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【简答题】
如图，在直角梯形OABC中，OA∥CB，A、B两点的坐标分别为A（15,0），B（10,12），动点P、Q分别从O、B出发，点P以每秒2个单位长度的速度沿OA向终点A运动，点Q以每秒1个单位的速度沿BC向终点C运动，当点P停止运动时，点Q也同时停止运动。线段OB、PQ相交D，过点D作DE∥OA，交ABE，连接QE并延长，交x轴F。设动点P、Q的运动时间为t（单位：秒） （1）当t为何值时，四边形PABQ是等腰梯形？ （2）当t=2秒时，求梯形OFBC的面积； （3）是否存在点P，使△PQF是等腰三角形？若存在，请求出点P的坐标；若不存在，请说明理由。
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