Electrodynamics and Relativity — David J. Griffiths
Physics · spacetime-diagrams
Problem
Inertial system Sˉ moves in the x direction at speed 53c relative to system S. (The xˉ axis slides along the x axis, and the origins coincide at t=tˉ=0, as usual.)
(a) On graph paper set up a Cartesian coordinate system with axes ct and x. Carefully draw in lines representing xˉ=−3,−2,−1,0,1,2, and 3. Also draw in the lines corresponding to ctˉ=−3,−2,−1,0,1,2, and 3. Label your lines clearly.
(b) In Sˉ, a free particle is observed to travel from the point xˉ=−2 at time ctˉ=−2 to the point xˉ=2 at ctˉ=+3. Indicate this displacement on your graph. From the slope of this line, determine the particle's speed in S.
(c) Use the velocity addition rule to determine the velocity in S algebraically, and check that your answer is consistent with the graphical solution in (b).