题目内容
(1)加速运动的时间和减速运动的时间之比;
(2)AB的总长度。
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115542830609.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115542814453.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115542830609.gif)
(1)设质点做加速直线运动的时间为
,减速直线运动的时间为
,
则
① (2分)
由题可得加速运动的末速度等于减速运动的初速度,由
得
②(3分)
所以加速运动的时间和减速运动的时间之比为:
(2分)
(2)由
,
得:
AB的长度为
③(3分)
由①②③得
(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115542876199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115542970204.gif)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115542986270.gif)
由题可得加速运动的末速度等于减速运动的初速度,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115543017418.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115543064570.gif)
所以加速运动的时间和减速运动的时间之比为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115542814453.gif)
(2)由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115543095523.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115543110514.gif)
AB的长度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115543126714.gif)
由①②③得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115542830609.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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