KinematicsMotioninOneDimension在一維運動運動課件

MotioninOneDimension

MotioninOneDimension1KeyTerminologyDistanceSpeedTime*Theseareallscalarquantities -onlymagnitudeDisplacementVelocityAcceleration*Theseareallvectorquantities -magnitudeanddirectionKeyTerminologyDistanceDispla2Distancevs.DisplacementDISTANCETotaltraveledPathdependentScalarquantityBothusethesamevariableandunitsVariable:d(sometimes:x,r,?)Units:mDISPLACEMENTChangeinpositionPathindependentVectorquantityDistancevs.DisplacementDIST3CheckyourunderstandingAnodometerinyourcarshows:DistanceCheckyourunderstandingAnodo4ExampleThefollowingisalistofgainsandlosesofaBearspossessionFirstdown:gain8yardsPenaltylose10yardsSeconddown:gain11yardsThirddown:lose1yardWhatisthetotaldistance?Whatisthetotaldisplacement?ExampleThefollowingisalist5Speedvs.VelocityDIFFERENCESSpeed:howfast(scalar)AlwayspositiveExample:25m/sVelocity:howfastinacertaindirection(vector)CanbepositiveornegativeExample:25m/sNorthSIMILARITIESVariable:vUnits:m/sSpeedvs.VelocityDIFFERENCES6CheckyourUnderstandingAspeedometerinyourcarshows:SpeedCheckyourUnderstandingAspee7CheckyourunderstandingJimtravelsfromPalatinetoChicagoat65mph.SusietravelsfromChicagotoPalatineat65mph.Arethevelocitiesequal?No,differentdirectionsCheckyourunderstandingJimtr8FirstEquation!v=(df-di)/(tf-ti)ORcommonlywrittenasv=?d/?t*?meanschangeAverageSpeed/Velocity

FirstEquation!AverageSpeed/V9SampleProblemIngym,youhavetorunthe100mdash.Ifyourunitin18s,whatwasyourvelocity?SampleProblemIngym,youhave10SampleProblemAfreakyfastJimmyJohnsdeliverymanmakesadeliverythatis2.2milesawayandittakeshim9min.Whatishisaveragevelocityinmi/hr?SampleProblemAfreakyfastJi11Technicaldifferencebetweencalculatingspeedandvelocity:SPEED(AVERAGE)Totaldistancetraveleddividedbythetotaltimeelapsed**Example:RoundtripdrivetoschoolVELOCITYTotaldisplacementdividedbytotaltimeTechnicaldifferencebetweenc12AchangeinvelocityVectorquantityPositivevs.NegativeAcceleration+velocityand+acceleration=_____+velocityand-acceleration=_____-velocityand-acceleration=_____-velocityand+acceleration=_____Variable:aUnits:m/s/sorm/s2Equation: a=(vf-vi)/(tf-ti)ORcommonlywrittenas: a=?v/?tAccelerationAchangeinvelocityEquation:13CheckyourunderstandingName3waystoaccelerateyourcar:StepongaspedalSteponbrakepedalTurnsteeringwheelCheckyourunderstandingName314SampleProblemAcaracceleratesfromastopsignuptoaspeedof11m/s.Ifittakes4todoso,whatisthecar’sacceleration?SampleProblemAcaraccelerate15VelocityandAccelerationSampleProblemsProblem1:Howlongdoesittakeaturtletotravel1,000mifitcantravelatapaceof1.3m/s?Problems2:Whatisthechangeinvelocityifanobjectacceleratesat2m/s2for4.5seconds?

Iftheobjectstartedat3m/s,whatisitsfinalspeed?VelocityandAccelerationSamp16MotionGraphsDISTANCEVS.TIMEGRAPHSVELOCITYVS.TIMEGRAPHSSlopeisaccelerationSlope=rise/run=velocity/time=ACCELERATIONAreaundergraphisdistancetraveledArea=base*height=velocity*time=DistanceSlopeisvelocitySlope=rise/run=distance/time=VelocityMotionGraphsVELOCITYVS.TIME17GeneralGraphTrendsStraightLines–CONSTANTCurvingLines–CHANGINGFlatLine-ZEROSteepertheslope,thehigherthevalueGeneralGraphTrendsStraightL18Whatcanyoutellmeaboutaccelerationonthesegraphs?Whatcanyoutellmeaboutacc19Big5EquationsDefinitionofaveragevelocity: (vi+vf)/2Distance=rate*time: d=vavg*tDefinitionofacceleration(finalvelocity): vf=vi+atTimeless: vf2=vi2+2a?dPosition: ?d=vit+1/2at2Big5EquationsDefinitionofa20ChecklistforSuccessEquation?xvivf?taDefinitionofaveragevelocity:vavg=(vi+vf)/2Distance=rate*time:x=vavg*t√√√√○Definitionofacceleration(finalvelocity):vf=vi+at○√√√√Timeless:vf2=vi2+2a?x√√√○√Position:?x=vit+1/2at2√√○√√ChecklistforSuccessEquation?21ProblemSolvingStrategiesIdentifygivensLookforhiddengivensIdentifyunknown(s)ComparegivensandunknownstoequationsInthebeginning:chartRe-readproblemifstuck*alwaysshowyourwork(G.U.E.S.S.)ProblemSolvingStrategiesIde22SampleProblemWhatisStarlinCastro’saccelerationasherunstowardfirstbaseifhereachesthebasewithaspeedof6.5m/s?Thedistancebetweentheplatesis27.432meters.SampleProblemWhatisStarlin23SampleProblem#2Anairplanecanaccelerateatarateof4.9m/s2.Ifittakes45sfortheplanetostarttoelevateandtheplanestartsfromrest,whatistheminimumlengthofrunwayrequired?SampleProblem#2Anairplanec24StoppingDistanceSampleSeeingastops