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Chapter 6A. Acceleration

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Chapter 6A. Acceleration ChapterChapter 6A.6A. AccelerationAcceleration AAA PowerPointPowerPointPowerPoint PresentationPresentationPresentation bybyby PaulPaulPaul E.E.E. Tippens,Tippens,Tippens, ProfessorProfessorProfessor ofofof PhysicsPhysicsPhysics SouthernSouthernSouthern PolytechnicPolytechnicPolytechnic StateStateState UniversityUniversityUniversity © 2007 The Cheetah: A cat that is built for speed. Its strength and agility allow it to sustain a top speed of over 100 km/h. Such speeds can only be maintained for about ten seconds. Photo © Vol. 44 Photo Disk/Getty Objectives:Objectives: AfterAfter completingcompleting thisthis module,module, youyou shouldshould bebe ableable to:to: •• DefineDefine andand applyapply conceptsconcepts ofof averageaverage andand instantaneousinstantaneous velocityvelocity andand acceleration.acceleration. •• SolveSolve problemsproblems involvinginvolving initialinitial andand finalfinal velocityvelocity,, accelerationacceleration,, displacementdisplacement,, andand timetime.. •• DemonstrateDemonstrate youryour understandingunderstanding ofof directionsdirections andand signssigns forfor velocity,velocity, displacement,displacement, andand acceleration.acceleration. •• SolveSolve problemsproblems involvinginvolving aa freefree--fallingfalling bodybody inin aa gravitationalgravitational fieldfield.. UniformUniform AccelerationAcceleration inin OneOne Dimension:Dimension: •• MotionMotion isis alongalong aa straightstraight lineline (horizontal,(horizontal, verticalvertical oror slanted).slanted). •• ChangesChanges inin motionmotion resultresult fromfrom aa CONSTANTCONSTANT forceforce producingproducing uniformuniform acceleration.acceleration. •• TheThe causecause ofof motionmotion willwill bebe discusseddiscussed later.later. HereHere wewe onlyonly treattreat thethe changes.changes. •• TheThe movingmoving objectobject isis treatedtreated asas thoughthough itit werewere aa pointpoint particle.particle. DistanceDistance andand DisplacementDisplacement DistanceDistance isis thethe lengthlength ofof thethe actualactual pathpath takentaken byby anan object.object. ConsiderConsider traveltravel fromfrom pointpoint AA toto pointpoint BB inin diagramdiagram below:below: DistanceDistance ss isis aa scalarscalar quantity (no direction): B quantity (no direction): s = 20 m ContainsContains magnitudemagnitude onlyonly A andand consistsconsists ofof aa numbernumber andand aa unit.unit. (20(20 m,m, 4040 mi/h,mi/h, 1010 gal)gal) DistanceDistance andand DisplacementDisplacement DisplacementDisplacementDisplacement isisis thethethe straightstraightstraight-line--lineline separationseparationseparation ofofof twotwotwo pointspointspoints ininin aaa specifiedspecifiedspecified direction.direction.direction. A vector quantity: D = 12 m, 20o B Contains magnitude A AND direction, a number, unit & angle. (12 m, 300; 8 km/h, N) DistanceDistance andand DisplacementDisplacement ••• ForForFor motionmotionmotion alongalongalong xxx ororor yyy axis,axis,axis, thethethe displacementdisplacementdisplacement isisis determineddetermineddetermined bybyby thethethe xxx ororor yyy coordinatecoordinatecoordinate ofofof itsitsits finalfinalfinal position.position.position. Example:Example:Example: ConsiderConsiderConsider aaa carcarcar thatthatthat travelstravelstravels 888 m,m,m, EEE thenthenthen 121212 m,m,m, W.W.W. NetNet displacementdisplacement DD isis from the origin to the from the origin to the D finalfinal position:position: 8 m,E x DD == 44 m,m, WW x = -4 x = +8 WhatWhat isis thethe distancedistance 12 m,W traveled?traveled? 20 m !! TheThe SignsSigns ofof DisplacementDisplacement •• DisplacementDisplacement isis positivepositive (+)(+) oror negativenegative ((--)) basedbased onon LOCATIONLOCATION.. Examples: 2 m The displacement is the y-coordinate. Whether motion is -1 m up or down, + or - is based on LOCATION. -2 m TheThe directiondirection ofof motionmotion doesdoes notnot matter!matter! DefinitionDefinition ofof SpeedSpeed ••• SpeedSpeedSpeed isisis thethethe distancedistancedistance traveledtraveledtraveled perperper unitunitunit ofofof timetimetime (a(a(a scalarscalarscalar quantity).quantity).quantity). s 20 m s = 20 m B v = = t 4 s A vv== 55 m/sm/s Not direction dependent! Time t = 4 s DefinitionDefinition ofof VelocityVelocity ••• VelocityVelocityVelocity isisis thethethe displacementdisplacementdisplacement perperper unitunitunit ofofof time.time.time. (A(A(A vectorvectorvector quantity.)quantity.)quantity.) s = 20 m D 12 m B v D=12 m t 4 s A o 20 vv == 33 m/sm/s atat 202000 NN ofof EE Time t = 4 s Direction required! ExampleExample 1.1. AA runnerrunner runsruns 200200 m,m, east,east, thenthen changeschanges directiondirection andand runsruns 300300 m,m, westwest.. IfIf thethe entireentire triptrip takestakes 6060 ss,, whatwhat isis thethe averageaverage speedspeed andand whatwhat isis thethe averageaverage velocity?velocity? RecallRecall thatthat averageaverage s = 300 m s = 200 m speedspeed isis aa functionfunction 2 1 onlyonly ofof totaltotal distancedistance andand totaltotal timetime:: start TotalTotal distance:distance: ss == 200200 mm ++ 300300 mm == 500500 mm total path 500 m Average speed Avg. speed time 60 s 8.33 m/s DirectionDirection doesdoes notnot matter!matter! ExampleExample 11 (Cont.)(Cont.) NowNow wewe findfind thethe averageaverage velocity,velocity, whichwhich isis thethe netnet displacementdisplacement divideddivided byby timetime.. InIn thisthis case,case, thethe directiondirection matters.matters. x x tt == 6060 ss f 0 x = -100 m x = +200 m v f 1 t xo = 0 xx0 == 00 m;m; xxf == --100100 mm Direction of final 100 m 0 Direction of final v 1.67 m/s displacementdisplacement isis toto 60 s thethe leftleft asas shown.shown. Average velocity: v 1.67 m/s, West Note:Note: AverageAverage velocityvelocity isis directeddirected toto thethe west.west. ExampleExample 2.2. AA skysky diverdiver jumpsjumps andand fallsfalls forfor 600600 mm inin 1414 s.s. AfterAfter chutechute opens,opens, hehe fallsfalls anotheranother 400400 mm inin 150150 s.s. WhatWhat isis averageaverage speedspeed forfor entireentire fall?fall? 14 s TotalTotal distance/distance/ totaltotal time:time: xxAB 600 m + 400 m A v 625 m ttAB 14 s + 150 s 1000 m v v 6.10 m/s 164 s B AverageAverageAverage speedspeedspeed isisis aaa functionfunctionfunction 356 m onlyonlyonly ofofof totaltotaltotal distancedistancedistance traveledtraveledtraveled andandand thethethe totaltotaltotal timetimetime required.required.required. 142 s ExamplesExamples ofof SpeedSpeed Orbit 2 x 104 m/s Light = 3 x 108 m/s Jets = 300 m/s Car = 25 m/s SpeedSpeed ExamplesExamples (Cont.)(Cont.) Runner = 10 m/s Glacier = 1 x 10-5 m/s Snail = 0.001 m/s AverageAverage SpeedSpeed andand InstantaneousInstantaneous VelocityVelocity ... TheTheThe averageaverageaverage speedspeedspeed dependsdependsdepends ONLYONLYONLY ononon thethethe distancedistancedistance traveledtraveledtraveled andandand thethethe timetimetime required.required.required. s = 20 m B TheThe instantaneousinstantaneous C velocityvelocity isis thethe magn-magn- A itudeitude andand directiondirection ofof thethe speedspeed atat aa par-par- ticularticular instant.instant. (v(v atat Time t = 4 s pointpoint C)C) TheThe SignsSigns ofof VelocityVelocity ... VelocityVelocityVelocity isisis positivepositivepositive (+)(+)(+) ororor negativenegativenegative (((-)--)) basedbasedbased ononon directiondirectiondirection ofofof motion.motion.motion. + - FirstFirst choosechoose ++ direction;direction; + thenthen vvisis positivepositive ifif motionmotion isis withwith thatthat direction,direction, andand - negativenegative ifif itit isis againstagainst thatthat + direction.direction. AverageAverage andand InstantaneousInstantaneous vv AverageAverage Velocity:Velocity: InstantaneousInstantaneous Velocity:Velocity: xxx21 x vavg vtinst (0) ttt21 t slope x xx 2 x x xx 1 t tt Displacement, tt 1 tt 2 Time DefinitionDefinition ofof AccelerationAcceleration .. AnAn accelerationacceleration isis thethe changechange inin velocityvelocity perper unitunit ofof time.time. (A(A vectorvector quantity.)quantity.) .. AA changechange inin velocityvelocity requiresrequires thethe applicationapplication ofof aa pushpush oror pullpull ((forceforce).). AA formalformal treatmenttreatment ofof forceforce andand accelerationacceleration willwill bebe givengiven later.later. ForFor now,now, youyou shouldshould knowknow that:that: • The direction of accel- • The acceleration is eration is same as proportional to the direction of force. magnitude of the force. AccelerationAcceleration andand ForceForce F a 2F 2a PullingPullingPulling thethethe wagonwagonwagon withwithwith twicetwicetwice thethethe forceforceforce producesproducesproduces twicetwicetwice thethethe accelerationaccelerationacceleration andandand accelerationaccelerationacceleration isisis ininin directiondirectiondirection ofofof force.force.force. ExampleExample ofof AccelerationAcceleration + Force t = 3 s v0 = +2 m/s vf = +8 m/s The wind changes the speed of a boat from 2 m/s to 8 m/s in 3 s. Each second the speed changes by 2 m/s. WindWind forceforce isis constant,constant, thusthus accelerationacceleration isis constant.constant. TheThe SignsSigns ofof AccelerationAcceleration ••• AccelerationAccelerationAcceleration isisis positivepositivepositive (((+)++)) ororor negativenegativenegative (((-)--)) basedbasedbased ononon thethethe directiondirectiondirection ofofof forceforceforce... + ChooseChooseChoose +++ directiondirectiondirection first.first.first. F a (-) ThenThenThen accelerationaccelerationacceleration
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