A spaceship starts at rest with respect to frame S and accelerates with constant proper acceleration α. In Section 10.7, we showed that the speed of the spaceship with respect to S is given by v(τ) = tanh(α τ), where ¿ is the spaceship’s proper time (and c = 1). Let V be the spaceship’s 4-velocity, and let A be its 4-acceleration. In terms of the proper time τ,
(a) Find V and A in frame S, by explicitly using v(τ) = tanh(α τ).
(b) Write down V and A in the spaceship’s frame, S’.
(c) Verify that V and A transform like 4-vectors between the two frames.