高一物理匀变速直线运动规律的应用

匀变速直线运动匀变速直线运动 规律的应用规律的应用位移和时间的关系平均速度公式：平均速度公式：位移公式：位移公式：2tovvv注意：当注意：当a方向和方向和vo方向方向相反（作减速运动）时，相反（作减速运动）时，a取负值。取负值。tvattvtvvsoto2212vv0vttt/2V t/2 等于中间等于中间时刻的瞬时速度时刻的瞬时速度（仅适用于匀变速直线运动）（仅适用于匀变速直线运动）匀加速直线运动：匀加速直线运动：atOStOVtOV0a(3)匀变速直线运动的图象匀变速直线运动的图象匀减速直线运动：匀减速直线运动：StOatOVtOV0a七七.匀变速直线运动规律的应用匀变速直线运动规律的应用S=v0t+at221vt=v0+atvt2v02=2as221attvst位移中点的瞬时速度：位移中点的瞬时速度：2220tvv VS中中 推导：推导：2S中20V 2as2S中V V2S 中202t2tV 2as 2S中所以有：解得：所以有：解得：2220tvv V 中SaVtV0SSVS中中试用图象法分析，对匀变速直线运动试用图象法分析，对匀变速直线运动Vt中中和和VS中中的的大小关系。大小关系。V0VS中中匀加速直线运动和匀减速直线运动，匀加速直线运动和匀减速直线运动，都有都有VS中中Vt中中。问题讨论：问题讨论：VtOVtVt中中VS中中VtOV0VtVt中中例例1：发射枪弹时，枪弹在枪筒中的运动可以看作是匀：发射枪弹时，枪弹在枪筒中的运动可以看作是匀加速运动，如果枪弹的加速度为加速运动，如果枪弹的加速度为5105m/s2，枪筒长，枪筒长0.64m，枪弹射出枪口时的速度是多大，枪弹射出枪口时的速度是多大?解：已知：v0=0,s=0.64m,a=5105m/s2 根据位移和速度的关系式可得 vt2=2as小结：小结：匀变速直线运动规律的三个公式中，包匀变速直线运动规律的三个公式中，包括括5个物理量（或个物理量（或4个）个），如果已知其中，如果已知其中3个物理个物理量量，就一定可以通过列出公式求出其余的二个，就一定可以通过列出公式求出其余的二个未知量，这里要求熟练掌握三个公式，各物理未知量，这里要求熟练掌握三个公式，各物理量之间的关系，并能利用学过的数学知识处理量之间的关系，并能利用学过的数学知识处理物理问题，但物理问题，但利用数学表达式解答物理问题时，利用数学表达式解答物理问题时，必须注意其物理意义必须注意其物理意义，请看例题，请看例题3vt=v0+at(1)S=v0t+at2（2）21vt2v02=2as（3）连续相等时间内的位移差：连续相等时间内的位移差：（aT即为恒量）即为恒量）由此结论可用来求匀变速直线运动的由此结论可用来求匀变速直线运动的加速度。加速度。a=.即：即：你能证明吗？你能证明吗？SS2S1S3S2S4S3SnSn1aT2 2012021)(21aTTaTvsaTTvsnn证aT（aT即为恒量）即为恒量）TTTTTTS1S2S3SnSn+1V0a所以：所以：例例4有一个做匀变速直线运动的质点，有一个做匀变速直线运动的质点，它在两段连续相等的时间内通过的位移它在两段连续相等的时间内通过的位移分别是分别是24 和和64，连续相等的时间为，连续相等的时间为4，求质点的加速度大小，求质点的加速度大小 连续相等时间连续相等时间(T)内的位移之差等于一个内的位移之差等于一个恒量恒量.a=.2t20V2as00122ttvvvvatv中t20tttvtvtvvt v中2at21S2220tvv VS中中 SS2S1S3S2S4S3SnSn1aT2 规律规律Vtat221ats V2as 2t(4)匀变速直线运动的特例：匀变速直线运动的特例：初速度为零的匀加速直线运动初速度为零的匀加速直线运动A1s末、末、2s末、末、3s末、末、ns末的瞬时速度末的瞬时速度之比为：之比为：V1 V2 V3 Vn1 2 3 nS1 S2 S3 Sn12 22 32 n2S S S SN1 3 5 (2n1)特点：特点：B1s内、内、2s内、内、3s内、内、ns内的位移之比为：内的位移之比为：C第第1s内、第内、第2s内、第内、第3s内、内、第第ns内的内的位移之比为：位移之比为：t t t tN 1 (1)()()23n1n2D第第1个个S内、第内、第2个个S内、第内、第3个个S内、内、第第n个个S内的时间之比为：内的时间之比为：请大家自己证明！请大家自己证明！（1）初速度为零的匀加速直线运动的物体的）初速度为零的匀加速直线运动的物体的速度与时间成正比速度与时间成正比v1:v2:v3=t1:t2:t3vt=v0+at(1)当当V0=0时时vt=at(4)匀变数直线运动的物体在连续相同的时间间隔内位移匀变数直线运动的物体在连续相同的时间间隔内位移之差为常数，刚好等于加速度和时间间隔平方的乘积之差为常数，刚好等于加速度和时间间隔平方的乘积sII-sI=sIII-sII=at2（3）初速度为零的匀变速直线运动的物体在连）初速度为零的匀变速直线运动的物体在连续相同时间内续相同时间内位移位移之比为奇数比之比为奇数比（平均速度之比）（平均速度之比）（2）初速度为零的匀加速直线运动的物体）初速度为零的匀加速直线运动的物体位移与时间的平方成正比位移与时间的平方成正比当当V0=0时时S=v0t+at2（2）21S=at221（2）初速度为零的匀变速直线运动的物体的位）初速度为零的匀变速直线运动的物体的位移与时间的平方成正比。移与时间的平方成正比。（4）初数为零的匀加速直线运动的物体通过连）初数为零的匀加速直线运动的物体通过连续位移的时间比为续位移的时间比为t1:t2:t3:t4=1:4:3:2（5）初数为零的匀加速直线运动的物体通过连）初数为零的匀加速直线运动的物体通过连续相同位移的时间之比为续相同位移的时间之比为t1:t2:t3:t4=)1(:.:)34(:)32(:1nn平均速度之比平均速度之比例例2：一个滑雪的人，从：一个滑雪的人，从85m长的山坡上长的山坡上匀变速滑下，初速度是匀变速滑下，初速度是108ms，未速度，未速度是是5ms，他通过这段山坡需要多长时间？，他通过这段山坡需要多长时间？解法解法2：对于匀变速直线运动对于匀变速直线运动，有：smsmvvvt/4.3/258.120又又S ，所以，所以t 25stvvs解法解法1：(见教材见教材)巩固练习巩固练习 1汽车以汽车以10m/s的速度匀速行驶，在距车站的速度匀速行驶，在距车站25m时时开始制动，使车减速前进，到车站时恰好停下，求汽开始制动，使车减速前进，到车站时恰好停下，求汽车匀减速行驶时的加速度的大小为多少？车匀减速行驶时的加速度的大小为多少？3.做匀加速运动的物体，速度从做匀加速运动的物体，速度从v增加到增加到2v，经过的，经过的位移是位移是s，则它的速度从，则它的速度从2v增加到增加到4v、经过的位移是、经过的位移是，速度从，速度从4v增加到增加到8v，经过的位移是，经过的位移是_。2一个物体在一个物体在3s内通过了位移内通过了位移30m，同时它的速度变为原来的同时它的速度变为原来的4倍如果物倍如果物体做匀加速直线运动的物体，求物体的体做匀加速直线运动的物体，求物体的加速度加速度。例、一物体由静止开始做匀加速直线运动，它在第5s内平均速度为18m/s，这物体运动的加速度是_ _ _ _ _ _ _ _，1 0 s 末 的 速 度_m/s。4m/s2406.一汽车以一汽车以2 m/s的加速度刹车做匀减速直的加速度刹车做匀减速直线运动，求它在停止运动前的最后线运动，求它在停止运动前的最后1 通过通过的位移是多少的位移是多少?例、汽车以2m/s2的加速度由静止开始起动，则第5s末汽车的速度是_m/s，第5s内汽车的平均速度是_m/s，第5s汽车的位移是_m。1099【例题【例题3】A、B两汽车站在一条直线上相距为两汽车站在一条直线上相距为S，汽车从汽车从A站出发，先以加速度站出发，先以加速度a1做匀加速运动，做匀加速运动，后以加速度后以加速度a2做匀减速运动，到达做匀减速运动，到达B站时速度站时速度刚好为零若汽车要以最短的时间通过全程，求刚好为零若汽车要以最短的时间通过全程，求最短的时间为多少？汽车达到的最大速度为多最短的时间为多少？汽车达到的最大速度为多少？少？2121min)(2aasaat21212aasaavtmint1t2 联立联立解得：解得：设加速阶段的时间为设加速阶段的时间为t1，减速阶段，减速阶段的时间为的时间为t2，则有，则有a1t1 a1t2 Vmax S(Vmax tmin)/2 解：解：ABCOVtCABt1tminVmax点评：点评：从本例的求解过程中说明速度从本例的求解过程中说明速度图象图象解题的好处。解题的好处。小结：解物理题目不同于解数学题，必须对物理过程有非常清楚的认识，认真审题，弄清题意，明确已知物理量和要求的物理量，再选选择合适的公式去解题择合适的公式去解题还应根据具体实际情根据具体实际情况进行必要的判断，看是否符合题意况进行必要的判断，看是否符合题意，以便得出正确的结果例例3：汽车刹车前速度为：汽车刹车前速度为5m/s。刹车获得加速度大小。刹车获得加速度大小为为0.4m/s2（1）求汽车刹车开始后）求汽车刹车开始后20s内滑行的距离。内滑行的距离。（2）从开始刹车到汽车位移为）从开始刹车到汽车位移为30m时所经历的时间。时所经历的时间。（3）静止前）静止前2.5s内汽车滑行的距离。内汽车滑行的距离。4.一个初速度为一个初速度为10m/s的物体沿光滑斜面上升的物体沿光滑斜面上升,加速度加速度的大小为的大小为4.0m/s2,方向和初速度相反方向和初速度相反,则该物体通过则该物体通过12m的位移所用时间为多少的位移所用时间为多少?ABsVAVB5.如图如图235所示所示,A和和B两物体相距两物体相距s=7m，物体，物体A在在水平拉力和摩擦力的作用下，正以水平拉力和摩擦力的作用下，正以VA=4m/s的速度的速度向右匀速运动，而物体向右匀速运动，而物体B此时的速度此时的速度VB10 m/s，由，由于摩擦力作用向右匀减速运动，加速度于摩擦力作用向右匀减速运动，加速度a=2m/s2那那么，物体么，物体A追上物体追上物体 B所用的时间为多少？所用的时间为多少？http:/ CHAPTER I A STROLLING PIANO“Why did she choose Morning-Glory as her tribe name?”asked M?nkw?n the Rainbow of Sesoo the Flame,as Rainbow and Flame,with girlish arms entwining,stood beneath the shelter of the Silver Twins,two kingly birch-trees,so identical in stature even to their topmost jeweled crowns of leaves flashing in the July sun,so alike in the silver symmetry of each fair limb as to be named the Twins.These silver kings were one-hearted,too,in their benevolent purpose in life,which was to unite in casting a brotherly shade over a certain corner of the broad city playground,dotted with children from every clime,and incidentally to fan the flushed cheeks of the two girls directly beneath them,bound together by a girdling rainbow that played about their waists,woven by the suns shuttle amid the quivering birch-leaves,fit symbol of their binding Camp Fire sisterhood.Sesoos eyes danced,lit by a tiny golden flame that uncurled itself in their demure hazel like a firefly alighting on a brown leaf.She caught her lower lip between the pretty incisors that decorated the front of her mouth as she scrutinized the semi-distant figure of a sixteen-year-old girlperhaps nearer to seventeenclad in a loose lavender smock to her knees,whence to her ankles there was a gleam of white skirt,with the most bewitching,frilled summer“Tam”of lavender,matching her smock,shielding her brown head,sheltering her face,like the hood of a flower.This floral figure leaned against the open door of a handsome automobile which was standing upon the playground avenue.“Im sure its beyond me to tell why Jessica Holley(Jessica Dee Holley;she always likes to bring the unusual little middle name in,because it was her mothers,I suppose),why she chose Welatwesit,which is the only Indian equivalent she could find for Morning-Gloryliterally meaning Climbing Plant or Pretty Flower for her Camp Fire name.But I believe theres a story attached to the choice,some cunning little anecdote of her childhood.Wish I could ferret it out!She seems,always,to have been called Glory,nearly as much as Jessica,”answered Sesoo racily,she who in every-day life bore no flaming cognomen,but was plain little,gay little,Sally Davenport,as full of quips and quirks,of lightning impulses and sudden turns as the wheeling firefly in her eyes.“Goody!Id like to hear the anecdote,too.The Morning-Glory name suits her so well that I thought she must have dreamed itthat it came to her in sleepas I dreamed mine,”laughed the Rainbow,whose rightful name when she was not clad in a leather-fringed robe of khaki,in moccasins and head-band,and seated by a Council Fire,was Arline Champion.“But I call it absurd,meanly absurd,that if theres any story about her and her name,we should not hear it,we who have named our Camp Fire(and its the best in the city,too,though I say it myself!),our whole group or tribe of fourteen girls,after her,”she went on with a stamp of her foot on the playground sod and with rainbowed emphasis;she was the shell-tinted,demurely shining kind of fifteen-year-old girl who unconsciously aims at carrying a rainbow in her pocket,to brighten the dull or tear-wet day.“Oh!we didnt exactly name it after her,”demurred Sally.“She happened to come here last winter to visit those rich girls,the Deerings,who are all fluff an stuff;that exactly describes them,Olive and Sybil”There was the least little green tinge of the spitfire about Sesoos flame now as she shot a glance toward two girls seated in the waiting automobile together with an older woman,evidently chaperon to the band of girls.“Oh!I say,pinch me;I shouldnt have said that,should I,seeing that they brought us here in their car?But twas the first time they ever did it,though my father is head-bookkeeper in their fathers office at the Works;and Ill engage twas Morning-GloryJessicawho suggested it,as we all wanted to visit this playground where there are so many foreign children,to see them dance their folk dances,”she ran on,speech flitting away from its starting-point in the wake of her firefly dance,which vivaciously hovered from one object or group of objects to another.Arline waited for it to alight again on Jessica,as it presently did.“Well!as I was saying,”reverted Sally,“you remember how she came here last February just when we were beginning to organize our Camp Fire group,when we had secured Miss Darina Dewey as Guardian(I think shes a love of a Guardian and I like her unusual first name,too,though some of the girls dont!)but before we had applied for our Charter,when we were searching for a name for our new Camp Fire circle,raking over Indian names like leaves untilgoodness!we seemed half-smothered in them.”Sally paused for breath,breathlessly smothered,indeed,by the sunlit torrent of her own words,which had a trick of inundating a listener.“It was at our second meeting,I think,at Miss Deweys house,”she went on,“that Jessica came in,all snow an sparkle from her eyes to her toes,and introduced herself by showing a transfer card sign