A-level——physics——chapter2

PHYSICSAdvancedLevelCHAPTER1Measurement1.1PhysicalQuantitiesAllphysicalquantitiesconsistofaprecisenumericalvalueandastandardorunit.SI：theInternationalSystemofUnitsBasequantityorfundamentalquantity：BaseunitBasequantityorfundamentalquantity：BaseunitMasskilogramlengthmetretimesecondelectriccurrentamperetemperaturekelvinamountofsubstancemoleluminousintensitycandeladerivedquantityderivedunitAream2momentumkgm/spressurepascalWorkdonejoulepowerwattelectricchargecoulombPotentialdifferencevoltresistanceohmfrequencyhertzscalarquantityvectorunitdistancedisplacementspeedvelocitytemperatureaccelerationenergyforcepowermomentummassweightdensitymomentpressuretorquevolumeelectricfieldtimemagneticfluxdensitymagnitudescalarvectormagnitudeanddirectionAdditionandsubtractionofvectorsTheeffectoftheresultantvectorisentirelythesameasthecombinedactionofitsseparatevectors.Additionandsubtractionofvectorsinthesamedirection:additionofseparatevectorsinoppositedirection:subtractionofseparatevectorsindifferentdirection:parallelogram/triangle/headtotailmethodseparatevectors——componentsofvectorsCHAPTER2Kinematics2.1rectilinearmotionMotionisthechangeinpositionofaparticlewithrespecttotime.apointmassaidealisephysicalobjectDisplacementanddistanceDisplacementMagnitude：△x=x2-x1Direction：fromtheinitialpositiontothefinalpositionUnit：metreDistanceMagnitude：thelengthofpathtravelledUnit：metre012345-1-2-3-4-5ABCDDeterminethedisplacementandthedistancetravelledbyfourparticles:Particle1travellsfromAtoC.Particle2travellsfromDtoC.Particle3travellsfromBtoC,thenfromCtoD.Particle4travellsfromBtoA,thenfromAtoD.X/mNegativeorpositivesignfordisplacementindicatesdirection.Themagnitudeofthedisplacementandthedistancetravelledarethesameonlywhenanobjectmovesinonedirectioninastraightline.AveragespeedandconstantspeedUnit:m/sorms-1AveragevelocityUnit:m/sorms-1Itcorrespondstothedisplacementandthetimeinterval.InstantaneousvelocityItcorrespondstothepositionandtheparticularmoment.Unit:m/sorms-1InstantaneousspeedSpeedometerInstantaneousvelocityAveragevelocityAveragespeedInstantaneousspeedmagnitudeConstantvelocitymagnitudeAverageaccelerationUnit:m/s2orms-2Itcorrespondstothedisplacementandthetimeinterval.Question2Themotionofaparticletravellingalongthex-axisisdescribedbytheequationx(t)=10t+5t2(a)Findthedisplacementoftheparticleinthetimeintervalbetweent1=1sandt2=5s.(b)Findtheaveragevelocityinthistimeinterval.(c)Findtheinstantaneousvelocityattimet=3s.Question2Themotionofaparticletravellingalongthex-axisisdescribedbytheequationx(t)=10t+5t2(a)Findthedisplacementoftheparticleinthetimeintervalbetweent1=1sandt2=5s.Answer△x=x(t2)-x(t1)=160mQuestion2Themotionofaparticletravellingalongthex-axisisdescribedbytheequationx(t)=10t+5t2(b)Findtheaveragevelocityinthistimeinterval.Answer(b)inthepositivedirectionofthex-axis.Question2Themotionofaparticletravellingalongthex-axisisdescribedbytheequationx(t)=10t+5t2(c)Findtheinstantaneousvelocityattimet=3s.Answer(c)Whent=3s,v=40m/sInstantaneousaccelerationItcorrespondstothepositionandtheparticularmoment.Unit:m/s2orms-2Thechangeinvelocityataninstantoftimeiscalledinstantaneousacceleration.Question3Anobjectfallsfreelyfromrestwithaconstantaccelerationof9.8ms-2for3.0seconds.whatisthespeedoftheobjectattheendof3.0seconds.AnswerSignconventionTheaccelerationispositiveornegativedependsonwhetherthatparticleisspeedinguporslowingdown.Wetakethedirectiontotherightasthepositivedirectionandthedirectiontotheleftasnegative.Anobjectmovesinthepositivedirectionandspeedsup.accelerationTheobjectmovesinthepositivedirectionandslowsdown.decelerationTheobjectspeedsupinthenegativedirection.accelerationTheobjectslowsdownasitmovesinthenegativedirection.decelerationTheaccelerationvectorisintheoppositedirectionfromthevelocityvectors,theobjectisslowingdown.Inotherwords,whentheobject’saccelerationisinthesamedirectionasitsvelocity,theobject’sspeedincreases.Whentheyareinoppositedirections,thespeeddecreases.Anobjecthasapositiveaccelerationwhentheaccelerationvectorpointsinthepositivedirectionandanegativeacceleration,whentheaccelerationvectorpointsinthenegativedirection.Thesignofaccelerationdoenotindicatewhethertheobjectisspeedinguporslowingdown.speedingupv(+)—a(+);v(-)—a(-);slowingdown.v(+)—a(-);v(-)—a(+);vBACVelocityandaccelerationofaprojectedobjectGraphsx(m)t(s)x1x2t1t2Displacement-timegraphAtaconstantratex-tgraphGraphsv(m/s)t(s)v1v2t1t2Velocity-timegraphAtaconstantratev-tgraphvDisplacementvelocityandaccelerationofaprojectedobjectDeterminationofvelocityandaccelerationgraphicallyDisplacementofaprojectedobjectx(m)t(s)x-tgraphv(m/s)t(s)v-tgraphVelocityofaprojectedobjecta(m/s2)t(s)a-tgraphAccelerationofaprojectedobjectAreaunderthevelocity-timegraphIngeneral,Displacement=areaunderthev-tgraphv(m/s)t(s)v(m/s)t(s)t1t2Methodofsolvingkinematicsproblems(a)Drawdiagramstogainabetterunderstandingoftheproblem(b)List①theknownquantitiesthataregiven，②theunknownquantitiesrequired.(c)Definethepositivedirectionandusethecorrectsignconventionforalltheknownandunknownquantities.(d)Selectthemostappropriateequationsofmotion.Figureshowsthespeed-timegraphoftwobuses,AandB,travellinginthesamedirection.BusAovertakebusBattimet=0asshowninthegraph.InordertocatchupwithbusA,busBacceleratesuniformlyfor10suntilitreachesaconstantspeedof30m/s.Question4t(s)01020speed(m/s)3020100(a)WhatisthedistancetravelledbybusAduringthefirst10s?ABFigureshowsthespeed-timegraphoftwobuses,AandB,travellinginthesamedirection.BusAovertakebusBattimet=0asshowninthegraph.InordertocatchupwithbusA,busBacceleratesuniformlyfor10suntilitreachesaconstantspeedof30m/s.Question4t(s)01020speed(m/s)3020100(b)FindtheaccelerationofbusBduringthefirst10s?ABFigureshowsthespeed-timegraphoftwobuses,AandB,travellinginthesamedirection.BusAovertakebusBattimet=0asshowninthegraph.InordertocatchupwithbusA,busBacceleratesuniformlyfor10suntilitreachesaconstantspeedof30m/s.Question4t(s)01020speed(m/s)3020100(c)WhatisthedistancetravelledbybusBatt=10s?ABFigureshowsthespeed-timegraphoftwobuses,AandB,travellinginthesamedirection.BusAovertakebusBattimet=0asshowninthegraph.InordertocatchupwithbusA,busBacceleratesuniformlyfor10suntilitreachesaconstantspeedof30m/s.Question4t(s)01020speed(m/s)3020100(d)HowfarisbusAaheadofbusBatt=10s?ABFigureshowsthespeed-timegraphoftwobuses,AandB,travellinginthesamedirection.BusAovertakebusBattimet=0asshowninthegraph.InordertocatchupwithbusA,busBacceleratesuniformlyfor10suntilitreachesaconstantspeedof30m/s.Question4t(s)01020speed(m/s)3020100(e)Whatadditionaltimefromt=10swillittakebusBtojustovertakebusA?ABFigureshowsthespeed-timegraphoftwobuses,AandB,travellinginthesamedirection.BusAovertakebusBattimet=0asshowninthegraph.InordertocatchupwithbusA,busBacceleratesuniformlyfor10suntilitreachesaconstantspeedof30m/s.Question4t(s)01020speed(m/s)3020100(f)Bythen,whatwillbethedistancetravelledbyeachbussincet=0s?ABFigureshowsthespeed-timegraphoftwobuses,AandB,travellinginthesamedirection.BusAovertakebusBattimet=0asshowninthegraph.InordertocatchupwithbusA,busBacceleratesuniformlyfor10suntilitreachesaconstantspeedof30m/s.Question4t(s)01020speed(m/s)3020100(g)Findthetimetakenfromt=0sforthetwobusestoattainthesamespeed.ABFigureshowsthespeed-timegraphoftwobuses,AandB,travellinginthesamedirection.BusAovertakebusBattimet=0asshowninthegraph.InordertocatchupwithbusA,busBacceleratesuniformlyfor10suntilitreachesaconstantspeedof30m/s.Question4t(s)01020speed(m/s)3020100(h)Hence,orotherwise,findthefurthestdistanceseparatingthebusesbeforebusBovertakebusA.ABEquationsofmotiont(s)velocity(m/s)v<v>uABThevelocityincreasesataconstantrate.Hencetheaveragevelocityismidwaybetweenuandv.Displacement=areaunderthev-tgraph