题目

We all know the Olympic Games.___41___do you know the Mud Olympic Games which are sports games in the mud? Every year,about 400 people from all over Europe meet in a small town in northern Germany___42___(take) part in the Mud Olympics—the___43___(muddy) sports meeting in the world.It is held___44___the the beach when the tide is out,so it is very muddy.The sports meeting___45___(have) many traditional sports like football,volleyball and bicycle races,as well as some special and new activities___46___(play) in the mud.It raises money for a local charity. The advertisements of the s如图（1），直线与x轴、y轴分别交于点B、点C，经过B、C两点的抛物线与x轴的另一个交点为A，顶点为P．（1）求该抛物线的解析式及顶点P的坐标；（2）连结AC，在x轴上是否存在点Q，使以P、B、Q为顶点的三角形与△ABC相似？若存在，请求出点Q的坐标；若不存在，请说明理由；（3）动点M从B点开始沿BO边向点O以每秒2个单位的速度运动，动点N从点O开始沿OC边向点C以每秒1个单位的速度运动，当点M到达O点时，点N也随之停止运动．在整个运动过程中，求：线段MN的中点所经过的路程长．