题目内容
火车正以108km/h的正常速度行驶着,因前方出现意外情况而临时停车.停车前做加速度为
的匀减速运动,停止1min30s,又以
的加速度启动匀加速运动行驶,直到速度恢复正常为止.求因临时停车而延误的时间.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423792378.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423807421.gif)
135s
设火车正常行驶的速度为
,减速时的加速度为
,
则火车减速所需时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423854662.gif)
减速行驶距离![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423885773.gif)
设加速时的加速度为
,则火车加速过程所需时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423932670.gif)
加速行驶的距离![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423948791.gif)
于是此过程经历的总时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423963768.gif)
行驶的距离![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423979549.gif)
而正常情况下驶过这段距离所需时间为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423994681.gif)
故延误的时间是![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114424182537.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423823185.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423838208.gif)
则火车减速所需时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423854662.gif)
减速行驶距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423885773.gif)
设加速时的加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423901209.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423932670.gif)
加速行驶的距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423948791.gif)
于是此过程经历的总时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423963768.gif)
行驶的距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423979549.gif)
而正常情况下驶过这段距离所需时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114423994681.gif)
故延误的时间是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114424182537.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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