As shown in figure 1, in the rhombus ABCD, ∠ A = 60, point P starts from A and moves uniformly along AB, BC and CD at a speed of 2cm/s until the end point D, while point Q starts from A and P at the same time and moves uniformly along AD until the end point D, and the set time for point P to move is t(s). △ the area S(cm2) of apq is equal to the area of d.
(1) Find the speed of Q;
(2) Find the functional relationship of the line segment FG in Figure 2;
(3) Q: Is there such a T, PQ that can exactly divide the area of rhombic ABCD into 1: 5? If it exists, find the value of such t; If it does not exist, please explain why.
Solution: