(2013•黃岡)如圖,在平面直角坐標(biāo)系中,四邊形ABCD是梯形,其中A(6,0),B(3,
),C(1,
),動(dòng)點(diǎn)P從點(diǎn)O以每秒2個(gè)單位的速度向點(diǎn)A運(yùn)動(dòng),動(dòng)點(diǎn)Q也同時(shí)從點(diǎn)B沿B→C→O的線(xiàn)路以每秒1個(gè)單位的速度向點(diǎn)O運(yùn)動(dòng),當(dāng)點(diǎn)P到達(dá)A點(diǎn)時(shí),點(diǎn)Q也隨之停止,設(shè)點(diǎn)P,Q運(yùn)動(dòng)的時(shí)間為t(秒).
(1)求經(jīng)過(guò)A,B,C三點(diǎn)的拋物線(xiàn)的解析式;
(2)當(dāng)點(diǎn)Q在CO邊上運(yùn)動(dòng)時(shí),求△OPQ的面積S與時(shí)間t的函數(shù)關(guān)系式;
(3)以O(shè),P,Q頂點(diǎn)的三角形能構(gòu)成直角三角形嗎?若能,請(qǐng)求出t的值;若不能,請(qǐng)說(shuō)明理由;
(4)經(jīng)過(guò)A,B,C三點(diǎn)的拋物線(xiàn)的對(duì)稱(chēng)軸、直線(xiàn)OB和PQ能夠交于一點(diǎn)嗎?若能,請(qǐng)求出此時(shí)t的值(或范圍),若不能,請(qǐng)說(shuō)明理由).