AP_Physics_B_-_Graphical_Analysis_of_Motion.ppt

GraphicalAnalysisofMotion APPhysicsB Slope Abasicgraphmodel 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 Itisveryimportantthatyouareabletolookatagraphandexplainit smotioningreatdetail 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 Slope Abasicgraphmodel Let slookatanothermodel 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 Area the other basicgraphmodel AnotherbasicmodelforunderstandinggraphsinphysicsisAREA Let strytoalgebraicallymakeourformulaslookliketheoneabove We llstartwithourformulaforvelocity 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 Area the other basicgraphmodel Let suseournewmodelagain 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 HowcouldyoutranslatewhattheSLOPEisdoingonthegraphABOVEtotheYaxisonthegraphtot