题目内容
(12分)甲、乙两个小朋友玩跑步游戏.甲从静止开始起跑,经过
=5m距离能加速到最大速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416493213.gif)
,并能维持一段较长时间。乙从静止开始起跑,经过
=6m的距离能加速到最大速度
,以后只能维持这个速度
。设乙距离甲
时开始追击,而甲在乙开始跑后
后才开始起跑,假定甲、乙在加速阶段分别做匀加速运动,且均沿同一直线奔跑,求:
(1)求出甲乙加速度大小以及加速时间.
(2)乙要在自己匀速阶段追上甲,
值应在什么范围?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416477197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416493213.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416508387.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416539200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416555430.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416571244.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416586329.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416602237.gif)
(1)求出甲乙加速度大小以及加速时间.
(2)乙要在自己匀速阶段追上甲,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416617187.gif)
(1)
,
;
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416742367.gif)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416758584.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416695550.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416711263.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416711508.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416742367.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416758584.gif)
(1)根据
,得到甲的加速度大小为
——1分
根据
,得到乙的加速度大小为
——1分
根据
,得甲的加速时间为
——1分
根据
,得乙的加速时间为
——1分
(2)
若要求乙要在自己匀速阶段追上甲,则乙的运动时间为4秒末到8秒末
I:乙运动的时间为4s
乙在前4s内刚好加速到最大速度,所以位移为
——1分
而此时甲匀加速运动了3s钟,所以
——1分
值为
——1分
II:乙运动时间为8s
乙在4s到8s一直匀速运动,所以位移为
——1分
乙向前运动了![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416976545.gif)
而甲匀加了4s,运动了
="5m " ——1分
又匀速了3s,所以
, ——1分
甲向前运动了![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122417007552.gif)
值为
——1分
所以,
——1分
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416773422.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416695550.gif)
根据
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416805430.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416711508.gif)
根据
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416836374.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416711263.gif)
根据
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416851388.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416742367.gif)
(2)
若要求乙要在自己匀速阶段追上甲,则乙的运动时间为4秒末到8秒末
I:乙运动的时间为4s
乙在前4s内刚好加速到最大速度,所以位移为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416898401.gif)
而此时甲匀加速运动了3s钟,所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416914697.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416617187.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416945576.gif)
II:乙运动时间为8s
乙在4s到8s一直匀速运动,所以位移为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416945492.gif)
乙向前运动了
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416976545.gif)
而甲匀加了4s,运动了
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416477197.gif)
又匀速了3s,所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416992490.gif)
甲向前运动了
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122417007552.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416617187.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122417054519.gif)
所以,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122416758584.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目