(a) Compute the four-velocity components in O of a particle whose speed in O is v in the positive x direction, by using the Lorentz transformation from the rest frame of the particle.
(b) Generalize this result to find the four-velocity components when the particle has arbitrary velocity v, with |v| < 1.
(c) Use your result in (b) to express v in terms of the components {Uα}.
(d) Find the three-velocity v of a particle whose four-velocity components are (2, 1, 1, 1).