题目内容
(12分)甲车以加速度a1=3m/s2由静止开始作匀加速直线运动,乙车落后t0=2s钟在同一地点由静止开始,以加速度a2=4m/s2作匀加速直线运动,两车的运动方向相同,求:
(1)在乙车追上甲车之前,两车距离的最大值xm是多少?
(2)乙车出发后经多长时间t可追上甲车?此时它们离开出发点x多远?
(1)在乙车追上甲车之前,两车距离的最大值xm是多少?
(2)乙车出发后经多长时间t可追上甲车?此时它们离开出发点x多远?
(1)
(2) ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241437331911099.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733004347.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241437331911099.png)
(1)设两者达速度相同时,乙运动的时间为
,则甲运动的时间为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733285285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733379510.png)
得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733441293.png)
两者的最大距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733488875.png)
得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733004347.png)
(2)设乙运动时间
后追上甲
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733659824.png)
得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241437337371003.png)
X=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241437331911099.png)
本题考查匀变速执行那运动的追击问题,当辆汽车速度相等时距离最大,由速度相同可求得运动时间,再由运动学公式求得两汽车位移,从而求得距离差值,设乙运动时间t后追上甲车,位移相同,由运动时间相差2s可求得运动时间,从而求得乙车运动位移大小
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733238195.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733285285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733379510.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733441293.png)
两者的最大距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733488875.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733004347.png)
(2)设乙运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733628177.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143733659824.png)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241437337371003.png)
X=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241437331911099.png)
本题考查匀变速执行那运动的追击问题,当辆汽车速度相等时距离最大,由速度相同可求得运动时间,再由运动学公式求得两汽车位移,从而求得距离差值,设乙运动时间t后追上甲车,位移相同,由运动时间相差2s可求得运动时间,从而求得乙车运动位移大小
![](http://thumb2018.1010pic.com/images/loading.gif)
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