yxfwj 《Mechanics1历年考试真题分类汇编》Word文档下载推荐.docx
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yxfwj 《Mechanics1历年考试真题分类汇编》Word文档下载推荐.docx
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(ii)Giventhatthemanruns20mintheinterval20≤t≤24,findhowfarheisfromAwhent=40.
Question2
Thediagramshowsthevelocity-timegraphsforthemotionoftwocyclistsPandQ,whotravelinthesamedirectionalongastraightpath.BothcyclistsstartfromrestatthesamepointOandbothaccelerateat2ms−2uptoaspeedof10ms−1.Boththencontinueataconstantspeedof10ms−1.QstartshisjourneyTsecondsafterP.
(i)ShowinasketchofthediagramtheregionwhosearearepresentsthedisplacementofP,fromO,attheinstantwhenQstarts.
GiventhatPhastravelled16mattheinstantwhenQstarts,find
(ii)thevalueofT,
(iii)thedistancebetweenPandQwhenQ’sspeedreaches10ms−1.
Question3
AboyrunsfromapointAtoapointC.HepausesatCandthenwalksbacktowardsAuntilreachingthepointB,wherehestops.Thediagramshowsthegraphofvagainstt,wherevms−1istheboy,svelocityattimetsecondsafterleavingA.Theboyrunsandwalksinthesamestraightlinethroughout.
(i)FindthedistancesACandAB.
(ii)Sketchthegraphofxagainstt,wherexmetresistheboy,sdisplacementfromA.ShowclearlythevaluesoftandxwhentheboyarrivesatC,whenheleavesC,andwhenhearrivesatB.
Question4
ParticlesPandQstartfrompointsAandBrespectively,atthesameinstant,andmovetowardseachotherinahorizontalstraightline.TheinitialspeedsofPandQare5ms−1and3ms−1respectively.TheaccelerationsofPandQareconstantandequalto4ms−2and2ms−2respectively(seediagram).
(i)FindthespeedofPattheinstantwhenthespeedofPis1.8timesthespeedofQ.
(ii)GiventhatAB=51m,findthetimetakenfromthestartuntilPandQmeet.
Question5
Thediagramshowsthevelocity-timegraphforaliftmovingbetweenfloorsinabuilding.Thegraphconsistsofstraightlinesegments.Inthefirststagethelifttravelsdownwardsfromthegroundfloorfor5s,comingtorestatthebasementaftertravelling10m.
(i)Findthegreatestspeedreachedduringthisstage.
Thesecondstageconsistsofa10swaitatthebasement.Inthethirdstage,thelifttravelsupwardsuntilitcomestorestatafloor34.5mabovethebasement,arriving24.5safterthestartofthefirststage.Theliftacceleratesat2ms−2forthefirst3softhethirdstage,reachingaspeedofVms−1.Find
(ii)thevalueofV,
(iii)thetimeduringthethirdstageforwhichtheliftismovingatconstantspeed,
(iv)thedecelerationoftheliftinthefinalpartofthethirdstage.
Question6
Acartravelsinastraightlinewithconstantaccelerationams−2.ItpassesthepointsA,BandC,inthisorder,withspeeds5ms−1,7ms−1and8ms−1respectively.ThedistancesABandBCared1mandd2mrespectively.
(i)Writedownanequationconnecting(a)d1anda,(b)d2anda.(ii)Hencefindd1intermsofd2.
Question7、
Thediagramshowsthedisplacement-timegraphforacar’sjourney.ThegraphconsistsoftwocurvedpartsABandCD,andastraightlineBC.ThelineBCisatangenttothecurveABatBandatangenttothecurveCDatC.Thegradientofthecurvesatt=0andt=600iszero,andtheaccelerationofthecarisconstantfor0<
t<
80andfor560<
600.Thedisplacementofthecaris400mwhent=80.
(i)Sketchthevelocity-timegraphforthejourney.
(ii)Findthevelocityatt=80.
(iii)Findthetotaldistanceforthejourney.
(iv)Findtheaccelerationofthecarfor0<
80.
Question8
Thediagramshowsthevelocity-timegraphforthemotionofasmallstonewhichfallsverticallyfromrestatapointAabovethesurfaceofliquidinacontainer.ThedownwardvelocityofthestonetsafterleavingAisvms−1.Thestonehitsthesurfaceoftheliquidwithvelocity7ms−1whent=0.7.Itreachesthebottomofthecontainerwithvelocity5ms−1whent=1.2.
(i)Find
(a)theheightofAabovethesurfaceoftheliquid,
(b)thedepthofliquidinthecontainer.
(ii)Findthedecelerationofthestonewhileitismovingintheliquid.
(iii)Giventhattheresistancetomotionofthestonewhileitismovingintheliquidhasmagnitude0.7N,findthemassofthestone.
Question9
AtraintravelsfromAtoB,adistanceof20000m,taking1000s.Thejourneyhasthreestages.InthefirststagethetrainstartsfromrestatAandacceleratesuniformlyuntilitsspeedisVms−1.InthesecondstagethetraintravelsatconstantspeedVms−1for600s.Duringthethirdstageofthejourneythetraindeceleratesuniformly,comingtorestatB.
(i)Sketchthevelocity-timegraphforthetrain’sjourney.
(ii)FindthevalueofV.
(iii)Giventhattheaccelerationofthetrainduringthefirststageofthejourneyis0.15ms−2,findthedistancetravelledbythetrainduringthethirdstageofthejourney.
Question10
Atrainstartsfromrestatastationandtravelsinastraightlineuntilitcomestorestagainatthenextstation.Thedisplacement-timegraphabovereferstothejourney.
(i)Thespeedofthetrainisconstantfromt=120tot=440.Findthisspeed.
(ii)Giventhattheaccelerationofthetrainisconstantfromt=otot=120andfromt=440tot=480,makeasketchofthevelocity-timegraphforthejourney,showingthemaximumspeedofthetrain.
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