[UPSC CSE 2024] Special Theory of Relativity (Q322, 15M)

Consider three inertial frames of reference O, O' and O''. Let O' move with a velocity V with respect to O and O'' move with a velocity V' with respect to O'. Both velocities are in the same direction. Write down the transformation equations relating x, y, z, t with x', y', z', t' and also those relating x', y', z', t' with x'', y'', z'', t''. Hence obtain the relations between x, y, z, t and x'', y'', z'', t''. (The direction of velocity is chosen along the x-axis as per convention)