DO NOT confuse displacement with distance traveled不要混淆位移距离

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1、One-DimensionalKinematicsObjectsareconsideredasaparticle,avanishinglysmallobject.Kinematics–howabodymovesinspaceandtime.Fornowwewillconsidertranslationalmotion(norotation)first,alongaline–1-Dmotion,ultimatelyin2or3dimensions.Forthe1-Dcase,weneedonlyconsider+or–directionsofmotion.Sofor

2、themoment,wewillconsidervariableslikedisplacement,velocity,andaccelerationasscalarquantities,althoughtheyareVECTORS.ThedisplacementfrompositiontoisgivenbyThedisplacementwithrespecttotheoriginofacoordinatesystemismerelyx.Wedefinetheaveragevelocityi.e.-thechangeinx(thedisplacement=)occu

3、rringinthetimeintervalDONOTconfusedisplacementwithdistancetraveled.Ex.-1000100200300displacementdistancetraveledAv.Vel.Av.SpeedDr.MichaelJ.BrienzaPage11Editedon7/25/21Forourexamplewecouldhaveforx(t)Arbitraryx(t)Slope=Px(t)(m.)t(s)-100-200Note:t(s)2015105100200x(m)xfIfweallowtoapproach

4、0,i.e.uniformlythen,thenwewillgettheslopeofthetangentlineatatimet,mid-waybetweentf&tiatpointP.SlopeoftangentlineatPisDr.MichaelJ.BrienzaPage11Editedon7/25/21InstantaneousvelocityistheRATEofCHANGEofdisplacement.Inasimilarfashion,wecanlookatthefunction.ThatisgraphicallywemighthavePt(sec

5、.)Slopeoflinethrough=AVERAGEACCELERATIONtfSlopeofatPisINSTANTANEOUSACCELERATIONSoifweknowx(t)WecanfindandLikevelocity,average&instantaneousaccelerationscanbequitedifferent.Atthepointabovetheacceleration(theslopeofisnegative.Dr.MichaelJ.BrienzaPage11Editedon7/25/21246-0.2-0.10.10.2-6-4

6、-2Considerthefollowingrelationshipsof.x(t)(m)t10987643215Areaundercurvefromt=7tot=8isthefromt=7to8isaplotoftheslopeofx(t)1m/st-1m/sAreaunderisthechangeinvelocityfromt=2tot=3isaplotoftheslopeoftDr.MichaelJ.BrienzaPage11Editedon7/25/21TheSPECIALCaseofCONSTANTManyofoureverydayexperiences

7、arethosewhere=CONSTANT.Freelyfallingbodies,i.e.abodythatisONLYactedonbygravity,canbeconsideredtohaveaconstantacceleration.SoundertheassumptionofconstantaccelerationovertheofinterestwecanderivesomeveryusefulexpressionsrelatingIfaisaconstant,itsaverageandinstantaneousvaluesarethesame=a.

8、There