Inertial system S moves in the x direction at speed 3/5-c relative to system S. (The x axis slides long the x axis, and the origins coincide at t = t = 0, as usual.)

(a) On graph paper set up a Cartesian coordinate system with axes ct and x. Carefully draw in lines representing x = – 3, –2, – 1, 0, 1, 2, and 3. Also draw in the lines corresponding to ct = –3, –2, –1, 0, 1,2, and 3. Label your lines clearly.

(b) In S, a free particle is observed to travel from the point x = –2 at time ct = –2 to the point x = 2 at ct = + 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).