题目内容
如图所示,AB为粗糙程度不变的水平地面,BC为粗糙程度不变的斜面,B点有微小的圆弧与两个面相切过渡。一物体(可看作质点)从A点以某一速度出发做匀减速运动并冲上斜面BC直到速度为零,以出发点为计时起点,各时间点的速度如下表所述。试求物体在斜面上运动的最远距离。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021410245964.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021410245964.jpg)
t(s) | 0 | 1 | 2 | 3 | 4 | 5 |
V(m/s) | 15 | 13 | 11 | 8 | 4 | 0 |
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141040682.png)
试题分析:从表中可得物体在AB方向上运动的加速度为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141071652.png)
在BC方向上运动的加速度为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141087657.png)
设物体在AB方向上运动的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141102291.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141118611.png)
设物体在BC方向上运动的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141180327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141196596.png)
又知道
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141196542.png)
联立解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141227601.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002141227862.png)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021412431345.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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