IOllow tnereirom. 7. Show that two successive L.T. corresponding to speeds v, and v, are equivalent to a single L.T. V +V2 corresponding to a speed of v = V V2 1+ c2 Hint: Consider three inertial frames S, S', S". Let S' move with speed v, relative to S and let S" move with speed v, relative to S'. Then x = T, (x v,t) etc. and x" = T,(x v,t) etc. - Show that x' = r,r2 1+ c2 - (V + v2)t V V2 = r,r, 1+ c2 V + v2 -t V V2 1+ c2 34 A Primer of Special Relativity V +v2 1 = T(x vt) where and v = /2 V V2 1+ c2