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1.
(2023高二下·辽宁期末)
滑草超级大滑梯深受大人和小孩的喜爱。滑草大滑梯由倾角为
的倾斜滑道和水平滑道平滑连接,如图所示。某同学坐在滑垫上从A点由静止下滑,在倾斜部分做匀加速直线运动,经过B点后在水平部分开始做匀减速直线运动,最后停在C点,整个过程中人与草坪不接触。从刚下滑开始计时,运动过程中该同学的速度大小与对应的时刻如表所示,求:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmath%3E)
| 0.0 | 1.0 | 2.0 | … | 9.0 | 10 | 11 | … |
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmo%3E%E2%8B%85%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
| 0.0 | 2.0 | 4.0 | … | 11 | 6.0 | 1.0 | … |
![](//tikupic.21cnjy.com/2023/08/19/a0/24/a024ff47b3d82ee2b563a4d15bdfa545_344x124.png)
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(1)
滑垫运动的总时间
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3E%E6%80%BB%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
;
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(2)
滑垫经过
B点时的速度大小
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
。
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