtonian physics: k = 1 2 m0v2. (b) use taylor's inequality to estimate the difference in these expressions for k when |v| ≤ 50 m/s.