UNIT 1

Kinematics (One-Dimensional)

APUnit1:OneDimensionalKinematics-ExamplesandTryThisProblemsEx.1Aturtleandarabbitengageinafootraceoveradistanceof4.00km.Therabbitruns0.500kmandthenstopsfora90.0-minnap.Uponawakening,herememberstheraceandrunstwiceasfast.Finishingthecourseinatotaltimeof1.75h,therabbitwinstherace.(a)Calculatetheaveragespeedoftherabbit.(b)Whatwashisaveragespeedbeforehestoppedforanap?Ans.a)2.29km/hb)9.00km/hTryThis1:EstimatetheaveragespeedoftheApollospacecraftinmeterspersecond,giventhatthecrafttookfivedaystoreachtheMoonfromEarth.(TheMoonis3.8×108mfromEarth.)Answer~900m/sEx.2AtrainmovesslowlyalongastraightportionoftrackaccordingtothegraphofpositionversustimeinFigure2.7a.Find(a)theaveragevelocityforthetotaltrip,(b)theaveragevelocityduringthefirst4.00sofmotion,(c)theaveragevelocityduringthenext4.00sofmotion,(d)theinstantaneousvelocityatt2.00s,and(e)theinstantaneousvelocityatt=9s.

TryThis2:Figure2.7babovegraphsanotherrunofthetrain.Find(a)theaveragevelocityfromOtoC(b)theaverageandinstantaneousvelocitiesfromOtoA(c)theapproximateinstantaneousvelocityatt=6.0s;and(d)theaverageandinstantaneousvelocityatt=9.0s.Answers(a)0m/s(b)bothare0.5m/s(c)2m/s(d)bothare2.5m/sEx.3Abaseballplayermovesinastraight-linepathinordertocatchaflyballhittotheoutfield.HisvelocityasafunctionoftimeisshowninFigure2.11a.FindhisinstantaneousaccelerationatpointsA,B,andC.

TryThis3:Repeattheaboveproblemusingfigure(b).Ans.A)-3.0m/s2B)1.0m/s2C)0m/s2

Ex.4(a)Aracecarstartingfromrestacceleratesataconstantrateof5.00m/s2.Whatisthevelocityofthecarafterithastraveled1.00x102ft?(b)Howmuchtimehaselapsed?Ans.a)17.5m/sb)3.50sTryThis4:Supposethedriverinthisexamplenowslamsonthebrakes,stoppingthecarin4.00s.Find(a)theaccelerationand(b)thedistancethecartravelswhilebraking,assumingtheaccelerationisconstant.Ans.(a)4.38m/s2(b)35.0m

Ex.5Acartravelingataconstantspeedof24.0m/spassesatrooperhiddenbehindabillboard.Onesecondafterthespeedingcarpassesthebillboard,thetroopersetsoffinchasewithaconstantaccelerationof3.00m/s2.(a)Howlongdoesittakethetroopertoovertakethespeedingcar?(b)Howfastisthetroopergoingatthattime?a)16.9sb)50.7m/s

TryThis5:Amotoristwithanexpiredlicensetagistravelingat10.0m/sdownastreet,andapolicemanonamotorcycle,takinganother5.00stofinishhisdonut,giveschaseatanaccelerationof2.00m/s2.Find(a)thetimerequiredtocatchthecarand(b)thedistancethetroopertravelswhileovertakingthemotorist.Answers(a)13.7s(b)188m

Ex.6Atypicaljetlinerlandsataspeedof160mi/handdeceleratesattherateof(10mi/h)/s.Iftheplanetravelsataconstantspeedof160mi/hfor1.0safterlandingbeforeapplyingthebrakes,whatisthetotaldisplacementoftheaircraftbetweentouchdownontherunwayandcomingtorest?Ans.644mTryThis6:Ajetlandsat80.0m/s,thepilotapplyingthebrakes2.00safterlanding.Findtheaccelerationneededtostopthejetwithin5.00x102m.Ans.-9.41m/s2Ex.7Astoneisthrownfromthetopofabuildingwithaninitialvelocityof20.0m/sstraightupward,ataninitialheightof50.0mabovetheground.Thestonejustmissestheedgeoftheroofonitswaydown.Determine(a)thetimeneededforthestonetoreachitsmaximumheight,(b)themaximumheight,(c)thetimeneededforthestonetoreturntotheheightfromwhichitwasthrownandthevelocityofthestoneatthatinstant,(d)thetimeneededforthestonetoreachtheground,and(e)thevelocityandpositionofthestoneatt5.00s.Ans.a)2.04sb)20.4mc)4.08sd)5.83se)v=-29m/s,y=-22.5m

TryThis7:Aprojectileislaunchedstraightupat60.0m/sfromaheightof80.0m,attheedgeofasheercliff.Theprojectilefalls,justmissingthecliffandhittingthegroundbelow.Find(a)themaximumheightoftheprojectileabovethepointoffiring,(b)thetimeittakestohitthegroundatthebaseofthecliff,and(c)itsvelocityatimpact.Ans.(a)184m(b)13.5s(c)72.3m/sEx.8Arocketmovesstraightupward,startingfromrestwithanaccelerationof29.4m/s2.Itrunsoutoffuelattheendof4.00sandcontinuestocoastupward,reachingamaximumheightbeforefallingbacktoEarth.(a)Findtherocket’svelocityandpositionattheendof4.00s.(b)Findthemaximumheighttherocketreaches.(c)Findthevelocitytheinstantbeforetherocketcrashesontheground.Ans.a)vb=118m/sandyb=235mb)ymax=945mc)v=-136m/sTryThis8:Anexperimentalrocketdesignedtolanduprightfallsfreelyfromaheightof2.00x102m,startingatrest.Ataheightof80.0m,therocket’senginesstartandprovideconstantupwardaccelerationuntiltherocketlands.Whataccelerationisrequiredifthespeedontouchdownistobezero?Ans.14.7m/s2

Unit1Problems:One-DimensionalKinematics

Video1.1-Velocity1.Thespeedofanerveimpulseinthehumanbodyisabout100m/s.Ifyouaccidentallystubyourtoeinthedark,estimatethetimeittakesthenerveimpulsetotraveltoyourbrain.Assumeyourheighttobeabout2m.(Ans..02sec)2.Apersontravelsbycarfromonecitytoanotherwithdifferentconstantspeedsbetweenpairsofcities.Shedrivesfor30.0minat80.0km/h,12.0minat100km/h,and45.0minat40.0km/handspends15.0mineatinglunchandbuyinggas.(a)Determinetheaveragespeedforthetrip.(b)Determinethedistancebetweentheinitialandfinalcitiesalongtheroute.(Ans.a)52.9km/hb)90km)3.Agraphofpositionversustimeforacertainparticlemovingalongthex-axisisshown.Findtheaveragevelocityinthetimeintervalsfrom(a)0to2.00s,(b)0to4.00s,(c)2.00sto4.00s,(d)4.00sto7.00s,and(e)0to8.00s.(Ans.a)5m/sb)1.25m/sc)-2.5m/sd)-3.33m/se)0m/s)4.Amotoristdrivesnorthfor35.0minutesat85.0km/handthenstopsfor15.0minutes.Hethencontinuesnorth,traveling130kmin2.00h.(a)Whatishistotaldisplacement?(b)Whatishisaveragevelocity?(Ans.a)180kmb)63.4km/h)5.Atennisplayermovesinastraight-linepathasshown.Findheraveragevelocityinthetimeintervalsfrom(a)0to1.0s,(b)0to4.0s,(c)1.0sto5.0s,and(d)0to5.0s.(Ans.a)4m/sb)-.5m/sc)-1m/sd)0m/s)6.Atortoisecanrunwithaspeedof0.10m/s,andaharecanrun20timesasfast.Inarace,theybothstartatthesametime,buttheharestopstorestfor2.0minutes.Thetortoisewinsbyashell(20cm).(a)Howlongdoestheracetake?(b)Whatisthelengthoftherace?(Ans.a)130secb)13m)

Video1.2-Acceleration

7.Acertaincariscapableofacceleratingatarateof10.60m/s2.Howlongdoesittakeforthiscartogofromaspeedof55mi/htoaspeedof60mi/h?(Ans.3.7sec)8.Thevelocityvs.timegraphforanobjectmovingalongastraightpathisshownbelow.Findtheaverageaccelerationoftheobjectduringthetimeintervals0to5.0s,5.0sto15s,and0to20s.(Ans.0m/s2,1.6m/s2,and.8m/s2)9.Acaristravelingdueeastat25.0m/satsomeinstant.(a)Ifitsconstantaccelerationis0.75m/s2dueeast,finditsvelocityafter8.5shaveelapsed.(b)Ifitsconstantaccelerationis0.75m/s2duewest,finditsvelocityafter8.5shaveelapsed.(Ans.a)31.4m/seastwardb)18.6m/seastward)10.Atruckcovers40.0min8.50swhilesmoothlyslowingdowntoafinalvelocityof2.80m/s.(a)Findthetruck’soriginalspeed.(b)Finditsacceleration.(Ans.a)6.61m/sb)-.448m/s2)11.ACessnaaircrafthasaliftoffspeedof120km/h.(a)Whatminimumconstantaccelerationdoestheaircraftrequireifitistobeairborneafteratakeoffrunof240m?(b)Howlongdoesittaketheaircrafttobecomeairborne?(Ans.a)2.32m/s2b)14.4sec)

12.Acarstartsfromrestandtravelsfor5.0swithauniformaccelerationof1.5m/s2.Thedriverthenappliesthebrakes,causingauniformaccelerationof-2.0m/s2.Ifthebrakesareappliedfor3.0s,(a)howfastisthecargoingattheendofthebrakingperiod,and(b)howfarhasthecargone?(Ans.a)1.5m/sb)32m)

Video1.3-FreelyFallingObjects13.Aballisthrownverticallyupwardwithaspeedof25.0m/s.(a)Howhighdoesitrise?(b)Howlongdoesittaketoreachitshighestpoint?(c)Howlongdoestheballtaketohitthegroundafteritreachesitshighestpoint?(d)Whatisitsvelocitywhenitreturnstothelevelfromwhichitstarted?(Ans.a)31.9mb)2.55secc)2.55secd)-25m/s)14.Acertainfreelyfallingobjectrequires1.50stotravelthelast30.0mbeforeithitstheground.Fromwhatheightabovethegrounddiditfall?(Ans.38.2m)15.Asmallmailbagisreleasedfromahelicopterthatisdescendingsteadilyat1.50m/s.After2.0s,(a)whatisthespeedofthemailbag,and(b)howfarisitbelowthehelicopter?(Ans.a)-21.1m/sb)19.6m)16.Amodelrocketislaunchedstraightupwardwithaninitialspeedof50.0m/s.Itaccelerateswithaconstantupwardaccelerationof2.00m/s2untilitsenginesstopatanaltitudeof150m.(a)Whatisthemaximumheightreachedbytherocket?(b)Howlongafterliftoffdoestherocketreachitsmaximumheight?(c)Howlongistherocketintheair?(Ans.a)308mb)8.51secc)16.4sec)

ConceptualQuestions:One-DimensionalKinematics1.Ifthevelocityofaparticleisnonzero,cantheparticle’saccelerationbezero?Explain.2.Ifthevelocityofaparticleiszero,cantheparticle’saccelerationbezero?Explain.3.Ifacaristravelingeastward,canitsaccelerationbewestward?Explain.4.Thefigurebelowshowsstrobephotographstakenofadiskmovingfromlefttorightunderdifferentconditions.Thetimeintervalbetweenimagesisconstant.Takingthedirectiontotherighttobepositive,describethemotionofthediskineachcase.Forwhichcaseis(a)theaccelerationpositive?(b)theaccelerationnegative?(c)thevelocityconstant?5.Aballisthrownverticallyupward.(a)Whatareitsvelocityandaccelerationwhenitreachesitsmaximumaltitude?(b)Whatistheaccelerationoftheballjustbeforeithitstheground?

6.Considerthefollowingcombinationsofsignsandvaluesforthevelocityandaccelerationofaparticlewithrespecttoaone-dimensionalx-axis.Considerthepositivedirectiontobeeastandthenegativedirectionwest.Describewhattheparticleisdoingineachcase:e.g.-Movingtothewestandslowingdown,Movingtotheeastataconstantvelocity,etc.

Unit1LabActivityInthislabactivityyourgroupwillapplythekinematicsformulasforone-dimensionalmotion.Afterdeterminingtheaccelerationofaballrollingdownaramp,youwillusethisinformationtopredicttimeanddistancemeasurementsfortheballafterithaslefttheramp.Materials:1)MetalRamp2)Ball3)Timer4)MeasuringTapeProblemStatement:Yourtaskistopredicthowfaraballwhichhasbeenrolleddownarampwilltravelin2s,3s,4s,5s,and6safterreachingthebottomoftheramp.Youwilldothisforthreedifferentheightsoframp.Forthefirstheightoftheramp,youmustshowallofyourcalculations:Howyoudeterminedtheacceleration,howyoucalculatedyourpredictedvaluesfordistance.Fortheothertwoheightsoftheramp,youmayjustshowtheresultsofyourcalculationsintableform.Besuretoincludeallunitsofmeasurementinyourresults.AnalysisQuestions:1)Drawagraphforeachdifferentheightoframpmakingthex-axistime(inseconds)andthey-axisdistancetraveledinmeters.Plotaline(orcurve)ofbestfitthroughyourdata.Doyouexpectalineargraphoracurvedgraph?Discusswhatyoupredictversuswhatyouactuallyobserve.Iftherearedifferences,discusspossiblereasonsforthem.(Itmaybehelpfultoactuallyplotyourexpectedresultsonthegraphalongwithyouractualresults.Thiswillallowyoutocomparethemmoreaccurately.)2)Whatsourcesoferrormayhaveaffectedyourresults?Howcouldyoupossiblyovercometheseinthefuture?

PhysicsLabReportChecklistParticipantNames:____________________________________________________________Pd.______LabTitle:_____________________________________________DueDate________________OverallReportFormat

1.TitlePagecontainsGroupnames,ExperimentTitle,DateDue,andPeriod2.Allsectionsreportarepresent,inproperorder,andareclearlylabeledinBoldUnderlineprint.

01

Introduction 1.Thereisaclearstatementofthepurpose/objectiveofthelab.2.Thereisabriefdiscussionoftherelevantbackgroundinformationandtheoryinvolvedinthelab.

012

012

ExperimentalProcedure

1.Thereisaclearwrittendescriptionoftheproceduresfollowedintheexperiment.2.Thereisadiagramorpictureoftheexperimentset-upwithcomponentslabeled.

012

012

RawData 1.Allcollecteddatafromtheexperimentispresentedintableformorotherappropriateformat.2.Unitsofmeasurementsareclearlyindicated.

012

01Analysis 1.Asampleofeachtypeofcalculationneededin

theexperimentisprovidedandisdonecorrectly.2.ResultsofcalculationsarepresentedforALLdataintableform.3.Graphsofdataareincluded,areneat,clearlytitled,anddisplayappropriateunitsandscales.4.Sourcesofmeasurementerrorareindicatedanddiscussed.

012

012

012

012

Conclusions 1.Finalconclusionofthelabisclearlystatedandshowsunderstandingoftheobjectiveofthelab.2.Suggestionsforhowthelabcouldbeimprovedareincluded.(Whatwouldyouhavedonedifferentlyifyouweredoingthelabagain?)

0123

012

Note:Labreportsmustbetyped,nothandwritten,withthefollowingexceptions:1)Graphsmaybedonebyhandongraphpaper.2)Samplecalculationsmaybeneatlyhandwritten.

TotalScore:________/25Comments:__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

MultipleChoiceQuestions 12.3.

FreeResponseQuestions#1.

#2.

#3.

#4.