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【简答题】
如图，在平面直角坐标系中，点O为坐标原点，A点的坐标为(3，0)，以OA为等边三角形OAB，点B在第一象限，过点B作AB的垂线交x轴C．动点P从O点出发沿OC向C点运动，动点Q从B点出发沿BA向A点运动，P，Q两点同时出发，速度均为1个单位／秒。设运动时间为t秒． （1）求线段BC的长； （2）连接PQ交线段OBE，过点E作x轴的平行线交线段BCF。设线段EF的长为m，求m与t之间的函数关系式，并直接写出自变量t的取值范围： （3）在（2）的条件下，将△BEF绕点B逆时针旋转得到△BE′F′，使点E的对应点E′落在线段AB上，点F的对应点是F′，E′F′交x轴G，连接PF、QG，当t为何值时， ?
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