通过“30m折返跑”的测试成绩可以反应一个人的身体素质。在平直的跑道上一学生站立在起点线A处,当听到起跑口令后(测试员同时开始计时),跑向正前方30m处的折返线,到达折返线B处时,用手触摸固定在折返线处的标杆,再转身跑回起点线,返程无需减速,到达起点线处时停止计时,全过程所用时间即为折返跑的成绩。学生加速或减速过程均视为匀变速,触摸杆的时间不计,某同学加速时的加速度大小为
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2.5%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmsup%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
, 减速时的加速度大小为
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmsup%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
, 到达折返线处时速度需减小到零,并且该生全过程中最大速度不超过
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E12%3C%2Fmn%3E%3Cmi+mathvariant%3D%22normal%22%3Em%3C%2Fmi%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Es%3C%2Fmi%3E%3C%2Fmath%3E)
。 求:
(1)该学生返程(B到A过程)最快需多少时间;
(2)该学生“30m折返跑”的最好成绩。