AP_Physics_B_-_Graphical_Analysis_of_Motion

GraphicalAnalysisofMotion,APPhysicsB,SlopeAbasicgraphmodel,AbasicmodelforunderstandinggraphsinphysicsisSLOPE.,Usingthemodel-Lookattheformulaforvelocity.Whogetstoplaytheroleoftheslope?Whogetstoplaytheroleofthey-axisortherise?Whogettoplaytheroleofthex-axisortherun?Whatdoesallthemean?ItmeansthatifyouraregivenaDisplacementvs.Timegraph,tofindthevelocityofanobjectduringspecifictimeintervalssimplyfindtheslope.,Velocity,Displacement,Time,Displacementvs.Timegraph,Whatisthevelocityoftheobjectfrom0secondsto3seconds?,Thevelocityistheslope!,Displacementvs.Timegraph,Whatisthevelocityoftheobjectfrom7secondsto8seconds?Onceagain.findtheslope!,Avelocityof0m/s.Whatdoesthismean?Itissimple.theobjecthassimplystoppedmovingfor1second.,Displacementvs.Timegraph,Whatisthevelocityfrom8-10seconds?Youmustremember!Tofindthechangeitisfinal-initial.,Theanswerisnegative!Itisnosurprise,becausetheslopeisconsideredtobenegative.Thisvaluecouldmeanseveralthings:TheobjectcouldbetravelingWESTorSOUTH.Theobjectisgoingbackwards-thisbeingthemorelikelychoice!YoushouldalsounderstandthattheslopedoesNOTchangefrom0-3s,5to7sand8-10s.ThismeansthattheobjecthasaCONSTANTVELOCITYorITISNOTACCELERATING.,Example,Itisveryimportantthatyouareabletolookatagraphandexplainitsmotioningreatdetail.Thesegraphscanbeveryconceptual.,Lookatthetimeintervalt=0tot=9seconds.Whatdoestheslopedo?,Itincreases,thevelocityisincreasing,Lookatthetimeintervalt=9tot=11seconds.Whatdoestheslopedo?,Noslope.ThevelocityisZERO.,Lookatthetimeintervalt=11tot=15seconds.Whatdoestheslopedo?,Theslopeisconstantandpositive.Theobjectismovingforwardsataconstantvelocity.,Lookatthetimeintervalt=15tot=17seconds.Whatdoestheslopedo?,Theslopeisconstantandnegative.Theobjectismovingbackwardsataconstantvelocity.,SlopeAbasicgraphmodel,Letslookatanothermodel,Whogetstoplaytheroleoftheslope?Whogetstoplaytheroleofthey-axisortherise?Whogettoplaytheroleofthex-axisortherun?Whatdoesallthemean?ItmeansthatifyouraregivenaVelocityvs.Timegraph.Tofindtheaccelerationofanobjectduringspecifictimeintervalssimplyfindtheslope.,Acceleration,Velocity,Time,Velocityvs.TimeGraph,Whatistheaccelerationfrom0to6s?,Whatistheaccelerationfrom6to9s?,Youcouldsayoneoftwothingshere:TheobjecthasaZEROaccelerationTheobjecthasaCONSTANTvelocity,Whatistheaccelerationfrom14to15s?,AnegativeaccelerationissometimescalledDECELERATION.Inotherwords,theobjectisslowingdown.Anobjectcanalsohaveanegativeaccelerationifitisfalling.Inthatcasetheobjectisspeedingup.CONFUSING?BecarefulandmakesureyouunderstandWHYthenegativesignisthere.,Velocityvs.TimeGraph,Conceptuallyspeaking,whatistheobjectdoingduringthetimeintervalt=9tot=13seconds?,Doesthesteepnessorslopeincreaseordecrease?,TheslopeINCREASES!,Accordingtothegraphtheslopegetssteeperorincreases,butinanegativedirection.,Whatthismeansisthatthevelocityslowsdownwithagreaterchangeeachsecond.Thedeceleration,inthiscase,getlargereventhoughthevelocitydecreases.,Thevelocitygoesfrom60to55(achangeof5),thenfrom55to45(achangeof10),thenfrom45to30(achangeof15),thenfrom30to10(achangeof20).DoyouseehowthechangegetsLARGERasthevelocitygetsSMALLER?,Areathe“other”basicgraphmodel,AnotherbasicmodelforunderstandinggraphsinphysicsisAREA.,Letstrytoalgebraicallymakeourformulaslookliketheoneabove.Wellstartwithourformulaforvelocity.,Whogetstoplaytheroleofthebase?Whogetstoplaytheroleoftheheight?Whatkindofgraphisthis?,WhogetstoplaytheroleoftheArea?,AVelocityvs.Timegraph(velocity=y-axis&time=x-axis),Time,Velocity,Displacement,Example,Whatisthedisplacementduringthetimeintervalt=0tot=5seconds?,Thathappenstobethearea!,Whatisthedisplacementduringthetimeintervalt=8tot=12seconds?,Onceagain.wehavetofindthearea.,DuringthistimeperiodwehaveatriangleANDasquare.WemustfindtheareaofeachsectionthenADDthemtogether.,Areathe“other”basicgraphmodel,Letsuseournewmodelagain,butforourequationforacceleration.,Whatdoesthismean?Whogetstoplaytheroleofthebase?Whogetstoplaytheroleoftheheight?Whatkindofgraphisthis?WhogetstoplaytheroleoftheArea?,Time,Acceleration,AnAccelerationvs.Timegraph(acceleration=y-axis&time=x-axis),TheVelocity,Accelerationvs.TimeGraph,Whatisthevelocityduringthetimeintervalt=3andt=6seconds?FindtheArea!,Summary,Thereare3typesofMOTIONgraphsDisplacement(position)vs.TimeVelocityvs.TimeAccelerationvs.TimeThereare2basicgraphmodelsSlopeArea,Summary,t(s),t(s),t(s),x(m),v(m/s),a(m/s/s),slope=v,slope=a,area=x,area=v,ComparingandSketchinggraphs,Oneofthemoredifficultapplicationsofgraphsinphysicsiswhengivenacertaintypeofgraphandaskedtodrawadifferenttypeofgraph,t(s),x(m),slope=v,t(s),v(m/s),List2adjectivestodescribetheSLOPEorVELOCITY,TheslopeisCONSTANT,TheslopeisPOSITIVE,HowcouldyoutranslatewhattheSLOPEisdoingonthegraphABOVEtotheYaxisonthegraphtotheright?,Example,