题目内容
质点由A点出发沿直线AB运动,行程的第一部分是加速度为
的匀加速运动,接着做加速度为
的匀减速直线运动,抵达B点时恰好静止,如果AB的总长度为S,试求质点走完AB全程所用的时间t?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114424868206.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114424884208.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114424962670.gif)
设质点的最大速度为V,前、后两段运动过程平均速度相等,均为
.
全过程:
……(1)
匀加速过程:
……(2)
匀减速过程:
……(3)
由(2)(3)代入(1)得:
即
将V代入(1)得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144251491127.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114424977223.gif)
全过程:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114425008728.gif)
匀加速过程:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114425040376.gif)
匀减速过程:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114425086389.gif)
由(2)(3)代入(1)得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114425118585.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114425133640.gif)
将V代入(1)得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144251491127.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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