Temporal separation between two events, events A and B occur with the following space time coordinates in the reference frames of Figure according to the unprimed frame, (xA, tA) and (xB, tB) according to the primed frame, (xA, tA) and (xB, tB).In the unprimed frame, Δt = tB ?? tA = 1.00μs and Δx = xB ?? xA = 240 m.

(a) Find an expression for Δt in terms of the speed parameter B and the given data. Graph Δt' versus β for the following two ranges of β:

(b) 0 to 0.01 and

(c) 0.1 to 1.

(d) At what value of B is Ar' minimum and

(e) What is that minimum?

Event Unprimed Primed (xA, tA) (Xg, Ig) (xA, t) (rg, tB) x" A XA (a) Event A (b) Event B