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Ќ  H+4 44 <DL!44` X!H____________________________________________________  ( ____________________________________________________  > "]8"  -44` X!444X!-]823  0 `   Whydidyouusewordssuchas__________________________?]8Y݌ T` !` ! Ќ  H+4 44 <DL!44` X!H____________________________________________________  j ____________________________________________________  "]8"  -44` X!444X!-]823  0 `   Sometimes,measurementsrequirea_____________tomake   themcomplete.]8P݌2 ` !` ! Ќ  "]8"  ]8423  0 `   Measurementsthatdo______requireadirectionarecalled H  _________quantities.Examplesofscalarquantitiesare:]84a݌^ ` !` ! Ќ  ` X?"< <<DL!44` X!?________ex.____________ t  ________ex.____________  "]8"  X` -44` X!<<<X!-]8 23  0 `   Measurementsthat_____requireadirectionarecalled  ___________quantities.Example:_________________]8 ݌0` !` ! Ќ  "]8"  ]823  0 `   Directionisalwayswritten________thenumberandthe F followingformatis___________used#X{XX\X}i#.]8݌\` !` ! Ќ  "^k"  XB% <DL!44` X!B#X:XXX{^k0 23  0< ! !  X}XX#X:North=_______^kw݌r<!<! Ќ  "^k"  <% <DL!  X!<#X:XXX}^kC0 23  0< ! !  X}XX#X:East=_______^kC݌<!<! Ќ  "^k"  <% <DL!  X!<#X:XXX}^k0 23  0< ! !  X}XX#X:South=_______^k݌(<!<! Ќ  "^k"  <% <DL!  X!<#X:XXX}^k0 23  0< ! !  X}XX#X:West=_______^kr݌@<!<! Ќ  "]8"  X*44` X!  X!*]8= 23  0 `   Directionisarrangedonanobjectcalleda____________and X NorthisALWAYSpointing_______.]8= ݌n ` !` ! Ќ  XH+ 4 <DL!44` X!H"]8"  X*44` X!X!*]8!23  0 `   Onewaytoremembertheorderonacompassis &l   _______________]8!^"݌(!` !` ! Ќ  H+4 44 <DL!44` X!H ,_____________________________________ )"   XE+ 4 <DL!444X!E 4*#!  J+$"  `,%#  4    <   _XXXX}_UX_XUnit3Lesson3!Page2# _U˟$##X}X $# v-&$ )    X}XXX}X}XXX}    & X %  DISPLACEMENT% &  %Ԍ t ЌX}XXX}X}XXX}  "]8"  ?(4 4 <DL!X!?]8&23  0 4   Displacementisthe_____________AND_____________traveled  betweenthe_______________and_________ofatrip.]8&1'݌,4!4! Ќ  "]8 "  ?(4 4 <DL!44X!?]8@(23  0 4   Displacementisa____________quantity.'Xt&]8@((݌ B4!4! Ќ  "]8 "  ?(4 4 <DL!44X!?]8q)23  0 4   Itssymbolis_______.Noticethisisalmostthesameas  X ____________,exceptthereisan__________ontopofthed.]8q))݌ n4!4! Ќ  "]8 "  ?(4 4 <DL!44X!?]8*23  0 4   Ifasymbolhasan_________ontopofit,thenitisavector   quantity(therefore,ithasa____________).]8*]+݌4!4! Ќ  "]8 "  ?(4 4 <DL!44X!?]8f,23  0 4   -   XX}%&*yied~=Rp@ "0 d REaRR7$%(*yied~ p@ "0;_ d;_E$$-  X}X Whenwediscuss+X XXX}_D X}X X+Xd_,weneedtohavea______________________. $ Areferencepointisthepointfromwhichwe____________our :  ________.Exampleofreferencepointsare________ona P  ____________line,the_____________pointforatrip,or(,) f  onan(,)axis.]8f,,݌| 4!4! Ќ  "]8 "  ?(4 4 <DL!44X!?]8023  0 4   Letslookatanexample:]80=1݌ 4!4! Ќ  -   XX}%,<yied~H Rp@ "0H dH RE$ x R R -&%.<yied~lRp@ "0 d RE RR %0<yied~lRp@ "0 d RERRE%2<yied~lRp@ "0 d RERR56<k[W@~l p @X@ EH  H 58<k[W@~\ p @X@ E8 859<k[W@~lXH g p @X@ EH H gH H H g5:<k[W@~X g p @X@ E  g  g 5;<k[W@~X g p @X@ E  g  g -  X}X  4    1  G "]8"  ?(4 4 <DL!44X!?]8n823  0 4   Onthisnumberline,0isthereferencepointfromwhichwewill ] measure___________________.]8n88݌s4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]8923  0 4   Ineedtodrawa_____________bythenumberlineinorderto  knowwhat_____________Imtraveling.]89A:݌4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]8F;23  0 4   PointAis__________fromthereferencepointandpointBis ) __________fromthereferencepoint.]8F;;݌?4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]8<23  0 4   -   XX}%=Ayied~(R p@ "0 d RE }"RRu 2" %?Ayied~D p@ "0;_ d;_E /" != -  X}X IfItravelfrompointAtopointB,whatismychangein U  displacement?]8<=݌k!4!4! Ќ  <% <DL!44X!<+X XXX}  ,_D X}X X+Xd_Ԁ=___________ "  "]8"  , -4 X   X!-]8@23  0 4   IfItravelfrompointBtopointA,whatismychangein ## displacement?]8@ A݌$94!4! Ќ  B% <DL!4 X B-   XX} %BFyied~;Rp@ "0 d RE %RRu % %DFyied~Dp@ "0;_ d;_E % %-  X}X +X XXX}_D X}X X+Xd_Ԁ=____________ %O  -, X   X!-@22_XXXX}_UX_XUnit3Lesson3!Page3# _UD##X}X D#Ԉ  ]-&$ "]8"    ]8E23  0 4   -   XX}%GKyied~Rp@ "0 d RE RRu ;%IKyied~Dp@ "0;_ d;_E 8 =-  X}X IfItravelfromthereferencepointtopointB,andthenfrompointB t topointA,whatismychangeindisplacement?]8EE݌4!4! Ќ  B% <DL!, X B-   XX} %LPyied~Rp@ "0 d RE RR e %NPyied~pp@ "0;_ d;_ELb  =-  X}X +X XXX}D X}X X+Xd=____________ , "]8"  -4 X   X!-]8J23  0 4   Why?Because+X XXX}D X}X X+Xdismy_____________AND______________  B fromthe________________ofmytriptothe________ofmy  X trip.]8JTK݌ n4!4! Ќ  "]8"  X,044` X!4 X 0 ]8L23  0 4   -   XX}%QhfVRd~t rpp@ 04LpEPpp5 5Shk[W@~N d @ p @X@ E*r @ *r @5Thk[W@~N  @ p @X@ E* @ * @5Uhk[W@~ @ p @X@ Ez .@z .@5Vhk[W@~ @ p @X@ E.@.@%Whivfbd~L Gp@ 0 ddHHE(U %Yhivfbd~L Gp@ 0 ddHHE(U %Zhjvfbd~L p@ 0 ddHHE(O%\hjvfbd~L p@ 0 ddHHE(O%]hkvfbd~Gp@ 0 ddHHE\U %_hkvfbd~Gp@ 0 ddHHE\U %`hlvfbd~p@ 0 ddHHE\O%bhlvfbd~ p@ 0 ddHHE\O5chk[W@~ @! p @X@ E  @   @ 5dhk[W@~ @" p @X@ E @  @!5ehk[W@~@# p @X@ Ez @z @"5fhk[W@~ @$ p @X@ Ev @ v @#5ghk[W@~ @% p @X@ Ev @ v @$-  X}X Example:]8L9M݌4!4! Ќ  H+ 4 <DL!44` X!H $  :   P   f   |     "]8"  *44` X!X!*]8Z23  0 4   Onmywayhomefromschool,Istopatthemallandthebank.]8ZZ݌44!4! Ќ  "]8"  XB% <DL!44` X!B#X:XXX}]8[23  0   X}XX#X:WhatismychangeinDISTANCEforthistrip?]8[U\݌J ! ! Ќ  B+` ` ` <DL!  X!B b  x "]8"  B% <DL!` ` ` X!B#X:XXX}]8]23  0   X}XX#X:WhatismychangeinDISPLACEMENTforthistrip?]8]?^݌ ! ! Ќ  B+ 4 <DL!  X!B   0  F X}XXX}X}XXX}    &  _  DRAWINGVECTORS_` _Ԍ \ ЌX}XXX}X}XXX}  "]8"  X?(4 4 <DL!X!?]8`23  0 4   Avectorcanalsobeshownbydrawingaline_____________withan r __________.Thelengthofthelinesegmentshowsthe________   ofthevectorandthearrowshowswhich____________thevector !* isin.]8`Pa݌"@4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]8b23  0 4   Example:1m[N]canbedrawnas:'\`]8bJc݌#V4!4! Ќ   $l  %   '   "(!  8)"   N*#!  d+$"  z,&# @!_XXXX}_UX_XUnit3Lesson3!Page4# _Ud##X}X d#Ԉ -'$    t "]8"  ?(4 4 <DL!44X!?]8e23  0 4   ThefollowingrulesMUSTbeusedwhendrawingvectors:]8ef݌4!4! Ќ   m (0yg]^`abcdef/ /""  ,XE.4 <DL!44X!E  X,E(4 4 <DL!4X!Erg2  1  .3   4   Drawa____________(__C)rgSh݌ , Ќ XX$ 44X!44X!$   ""  ,XE.4 <DL!44X!E  X,E(4 4 <DL!4X!E?i2  2  .3   4   Decideona_________andwriteitdown.Youwillalwaysdecideon  B what_______equals(__I).Example:1cm=5mor1cm=20km?i j݌  X Ќ XX$ 44X!44X!$   ""  ,XE.4 <DL!44X!E  X,E(4 4 <DL!4X!Ek2  3  .3   4   ACCURATELY________yourlinesegmentbasedonyour  n __________(__I).kgl݌   Ќ XX$ 44X!44X!$   ""  ,XE.4 <DL!44X!E  X,E(4 4 <DL!4X!Em2  4  .3   4   Addan________toyourlinesegmentsothatitpointsinthecorrect  ____________.(__I)mtn݌ $ Ќ XX$ 44X!44X!$   ""  ,XE.4 <DL!44X!E  X,E(4 4 <DL!4X!Eo2  5  .3   4   _________yourvector(__C)op݌ :  Ќ XX$ 44X!44X!$   ,XE.4 <DL!44X!E ,(Therefore,eachvectordiagramisworth___Iand___C) P   f   |     Example: 4 Drawthefollowingvectors: J -   XX}%osyied~4R&p@ "0 d RERRs%%qsyied~'p@ "0;_ d;_Epp%%=&-  X}X  `  t (00m / / X, ,""  ,XK.4 <DL!4X!K  X,E(4 4 <DL!4X!EQu2  a  )3   4   +X XXX}D X}X X+Xd=15km[W]Qu8v݌ G Ќ XX*4X!44X!*   XH+ 4 <DL!4X!H ]  s     -   XX}%vzyied~4R(p@ "0 d RERR'%xzyied~)p@ "0;_ d;_Ep%d=(-  X}X  ) ""  ,E.4 <DL!X!E  X,E(4 4 <DL!4X!Ey2  b  )3   4   +X XXX}D X}X X+Xd=6m[S]yz݌  Ќ X$ X!44X!$    &   ,%yied~*p@ "0;_ d;_E <=--  #X}X #Thetotaldisplacementforatripiscalledthe_______________  displacementandhasthesymbolof________.]83݌,4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]8a23  0 4   #X{XXX}#+X XXX{D #X{X X+X7#X}XXX{dRallowsustoseethe___________displacementfromwherewe B ______________towherewe______________.]8a͋݌X4!4! Ќ   n  ADDINGVECTORSWITHDIAGRAMS   "]8"  ?(4 4 <DL!44X!?]823  0 4   Whenwelearnedtodraw___________,theylookedsomethinglike  this:]8뮍݌$ 4!4! Ќ   :!  P"  f# "]8"  ?(4 4 <DL!44X!?]8<23  0 4   Thebeginningofthevector(theendwiththe____________)is |$ calledthe ________andtheendofthevectoriscalledthe %  ________.]8<݌&4 4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]823  0 4   -   XX} %yied~*Rp@ "0 d RE*RR[*.%yied~*p@ "0;_ d;_E *O*=/%yied~<Rp@ "0 d RE 'RRI '0%yied~p@ "0;_ d;_E ' '1-  #X}X ĭ# Tofind#X{XXX}}#+X XXX{D #X{X X+X#X}XXX{dR,wefollowthe ___________________rule,which 'J! meansweconnectthe_________ofthe_________vectortothe (`"  __________ofthe__________vector.]8Z݌)v#!4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]8\23  0 4   #X{XXX}.#+X XXX{D #X{X X+X2#X}XXX{dRisthenfoundbydrawingan_________fromthe_______of +$" the_________vectortothe________ofthe________vector.]8\Ȗ݌,%#4!4! Ќ  #X{XXX}x#_XXXX{_UX_X   ,-&$ Unit3Lesson3!Page6#C_Uː##X{XC#X}XXX{ -c'% Θ  "]8"  ?(4 4 <DL!44X!?]823  0 4   Example:]8럙 ݌t4!4! Ќ     , -   XX}%yied~< Rp@ "0 d RE RRQ 2%yied~ p@ "0;_ d;_ExN - =3-  #X}X #  B  STEPSFORFINDING#X{XXX}P#+X XXX{D #X{X X+X#X}XXX{dRWITHADIAGRAM  )  m (0 y g]^`abcdef/ / ""  ,XE.4 <DL!44X!E   q,E(M M <DL!4X!E%2  1  .3   M   Drawa___________(__C)%݌  ? Ќ Xq' 44X!MM X!'   ""  ,XE.4 <DL!44X!E   q,E(M M <DL!4X!E2  2  .3   M   Statethe_________(__C)݌  U Ќ Xq' 44X!MM X!'   ""  ,XE.4 <DL!44X!E   q,E(M M <DL!4X!E2  3  .3   M   Stateanappropriate________(__I)Ϣ݌  k Ќ Xq' 44X!MM X!'   ""  ,XE.4 <DL!44X!E   q,E(M M <DL!4X!Eȣ2  4  .3   M   -   XX}%yied~ )R p@ "0 d RERRQ4%yied~  p@ "0;_ d;_E5-  #X}X #_______thefirstvector(#X{XXX}'#+X XXX{D #X{X X+X#X}XXX{d1)toscaleand________it(__I,__C)ȣ݌  Ќ Xq' 44X!MM X!'   ""  ,XE.4 <DL!44X!E   q,E(M M <DL!4X!E2  5  .3   M   -   XX}%yied~ :R p@ "0 d REERRQ 6%yied~  p@ "0;_ d;_E  7-  #X}X i#_______thenextvector(#X{XXX}L#+X XXX{D #X{X X+XQ#X}XXX{d2)toscale,butstartdrawingitatthe    _______of#X{XXX}#+X XXX{D #X{X X+X(#X}XXX{d1andlabelit(__I,__C)݌ !  Ќ Xq' 44X!MM X!'   ""  ,XE.4 <DL!44X!E   q,E(M M <DL!4X!E)2  6  .3   M   -   XX}%yied~N)R p@ "0 d RE* `RR 78%yied~p@ "0;_ d;_E 7? 79-  #X}X ~#_______#X{XXX}n#+X XXX{D #X{X X+XU#X}XXX{dRandlabelit(__I,__C))݌ 7  Ќ Xq' 44X!MM X!'   ""  ,XE.4 <DL!44X!E   q,E(M M <DL!4X!EV2  7  .3   M   -   XX}%yied~?Rp@ "0 d RE RR M:%yied~pp@ "0;_ d;_ELMM;-  #X}X ī#__________#X{XXX}#+X XXX{D #X{X X+X#X}XXX{dRanduseyourscaletofigureouthowlongitis(__I, M  ___C)VE݌ c  Ќ Xq' 44X!MM X!'   ""  ,XE.4 <DL!44X!E   q,E(M M <DL!4X!E2  8  .3   M   -  Statea_______________sentence(__C)-  ݌ y Ќ Xq' 44X!MM X!'     ! ! g]^`abcdef(y0m "]8"  ?(4 4 <DL!44X!?]8x23  0 4   Example:Ms.Danielswalks25m[S]downthehallandthen15m[N]up 1 thehall.Whatisherresultantdisplacement?]8x݌G4!4! Ќ   ]  s      )  ?  U   k!  "   ##  $9  %O  &e   '{!  )"   *#!  1+$"  G,%# @!#X{XXX}˴#_XXXX{_UX_XUnit3Lesson3!Page7#C_Uˣ##X{XC»#X}XXX{Ԉ ]-&$    t  ADDINGVECTORSUSINGMATH   "]8"  ?(4 4 <DL!44X!?]8˼23  0 4   Whenaddingvectorsusingmath,weassign____________numbers , to_________and________and____________numbersto  B __________and__________.]8˼7݌ X4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]8x23  0 4   Letstrythiswiththesameexampleagain:]8x݌ n4!4! Ќ  "]8"  ?(4 4 <DL!44X!?]823  0 4   Ms.Danielswalks25m[S]downthehallandthen15m[N]upthehall.   Whatisherresultantdisplacement?]8뜿݌4!4! Ќ   $  :   P   f   |  -   XX}%yied~< Rp@ "0 d RERRW<%yied~ p@ "0;_ d;_ExT- ==-  #X}X ą#    wXSTEPSFORFINDING#X{XXX}B#+X XXX{_D #X{X X+X#X}XXX{dR_USINGMATH y  m (0yg]^`abcdef/ / ""  ,wE.4 <DL!44X!E  X,E(4 4 <DL!4X!E2  1  .3   4   __________whichdirectionis___________andwhichis  ______________(__C)݌ 1 Ќ wX$ 44X!44X!$   ""  ,wE.4 <DL!44X!E  X,E(4 4 <DL!4X!E2  2  .3   4   Listthe__________andconvertthedisplacementsto G ______________and____________numbers(__I,__C)݌ ] Ќ wX$ 44X!44X!$   ""  ,wE.4 <DL!44X!E  X,E(4 4 <DL!4X!E.2  3  .3   4   -   XX}%yied~ *Rp@ "0 d RERR}>%yied~Lp@ "0;_ d;_E(?-  #X}X u#Writethe____________for#X{XXX}#+X XXX{_D #X{X X+X_#X}XXX{dR_(__I).݌ s Ќ wX$ 44X!44X!$   ""  ,wE.4 <DL!44X!E  X,E(4 4 <DL!4X!Ek2  4  .3   4   Performthe_______________(__I)kL݌  Ќ wX$ 44X!44X!$   ""  ,wE.4 <DL!44X!E  X,E(4 4 <DL!4X!E@2  5  .3   4   Convertyouranswerbacktoa______________(__I)@!݌  Ќ wX$ 44X!44X!$   ""  ,wE.4 <DL!44X!E  X,E(4 4 <DL!4X!E&2  6  .3   4   Stateaconcludingsentence(1C)&݌ ) Ќ wX$ 44X!44X!$    ?  ***NOTE*** Themathmethod___________workswhenthevectorsare U  inthesame___________(orline).Example:EastandWest,orNorth k! andSouth,butNOTEastandSouth! "   ##   $9  %O  &e   '{!  )"   *#!  1+$"  G,%#    @S  @  @  @[  @  @   @c #X{XXX}#_XXXX{_UX_XUnit3Lesson3!Page8#C_UM##X{XCl#X}XXX{  ]-&$   EXAMPLES t    / /#X{XXX}#""  ,wE.4 <DL!44X!E  X,E(4 4 <DL!4X!E2  1  .3   4   X}XXX{Solvethisproblemusingthediagrammethod.݌ , Ќ wX$ 44X!44X!$   B+4 44 <DL!44X!B Xw Astudentleavesherhouseandtravels350m[W]tothemall,then  B 150m[W]tothegrocerystore,andfinally250m[E]toafriends  X house.Whatisthestudentsresultantdisplacement?  n  XE+ 4 <DL!444X!E#X{XXX}#""  ,E.4 <DL!X!E  X,E(4 4 <DL!4X!E2  2  .3   4   X}XXX{Solvethisproblemusingthemathmethod.݌ , Ќ X$ X!44X!$   XB+4 44 <DL!X!BWhilewalkingaroundinthemall,astudenttravels60m[N],then25m B [N]andthen95m[S].Whatisthestudentsresultantdisplacement? X #X{XXX}# XE+ 4 <DL!444X!EX}XXX{AnswerQuestions#17onp.165#X{XXX}"# %D _XXXX{_UX_X  Unit3Lesson3!Page9#C_U˟##X{XC# -&&  -O'' X{XXX{X}XXX{    & B   3.14VELOCITY  Ԍ t ЌX}XXX}X{XXX}  X}XXX{'Bt g]^`abcdef(y0m "]8"        !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~#X{XXX}#?(4 4 <DL!X!? , ]8f23  0    \X}XXX{Wevebeenlookingatthedifferencebetween_____________and , _______________thepastfewdays.Rememberthat  B _____________istheactual___________ofthetripyoutravelwhile  X ________________isthe_____________AND_____________  n fromthe_______________ofyourtriptothe________.#X{XX\X}I#]8f݌ !! Ќ  "]8"  ?(4 4 <DL!44X!?5l@\X@~1g~A  p @X@ E u~A~ u~A@]8E23  0    -  0XX{ 0%yied~ \<p@ "0X dX<Ej<<}6A%yied~D\tp@ "0L dLtE jtt* B%yied~ p@ "0 33d E&}XC5k[W@~ @ p @X@ E@@D5k[W@~T@ p @X@ E|b@|b@E5k[W@~P@ p @X@ E,@,@F5k[W@~H X@ p @X@ E$X@X$X@G5k[W@~X@ p @X@ EX@XX@H5k[W@~t @ p @X@ E| @ | @I5k[W@~t @ p @X@ E| @ | @J-  #X}X Ħ#Example:]8ES݌!! Ќ  E.4 <DL!44X!E5l\X@~1? p @X@ E} "?} "?K%|lhd~1_R" p^@ $$))" dp@E; 8R"R" $L5lM\X@~1? p @X@ E "? "?M5l\X@~1? p @X@ E} "?} "?N $ %|lhd~1]&R pb@ $$)&) dDpE &R&R LO :  5lP\X@~1A p @X@ E A AP P   f  #X{XXX}#"]8"  X,E(4 4 <DL!4X!E]8z23  0 4   X}XXX{IfItravelfrompointAtopointBtopointC,]8z݌| 4!4! Ќ  "]8"  X<% <DL!44X!<#X{XXX}A##X:XXX{]823  0   #X{XX#X:m#X}XXX{Whatismychangeindistance?__________]8݌  ! ! Ќ  "]8"  <% <DL!  X!<#X{XXX}##X:XXX{]823  0   #X{XX#X: #X}XXX{Whatismychangeindisplacement?___________]8,݌6 ! ! Ќ  B+ 4 <DL!  X!B N #X{XXX}#"]8"  X?(4 4 <DL!X!?]823  0 4   X}XXX{Rememberthatoneisa___________quantity(____________) d becauseit_____________havea____________andtheotherisa z ___________quantity(_______________)becauseit________  havea______________.]8=݌4!4! Ќ  #X{XXX}#"]8"  ?(4 4 <DL!44X!?]823  0 4   X}XXX{Nowweregoingtolookatthedifferencebetween____________ 0 and_____________.]8}݌F4!4! Ќ  #X{XXX}#"]8"  ?(4 4 <DL!44X!?]823  0 4   X}XXX{Does__________havea_____________?______.Therefore, \ __________isa___________quantity.]8 ݌r4!4! Ќ  #X{XXX}d #"]8"  ?(4 4 <DL!44X!?]8] 23  0 4   X}XXX{Velocityisa____________quantity.Itssymbolis______.   Velocityisthe_________and_____________fromthe !* ______________ofatriptothe_________ofatrip.Velocityis "@ the_________in______________dividedbythe_________in #V _________.]8]  ݌$l4!4! Ќ   %   '   "(!  8)"  #X{XXX} # N*#!  4+$"  ,%#  -&$ _XXXX{_UX_X  Unit3Lesson3!Page10#C_Uˇ ##X{XC # -r'%    "]8 "  ?(4 4 <DL!44X!?]8c23  0 4   X}XXX{Doesthislookfamiliar?Itistheexactsameformulafor t __________,exceptweuse______________insteadof  ____________inourcalculations.]8c݌,4!4! Ќ  #X{XXX}#"]8 "  ?(4 4 <DL!44X!?]8S23  0 4   X}XXX{Similartowhatwedidwithspeed,weregoingtobelookingat  B _____________velocity.]8S݌ X4!4! Ќ  #X{XXX}#"]8 "  ?(4 4 <DL!44X!?]823  0 4   X}XXX{Averagevelocityhasasymbolof_______andisdefinedasthe  n ___________changeof___________fromthe_________ofa   triptothe_______.]8e݌4!4! Ќ  #X{XXX}#"]8 "  ?(4 4 <DL!44X!?]823  0 4   X}XXX{Whatquantityhavewelookedatsofarthatdescribesour $ ___________changein____________? :  __________________________________]8R݌P 4!4! Ќ  #X{XXX}#"]8 "  ?(4 4 <DL!44X!?]823  0 4   X}XXX{Thereforeaveragevelocityisdefinedasfollows:]83݌f 4!4! Ќ   |      4  J  ` #X{XXX}z#"]8"  ?(4 4 <DL!44X!?]823  0 4   X}XXX{Letstakealookattheexampleagain:]8݌v4!4! Ќ  -   XX}%yied~<!R"p@ "0 d R"E !R"R" Q%yied~~&Rp@ "0 d &RE ~&R&R^ 3R5lS\X@~!S~A p @X@ E S~A~ S~AS5lT\X@~!? p @X@ Ej ?j ?T5lU\X@~!A p @X@ E A AU5k[W@~? p @X@ E` ?` ?V5k[W@~? p @X@ E` ?` ?W%yied~[<p@ "0X dX<E^[<<6X%yied~[tp@ "0L dLtE[ttk* Y%yied~p@ "0 33d E^XZ5k[W@~z @ p @X@ EV@V@[5 k[W@~6S@ p @X@ ES@S@\5 k[W@~@ p @X@ E@@]5 k[W@~ X@ p @X@ EX@XX@^5 k[W@~VX@ p @X@ E2X@X2X@_5 k[W@~6s @! p @X@ Es @ s @`5k[W@~6s @" p @X@ Es @ s @a-  #X}X #   s      ) #X{XXX}L#"]8"  ?(4 4 <DL!44X!?]8$23  0 4   X}XXX{IfItravelfrompointAtopointBtopointC]8$$%݌?4!4! Ќ   m (0yg]^`abcdef/ / -44, X!'44X!-""  ,XN.4 <DL!44, X!'N  344, X!'4X!3  X,&2  a  )3   `   Whatismychangeindistance?_________&'݌ U  Ќ XX644, X!'44, X!'6   K+4 44 <DL!44, X!'KIfittakesme2htomakethistrip,whatismyaveragespeed? k! Given: #X{XXX}k%#+X XXX{D #X{X X+X)#X}XXX{d= "   #X{XXX})#+X XXX{D #X{X X+XY*#X}XXX{t= ##  vav= $9 Formula: Calculations: %O ConcludingSentence: *#!  ,XH.4 <DL!444X!H#X{XXX}*#_XXXX{_UX_X  Unit3Lesson3!Page11#C_U+##X{XC+#X}XXX{ G,%# , ,~&$ Ї X,""  ,XK.4 <DL!4X!K  X,E(4 4 <DL!4X!E,2  b  )3   4   Whatismychangeindisplacement?_________,-݌ t Ќ XX*4X!44X!*   H+4 44 <DL!4X!HIfittakesme2htomakethistrip,whatismyaveragevelocity?  Given:#X{XXX},#X}XXX{e/"b `@E  be= , -   XX}%yied~R%p@ "0 d REh RR r c%yied~&p@ "0;_ d;_E o } $ =d-  #X}X U0# #X{XXX}/#+X XXX{_D #X{X X+X02#X}XXX{t_Ԁ=  I  _vav_=  _ Formula: Calculations:  u ConcludingSentence: A   XE+ 4 <DL!444X!E#X{XXX}2#! ! g]^`abcdef(y0m "]8"  X-44` <X!X!-]8423  0 `   X}XXX{NotethatdisplacementANDvelocitywill____________bein m  thesame______________.]844݌ ` !` ! Ќ  #X{XXX}C5#"]8"  344` X!44` <X!3]81623  0 `   X}XXX{Makesureyoupay______________towhatyouarebeingasked ; tofind!Thereisa_________differencebetween__________ Q and____________(wevejustseenthis).]8166݌g` !` ! Ќ  #X{XXX}6#"]8"  #X:XXX{ ,044,<X!44` X!0]8*823  0   #X{XX#X:W8#X}XXX{Ifyouaregivendistance,youMUSTfind_________andNOT } ____________!]8*88݌  ! ! Ќ  "]8"  B% <DL!44,<X!B#X{XXX}9##X:XXX{]8923  0   #X{XX#X:m:#X}XXX{Ifyouaregivendisplacement,youMUSTfind_____________  andNOT__________!]89:݌7 ! ! Ќ  #X{XXX}:#"]8"  ?(4 4 <DL!  X!?]8;23  0   X}XXX{Noticethat_______isthesameinbothsituations.Timeis M alwaysa__________quantityandwill_________havea c ____________.]8;H<݌y ! ! Ќ  #X{XXX}<#"]8"  ?(4 4 <DL!44X!?]8=23  0   X}XXX{Letslookatacoupleofexamples:]8=)>݌  ! ! Ќ  ,XE.4 <DL!44X!E !1  t (0yg]^`abcdef/ /"" , ,,K.4 <DL!4X!K  X,E(4 4 <DL!4X!E@2  1  .3   4   -   XX}%yied~">R'p@ "0 d RE $RR $e%yied~(p@ "0;_ d;_E^ $ `$=f-  #X}X ]A#Astudentwalkstoschoolin1500satanaveragevelocityof1.5m/s "G [S].Whatisthestudentsresultantdisplacement?@@݌ #] Ќ ,X*4X!44X!* ,  X,H+4 44 <DL!4X!H ,Given:#X{XXX}p>#+X XXX{_D #X{X X+XD#X}XXX{dR_= $s  #X{XXX}D#+X XXX{_D #X{X X+XxE#X}XXX{t_Ԁ= % -   XX}%yied~;R)p@ "0 d REh N'RR 'g%yied~*p@ "0;_ d;_E '} 'h-  #X}X !F# _vav_= '  Formula: Calculations: )(! #X{XXX}E#X}XXX{ConcludingSentence: k+$"  XE+ 4 <DL!444X!E#X{XXX}uH#_XXXX{_UX_X  Unit3Lesson3!Page12#C_U3I##X{XCRI#X}XXX{ -c'% qI""  ,E.4 <DL!X!E  X,E(4 4 <DL!4X!E'J2  2  .3   4   -   XX}% "yied~"R+p@ "0 d RE RR @ i%#"yied~,p@ "0;_ d;_E^ >  =j-  #X}X nK#Iftheresultantdisplacementofacaris135km[E]andittraveledfor , 1.8h,whatisthecarsaveragevelocity?'JK݌  B Ќ X$ X!44X!$   XB+4 44 <DL!X!BGiven:#X{XXX}I#+X XXX{_D #X{X X+XN#X}XXX{dR_=  X -   XX}%%'yied~R-p@ "0 d REh RR k%('yied~.p@ "0;_ d;_E } I =l-  #X}X FO# #X{XXX}N#+X XXX{_D #X{X X+X!Q#X}XXX{t_Ԁ=  n  _vav_=   Formula: Calculations:  ConcludingSentence: f   XE+ 4 <DL!444X!E""  ,E.4 <DL!X!E  X,E(4 4 <DL!4X!ER2  3  .3   4   -   XX}%*,yied~"@R/p@ "0 d RE RR m%-,yied~0p@ "0;_ d;_E^  9=n-  #X}X T#Astudenttravels8.2km[E]andthen4.5km[W].Thistriptakes3.2h.   Whatisthestudentsaveragevelocity?RS݌ 4 Ќ X$ X!44X!$   XB+4 44 <DL!X!BGiven:#X{XXX}wQ#+X XXX{D #X{X X+X-W#X}XXX{d1= J -   XX}%/1yied~")R1p@ "0 d RE RR o%21yied~2p@ "0;_ d;_E^  p-  #X}X ľW# #X{XXX}sW#+X XXX{D #X{X X+XY#X}XXX{d2= `  #X{XXX}Y#+X XXX{_D #X{X X+XMZ#X}XXX{t_Ԁ= v  XE+ 4 <DL!444X!E-   XX}%46yied~RR3p@ "0 d REh RRR q%76yied~4p@ "0;_ d;_E } r-  #X}X J[# 4  _vav_=   XB+4 44 <DL!X!BWAIT! Dowehavetheresultantdisplacement?_____.Howcanwe  getit?Rememberhowtoaddvectors? ,  XE+ 4 <DL!444X!E 4 Letsusethemathmethod(itsquicker) B  XStatement: X Given: n Formula: #R #X{XXX}Z#_XXXX{_UX_X  Unit3Lesson3!Page13#C_Ud_##X{XC_#X}XXX{ `+$" _  ,%#   Nowwecansolveforaveragevelocity: t Formula: Calculations:  ConcludingSentence:  X B+4 44 <DL!X!B#X{XXX}`# XE+ 4 <DL!444X!EX}XXX{AnswerQuestions#15onp.171#X{XXX}a# f  _XXXX{_UX_X  Unit3Lesson3!Page14#C_Ubb##X{XCb# -<'* b  X{XXX{X}XXX{    & B ?c  3.18DEFININGACCELERATION?cc _ݐcԌ Z ЌX}XXX}X{XXX}  X}XXX{@'BZcB+ 4 <DL!X!B! ! g]^`abcdef(y0t "]8"  #X{XXX}zd# X*44` X!X!*]8e23  0 `   X}XXX{Whatis______________?Accelerationis_____situations  > where___________is____________or_____________.]8eLf݌ T` !` ! Ќ  #X{XXX}f#"]8"  ]8g23  0 `   X}XXX{Accelerationisa__________quantitybecauseithasa  j ____________.]8gg݌` !` ! Ќ  #X{XXX} h#"]8"  ]8h23  0 `   X}XXX{Accelerationisdefinedasthe_________in___________    dividedbythe__________in________.]8hi݌  ` !` ! Ќ  #X{XXX}^i#"]8"  ]8Xj23  0 `   X}XXX{Noticethatwearedealingwith_________invelocity. x Therefore,theremustbean__________velocity(____)anda  _________velocity(____)sothat]8Xjj݌0` !` ! Ќ  #X{XXX}j#"]8"  ]8l23  0 `   X}XXX{Itsimportanttonotethat__________and_____________will \ ALWAYSbeinthesame____________.]8l=l݌r` !` ! Ќ  #X{XXX}l#"]8"  ]8m23  0 `   X}XXX{Whatarethethreeformulasthatwegetfromtheacceleration  formula?]8mm݌` !` ! Ќ  #X{XXX}m#"]8"  ]8n23  0 `   -  0XX{ 0%ACyied~Rp@ "0 d REh S!RR !s%DCyied~p@ "0<_ d<_E !} =t-  #X}X Vo#Nowletstakealookattheunits:]8no݌T ` !` ! Ќ  XE( <DL!44` X!Ea=______=______ j!  E+ 4 <DL!  X!E"]8"  X*44` XT$X!*]8Yr23  0 `   Sincebothsecondsare________adivisionline,they_____ #" ______crossout(otherwiseaccelerationwouldbemeasuredin $8 _____whichwouldntmakesense).]8Yrr݌%N` !` ! Ќ  ,Weactuallyendupgetting: &d   'z! #X{XXX}uo#"]8"  ,044` X!44` XT$0]8t23  0 `   X}XXX{Whatisam/s2?(________per____________________)]8tt݌)" ` !` ! Ќ  "]8 "  XB% <DL!44` X!B#X{XXX}5u##X:XXX{ ]8u23  0   #X{XX#X:rv#X}XXX{Itmeansthatforevery_________,anobjectismovingata *#! certain________(or__________).]8uv݌2+$" ! ! Ќ  #X{XXX}w# X?(4 4 <DL!  X!?_XXXX{_UX_X   H,%# Unit3Lesson3!Page15#C_UKx##X{XCjx#  ,&$ x"]8 "    X}XXX{]81y23  0 4   Whenwediscussacceleration,wereonlygoingtolookat t ___________acceleration(alsoknownas_________acceleration)  sothateverysecond,theobjects________(inm/s)will , ___________or___________.]81yy݌ B4!4! Ќ  #X{XXX}iy#"]8 "  ?(4 4 <DL!44X!?]8E{23  0 4   X}XXX{Youareprobablyfamiliarwith___________acceleration.This  X meansthatanobjectis____________its_________.]8E{{݌ n4!4! Ќ  #X{XXX}{#"]8 "  ?(4 4 <DL!44X!?]8}23  0 4   X}XXX{Whenwelookat_____________acceleration,weactuallymeanthat   anobjectis_____________,or____________itsspeed.]8}o}݌4!4! Ќ  ,XE.4 <DL!44X!EF@ $ #X{XXX}}#"]8 "  X,E(4 4 <DL!4X!E]8D23  0 4   X}XXX{Letslookatafewexamples:]8D݌: 4!4! Ќ   m (0yg]^`abcdef/ / ,X""  ,,E.4 <DL!44X!E  E(4 4 <DL!4X!EK2  1  .3      -   XX}%GIyied~Rp@ "0 d REh jRR u%JIyied~p@ "0<_ d<_E } =v-  #X}X Ą#Astudentisrunningtoclassbecausetheyarelate.Thestudentstarts P  runningat2m/s[E]andacceleratesto7m/s[E].Ifittakesthestudent f  5storeach7m/s[E],whatisthestudentsacceleration?K݌ |  Ќ ,,$ 44X!44X!$   B+4 44 <DL!44X!B   ,Given: A #X{XXX} #+X XXX{D #X{X X+X3#X}XXX{v=   -   XX}%LNyied~Rp@ "0 d REh RR tw%ONyied~p@ "0<_ d<_E n} #=x-  #X}X ļ# A #X{XXX}y#+X XXX{D #X{X X+X#X}XXX{t= 4  A a= J  , Formula: Calculations: `  ,E+ 4 <DL!444X!E ,  B+4 44 <DL!X!B , ,ConcludingSentence: , H.4 <DL!444X!H ! (00m #X{XXX}݈#E(4 4 <DL!4X!EX}XXX{Whatdoes1m/s2[E]mean?Itmeansthatforevery___________the X studentruns,he______________his_________by_________.So n inthisexample,thestudentstartsrunningat__________,andone   secondlaterisrunningat__________,andanothersecondlateris !& runningat___________,andsoon. "<  ,B+ 4 <DL!44X!B m (00! ,""  ,,E.4 <DL!X!E  E(4 4 <DL!4X!ED2  2  .3      Acarisdrivingatavelocityof20m/s[S]whenthedriverseesakidrun $h intotheroad.Ifthecarcandecelerateat4m/s2,howlongwillittake %~ thecartostop?D݌ '  Ќ ,,$ X!44X!$   B+4 44 <DL!X!B  ,Given:eRS/b `@E ( (ye߀= (! -   XX}%TVyied~R p@ "0 d REh 9*RR )z%WVyied~ p@ "0<_ d<_E )} )={-  #X}X ě# A #X{XXX}#+X XXX{D #X{X X+Xv#X}XXX{t= ;)"   A a= Q*#! Formula: Calculations: g+$" #X{XXX}#_XXXX{_UX_X  Unit3Lesson3!Page16#C_Ur##X{XC#X}XXX{ -'$ ConcludingSentence: t #X{XXX}#  E+ 4 <DL!444X!EAX}XXX{nswerQuestions#1,3onp171#X{XXX}# "  _XXXX{_UX_X  Unit3Lesson3!Page17#C_U˞##X{XC#