23.如圖,在Rt△ABC中,∠C=90°,AB=5,BC=3,點(diǎn)D為邊AB的中點(diǎn).點(diǎn)P從點(diǎn)A出發(fā),以每秒2個(gè)單位長(zhǎng)度的速度沿A-C-A的方向勻速運(yùn)動(dòng),回到點(diǎn)A時(shí)停止運(yùn)動(dòng),同時(shí)點(diǎn)Q從點(diǎn)C出發(fā),以每秒1個(gè)單位長(zhǎng)度的速度沿CB向終點(diǎn)B勻速運(yùn)動(dòng).點(diǎn)P不與點(diǎn)A、C重合.連接PQ、DP、DQ.設(shè)點(diǎn)P的運(yùn)動(dòng)時(shí)間為t(s).
(1)當(dāng)點(diǎn)P從點(diǎn)A向點(diǎn)C運(yùn)動(dòng)時(shí),AP=
;當(dāng)點(diǎn)P從點(diǎn)C向點(diǎn)A運(yùn)動(dòng)時(shí),AP=
.(用含t的代數(shù)式表示)
(2)當(dāng)DP⊥AB時(shí),求t的值.
(3)當(dāng)△CPQ與△ABC相似時(shí),求t的值.
(4)當(dāng)點(diǎn)P從點(diǎn)A向點(diǎn)C運(yùn)動(dòng)時(shí),作點(diǎn)A關(guān)于直線DP的對(duì)稱點(diǎn)A′,點(diǎn)A′不與△ABC的頂點(diǎn)重合,連結(jié)A′P,當(dāng)A′P與△ABC某一邊垂直時(shí),直接寫出t的值.