题目内容
汽车前方120m有一自行车正以6m/s的速度匀速前进,汽车以18m/s的速度匀速追赶自行车,若两车在同一条公路作同方向的直线运动,求:
(1)经多长时间,两车第一次相遇?
(2)若汽车追上自行车后立即刹车,汽车刹车过程中的加速度大小为2m/s2,则再经多长时间两车第二次相遇?
(1)经多长时间,两车第一次相遇?
(2)若汽车追上自行车后立即刹车,汽车刹车过程中的加速度大小为2m/s2,则再经多长时间两车第二次相遇?
(1)10s,(2)13.5s
试题分析:(1)设经
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155958790291.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155958899631.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155958993479.png)
所以经过10s两车第一次相遇.
(2)汽车的加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959087597.png)
设第二次追上所用的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959149327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959227820.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959352504.png)
设汽车从刹车到停下用时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959477327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959570594.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959695577.png)
停止前汽车的位移
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959867787.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959945321.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160000023758.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160000132545.png)
故再经过13.5s两车第二次相遇
点评:本题一定要注意汽车刹车停止时自行车还没追上汽车,不能直接用
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824155959227820.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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