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1、第课时匀变速直线运动的规律及特例 【测控导航】知识点题号1.匀变速直线运动基本公式的应用5、6、7、10、122.匀变速直线运动推论的应用2、3、83.自由落体运动1、4、94.竖直上抛运动1115题为单选题;69题为多选题1.(2011年重庆卷)某人估测一竖直枯井深度,从井口静止释放一石头并开始计时,经2 s听到石头落底声,由此可知井深约为(不计声音传播时间,重力加速度g取10 m/s2)(B)A.10 mB.20 mC.30 mD.40 m解析:石头下落看做自由落体,则h=gt2=20 m.2.(2011年安徽卷)一物体做匀加速直线运动,通过一段位移x所用的时间为t1,紧接着通过下一段位移
2、x所用的时间为t2,则物体运动的加速度为(A)A.B.C.D.解析:物体做匀加速直线运动,故某段时间内的平均速度等于中间时刻的瞬时速度.设v1=,v2=,由加速度定义式a=得a=,故选项A正确,选项B、C、D错误.3.(2013重庆市一中摸底)飞机从停机坪沿直线滑出,在第1秒内、第2秒内、第3秒内的位移分别是2 m、4 m、6 m,那么(D)A.飞机做匀加速运动B.飞机做匀速运动C.3秒内的平均速度是2 m/sD.3秒内的平均速度是4 m/s解析:由题意不能确定飞机是否做匀加速运动,而且飞机不是做匀速运动,选项A、B错误;3秒内的平均速度是= m/s=4 m/s,选项D正确,C错误.4.(20
3、12北京朝阳区一模)科技馆里有一个展品,该展品放在暗处,顶部有一个不断均匀向下喷射水滴的装置,在频闪光源的照射下,可以看到水滴好像静止在空中固定的位置不动,如图所示.某同学为计算该装置喷射水滴的时间间隔,用最小刻度为毫米的刻度尺测量了空中几滴水间的距离,由此可计算出该装置喷射水滴的时间间隔为(g取10 m/s2)(C)A.0.01 sB.0.02 sC.0.1 sD.0.2 s解析:第1滴水滴与第2滴水滴的间距为h1=10.0 cm-1.0 cm=9.0 cm,第2滴与第3滴的间距为h2=29.0 cm-10.0 cm=19.0 cm,所以相邻水滴间距之差为h=h2-h1=19.0 cm-9.
4、0 cm=10.0 cm=0.1 m,根据公式h=gT2可知,该装置喷射水滴的时间间隔为T= s=0.1 s.答案为C.5.(2012云南联考)汽车以24 m/s的速度在平直公路上行驶,急刹车时的加速度大小为4 m/s2,则自驾驶员急踩刹车开始,2 s末与5 s末时汽车的位移之比为(B)A.54B.47C.34D.43解析:自驾驶员急踩刹车开始,经过t0=v0/a=6 s汽车停止运动,所以2 s末汽车的位移为x1=v0t1-a=40 m,5 s末汽车的位移为x2=v0t2-a=245 m-452 m=70 m,所以x1x2=47.6.(2013济南外国语学校期中)给滑块一初速度v0,使它沿光滑
5、斜面向上做匀减速运动,加速度大小为,当滑块速度大小变为时,所用时间可能是(BC)A.B.C.D.解析:滑块末速度方向可能沿斜面向上,也可能沿斜面向下,即vt=或vt=,所以运动时间可能是t=或t=,故选项B、C正确.7.(2012西安质检)一辆汽车拟从甲地开往乙地,先由静止启动做匀加速直线运动,然后保持匀速直线运动,最后做匀减速直线运动,当速度减为0时刚好到达乙地.从汽车启动开始计时,如表给出了某些时刻汽车的瞬时速度,据表中的数据通过分析、计算可以得出汽车(AC)时刻/s1.02.03.05.07.09.510.5速度/(ms-1)3.06.09.012129.03.0A.匀加速直线运动经历的
6、时间为4.0 sB.匀加速直线运动经历的时间为5.0 sC.匀减速直线运动经历的时间为2.0 sD.匀减速直线运动经历的时间为4.0 s解析:汽车做匀加速直线运动的加速度为a1= m/s2=3.0 m/s2,匀加速直线运动经历的时间t1= s=4.0 s,选项A正确,选项B错误;汽车做匀减速直线运动的加速度大小为a2= m/s2=6.0 m/s2,匀减速直线运动经历的时间t2= s=2.0 s,选项C正确,选项D错误.8.(2013宜宾二中高三上学期期中)完全相同的三个木块并排地固定在水平面上,一颗子弹以速度v水平射入,若子弹在木块中做匀减速直线运动,且穿过第三块木块后速度为零,则子弹依次射入
7、每一木块时的速度比和穿过每一木块所用时间比分别是(BD)A.v1v2v3=321B.v1v2v3=1C.t1t2t3=1D.t1t2t3=(-)(-1)1解析:子弹受到的摩擦力f一定,故加速度也一定,由x=at2和x1=x2=x3得,t1t2t3=(-)(-1)1由v=at得,v1v2v3=(t1+t2+t3)(t2+t3)t3=1,故选项B、D正确.9.如图所示,小球从竖直砖墙某位置静止释放,用频闪照相机在同一底片上多次曝光,得到了图中1、2、3、4、5所示小球运动过程中每次曝光的位置.连续两次曝光的时间间隔均为T,每块砖的厚度为d.根据图中的信息,下列判断正确的是(BCD)A.位置“1”是
8、小球释放的初始位置B.小球做匀加速直线运动C.小球下落的加速度为D.小球在位置“3”的速度为解析:由题图可知相邻相等时间间隔的位移差都为d,选项B对;由x=aT2=d可知选项C对;位置“3”是小球从位置“2”到位置“4”的中间时刻,据推论有v3=,选项D对;位置“1”到位置“2”的距离与位置“2”到位置“3”的距离之比为23,位置“1”不是小球释放的初始位置,选项A错.10.(2013重庆市一中摸底)以72 km/h的速度行驶的列车,临时需要在某中途车站停车,因此以大小为0.4 m/s2的加速度减速进站,停车2 min,然后以0.5 m/s2的加速度匀加速出站,最后恢复原运行速度.试计算该列车
9、此次因临时停车共耽误多长时间.解析:根据题意,列车匀减速运动阶段,v0=72 km/h=20 m/s,a1=-0.4 m/s2,vt=0,由vt=v0+a1t1解得列车匀减速运动时间t1=50 s.匀减速运动位移x1=v0t1+a1=500 m.停车时间t2=2 min=120 s.匀加速运动阶段,v0=0,a2=0.5 m/s2,vt=20 m/s.由vt=v0+a2t3解得列车匀加速运动时间t3=40 s.匀加速运动位移x2=a2=400 m.因临时停车行驶总位移x=x1+x2=900 m,时间t=t1+t2+t3=210 s,若不停车,列车匀速运动需要时间t=x/v0=45 s.此次因临
10、时停车共耽误时间t=t-t=210 s-45 s=165 s.答案:165 s11.(2012德州模拟)在竖直的井底,将一物块以11 m/s的速度竖直地向上抛出,物块冲过井口时被人接住,在被人接住前1 s内物块的位移是4 m,位移方向向上,不计空气阻力,g取10 m/s2,求:(1)物块从抛出到被人接住所经历的时间;(2)此竖直井的深度. 解析:(1)设被人接住前1 s时刻物块的速度为v,则h=vt-gt2故v= m/s=9 m/s则物块从抛出到被人接住所用总时间为t=+t= s+1 s=1.2 s.(2)竖直井的深度为h=v0t-gt2=111.2 m-101.22 m=6 m.答案:(1)
11、1.2 s(2)6 m12.(2013成都六校联考)卡车原来以10 m/s的速度在平直公路上匀速行驶,因为路口出现红灯,司机从较远的地方开始刹车,使卡车匀减速前进,当车减速到2 m/s时,交通灯转为绿灯,司机当即停止刹车开始加速,并且只用了减速过程的一半时间就加速到原来的速度,从刹车开始到恢复原速共用了12 s.求:(1)减速与加速过程中的加速度大小;(2)开始刹车后2 s末及10 s末的瞬时速度大小.解析:(1)卡车先做匀减速运动,再做匀加速运动,其运动简图如图所示,设卡车从A点开始减速,则vA=10 m/s,用了t1时间到达B点,从B点又开始加速,用时t2到达C点,则vB=2 m/s,vC
12、=10 m/s,且t2=t1,t1+t2=12 s,可得t1=8 s,t2=4 s.由v=v0+at得,在AB段,vB=vA+a1t1在BC段,vC=vB+a2t2联立两式,并代入数据解得:a1=-1 m/s2,a2=2 m/s2.(2)2 s末的速度为v1=vA+a1t=10 m/s-12 m/s=8 m/s,10 s末的速度为v2=vB+a2t=2 m/s+2(10-8)m/s=6 m/s.答案:(1)1 m/s22 m/s2(2)8 m/s6 m/s以下是大学体验英语综合教程2(第三版)课后翻译答案Unit11. 任何年满18岁的人都有资格投票。(be eligible to, vote
13、)Answer:Anyone over the age of 18 is eligible to vote.2. 每学期开学前，这些奖学金的申请表格就会由学校发给每一个学生。(apply for, scholarship)Answer:A form to apply for these scholarships is sent by the university to every student before the start of every semester.3. 遵照医生的建议，我决定戒烟。(on the advice of)Answer:On the advice of my doc
14、tor, I decided to give up smoking.4. 公园位于县城的正中央。(be located in)Answer:The park is located right in the center of town.5. 这所大学提供了我们所需的所有材料和设备。(facilities)Answer:The university provides all the materials and facilities we desire.1. 他们花了多年的时间寻找内心的平静，但是收效甚微。(search for)Answer:They spent many years searc
15、hing for peace of mind, but with little success.2. 这种新药的成功研制已经使许多疾病的治疗发生了根本性的变革。(revolutionize)Answer:The successful development of the new drug has revolutionized the treatment of many diseases.3. 由于这个国家的经济不景气，这家公司濒于破产。(on the edge of)Answer:The company is on the edge of bankruptcy due to the econo
16、mic depression in the country.4. 大学毕业后他成为了一名护士。他认为护士这一职业可能很有发展前途。(rewarding)Answer:He became a nurse after college. He thought nursing could be a very rewarding career.5. 他像往常一样在文件上签了名。(just as)Answer:He signed his name on the paper just as he has always done it.Unit21. 警察们正忙着填写关于这场事故的各种表格。(fill out
17、)Answer:The policemen are busy fi lling out forms about the accident.2. 我想在还车之前把油箱加满。(fill up, fuel tank)Answer:I want to fi ll up the fuel tank before returning the car.3. 如果你要投诉，最好遵循正确的程序。(follow the procedure)Answer:If you want to make a complaint, youd better follow the correct procedure.4. 要不是约
18、翰帮忙，我们绝不会这么快就完成实验。(without)Answer:We couldnt have fi nished the experiment so soon without Johns help.5. 暴风雨之后，岸边的人们焦急地搜索湖面以期发现小船的踪迹。(scan for)Answer:After the storm, the people on the shore anxiously scanned the lake for any sign of the boat.1. 这个国家不大，但是在国际事务中它却发挥着重要作用。(play a role)Answer:This coun
19、try is not big, but it plays an important role in international affairs.2. 正是在我叔叔的帮助下，我得以克服困难，按时完成了任务。(it is . that)Answer:It was with the help of my uncle that I overcame the difficulty and completed the assignment in time.3. 毕业时他决定留在北京，而他最好的朋友却选择了去西藏。(while)Answer:While he decided to stay in Beiji
20、ng upon graduation, his best friend chose to go to Tibet.4. 在这次校园英语演讲比赛中，我们班的玛丽获得了第三名。(come in)Answer:In this Campus English Speaking Contest, Mary from our class came in third.5. 你应该知道学习弹钢琴需要有时间，有金钱，还要有毅力。(as well as)Answer:You should know that it takes time, money as well as perseverance to learn
21、to play the piano.Unit31. 我发现量入为出地过日子越来越难了。(increasingly)Answer:I find it increasingly difficult to live within my income.2. 现代政治家们都试图以电视讲话来影响普通百姓。(reach out)Answer:Modern politicians try to reach out to ordinary people in their TV speeches.3. 应该帮助学生对人生采取积极的态度。(adopt)Answer:Pupils should be helped t
22、o adopt a positive attitude to life.4. 希望全班同学参加这些讨论。(participate in)Answer:Everyone in the class is expected to participate in these discussions.5. 如果你犯了罪就必须受到惩罚。(crime)Answer:If you commit a crime you must expect to be punished.1.儿子的死让老妇人变得麻木痴呆了。(numb)Answer:The old woman was numbed by her sons dea
23、th.2.身处所有这些烦恼之中，他依然能保持乐观。(in the midst)Answer:In the midst of all troubles, he managed to remain cheerful.3. 虽有困难，他们还是设法坚持试验下去。(carry on)Answer:They managed to carry on their experiments in spite of the difficulties.4.我们必须淘汰不合格的申请人。(weed out)Answer:We have to weed out unqualified applicants.5. 医生要他减
24、少抽烟。(cut down on)Answer:The doctor told him to cut down on smoking.Unit41.她在公共汽车站一直等到末班车进站。(come in)Answer:She waited at the bus stop until the last bus came in.2.如果我们能帮得上忙，尽管和我们联系。(contact)Answer:If there is any way we can be of assistance, please do not hesitate to contact us.3 .他需要多少船务人员才能使他的游艇航行
25、？(crew, yacht)Answer:How many crew does he need to sail his yacht?4 .虽然她的新书没有上一本好，但是我还是喜欢它。(not quite as)Answer:I enjoyed her new book though its not quite as good as her last one.5 .我从未遇到过如此善良的人。(never before)Answer:Never before have I met such a kind person.1.公共汽车放慢速度并停下，让那位乘客上车。(slow down)Answer:
26、The bus slowed down and stopped to allow the passenger to get on board.2.许多车子都驶过去了，可是没有一辆愿意让我们搭便车。(roll by)Answer:Many vehicles rolled by, but no one offered us a ride.3 .请勿践踏草地。(get off)Answer:Please get off the grass.4.他按妻子的吩咐，一下班就去了市场。(make ones way)Answer:He made his way to the marketplace right
27、 after work, as his wife had asked him to do.5 .值得庆幸的是，史蒂夫 (Steve) 从自行车上摔下来时没有摔断骨头。(luckily)Answer:Luckily, Steve didnt break any bones when he fell off his bike.Unit51. 我们得把感情放在一边，从专业的角度来对待这件事。(from a professional standpoint)Answer:We have to put aside our emotions and take it from a professional s
28、tandpoint.2. 这部戏非常精彩，我很快就沉浸于激动人心的剧情之中。(lose oneself in)Answer:The play was so wonderful that I soon lost myself in the excitement of it.3 .她没有什么爱好除非你把看电视也算是一种爱好。(unless)Answer:She hasnt got any hobbies unless you call watching TV a hobby.4. 他说他是直接从市长本人那里得到这个信息的。(first-hand)Answer:He said that he had
29、 got the information first-hand from the Mayor himself.5 .既然你不能回答这个问题，我们最好问问别人。(since)Answer:Since you cant answer the question, perhaps wed better ask someone else.1. 由于公共汽车司机突然刹车，旅客们都不由自主地向前摔倒。(brake, pitch forward)Answer:All the passengers pitched forward because the bus driver braked sharply.2.
30、这个协议将冲破对自由贸易设置的障碍。(break through, obstacle)Answer:This agreement will break through the obstacles to free trade.3 .我刚放下叫出租车的电话，车就来了。(soon after)Answer:The taxi arrived soon after I rang for it.4. 在过去，不管我什么时候到家，我父母总会等我。(no matter)Answer:My parents always waited up for me no matter what time I got hom
31、e.5 .由于没有一方愿意让步，两个公司之间的对话完全破裂了。(break down)Answer:Talks between the two companies completely broke down, because neither of them wanted to give in.Unit61. 那件工作很难做，不过我想试试看。(have a shot)Answer:Its a difficult job, but Id like to have a shot.2. 这是一本关于商务实践而非理论的书。(as opposed to)Answer:This is a book abou
32、t business practice as opposed to theory.3. 社会活动从未耽误她的学习。(in the way)Answer:Social activities never get in the way of her studies.4. 直到1911年人们才发现第一种维生素。(It is not until . that)Answer:It was not until 1911 that the first of the vitamins was identified.5. 尽管年事已高，爷爷每天还帮忙做家务。(despite)Answer:Despite adva
33、nced years, Grandpa helps do housework every day.1. 我们的婚姻很幸福，但我们也曾经历过许多坎坷。(ups and downs)Answer:Our marriage is happy but weve had many ups and downs.2. 许多外语教师常常在课堂上自顾自地讲得太多。(be inclined to)Answer:Many teachers of foreign languages are inclined to talk too much themselves in class.3. 那位著名演员每天早晨锻炼一小时
34、以保持健康。(work out)Answer:The famous actor keeps fit by working out for an hour every morning.4. 与他促膝长谈之后，她的怀疑消失了。(melt away)Answer:After a long heart-to-heart talk with him, her suspicion melted away.5. 目前我们没有职位空缺，但我们肯定会记住您的申请。(keep in mind)Answer:We have no vacancies now, but well certainly keep your
35、 application in mind.Unit71. 他并不后悔说过的话，只是觉得他完全可以不用这种方式表达。(could have done)Answer:He did not regret what he had said but felt that he could have expressed it differently.2. 我们最好等到12月14日。那时大卫已考完试，就能和我们一起去度假了。(will have done)Answer:Wed better wait till 14 December. David will have had his exam by then,
36、 so hell be able to go on holiday with us.3. 他正在做一个新项目，年底前必须完成。(work on)Answer:Hes working on a new project which has to be finished by the end of the year.4. 他们让我们使用他们的实验室，作为回报，我们则让他们分享研究成果。(in return)Answer:They are letting us use their lab, and in return, we are sharing with them the results of o
37、ur research.5. 诸如打电话、听电话一类的事情占用了这位秘书的大部分时间。(take up)Answer:Such things as making and answering telephone calls take up most of the secretarys time.1. 他们把房子卖了后就到加拿大和女儿住在一起。(go off) Answer:They sold their house and went off to live in Canada with their daughter.2. 你下星期这个时候会在干什么？还是像平常一样干活。(will be doin
38、g)Answer:What will you be doing this time next week?Ill be working as usual.3. 他既聪明又勤奋，不久就接管了杂志的编辑工作。(editing; before long)Answer:He was intelligent and hard-working and before long he took over the editing of the magazine.4. 你话还没说完别人就挂断电话，难道你不恼火吗？(hang up)Answer:Dont you hate it when someone hangs up on you before you finish speaking?5. 让他们感到惊恐的是，他们的房顶着火了。(to ones horror)Answer:To their horror, the roof of their house caught fire.
