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11>> eellaakk eeddvviitt hhUUvv OPCV/SKM
22>> Dr. Pat Hiddleston RTI
muxviC¢aKNitviTüa fñak;TI 1
lT§plsikSa
cMnYn ³ eRbIviFIepSg² rYmTaMgmuFaKNna edIm,IedaHRsaycMeNaTgay² tamviFI edaybUkBIrcMnYnKt;
EdlmanplbUkminelIsBI 20.
kic©karvaytMél
1> kic©karenHRtUv)andak;[sisSeFVIenAcugqñaM bnÞab;BIsisS)aneronBIviFIepSg² dUcCakarbUkcMnYnKt;
karrab;vtßú kareRbIbnÞat;elx nig eFVIviFIbUktamCYrQr nigtamCYredk.
2> RKUdak;cMeNaT[sisSeFVIrYcKat;GancMeNaT. NavImanXøIcMnYn 9 RKab;. mþayrbs;nag [XøInag
6 RKab; EfmeTot TukCargVan;. etINavImanXøITaMgGs;b:un�an?
3> [sisS 2 b¤ 3 nak; GancMeNaTeT,Igvij edIm,I[sisSTaMgGs;KñacaMcMeNaTenaH.
4> bnÞab;mk Bnül;sisSfa kic©karEdlsisSRtUveFVI KWedaHRsaycMeNaTCa 5 rebobxus²Kña.
5> dMbUg RtUveRbIRmaméd edIm,IedaHRsaycMeNaT. [sisSrab;Rmamédrbs;eKrhUtdl; 9 rYcmk
rab;RmamédcMnYn 6 EfmeTot ehIysresrcMelIyEdleKrab;eXIj.
6> TI2 sisSbgðajcMelIy edayKUrRKab;XøI ehIyrab;. niyayeTAkan;sisSfa : RKUcg;[b¥Ún²KUr
rUbXøIcMnYn 9 ehIynwgcMnYn 6 EfmeTotenAkñúgesovePA. rYc rab;XøITaMgGs;enaH. qUtXøIEdl
b¥Ún²)anrab;rYc ehIysresrcMnYnsrub : . RKURtUvTukeBlevla[sisSeFVIkic©karenH.
7> TI3 sisSbgðajcMelIyedayeRbIbnÞat;elx. KUrbnÞat;elxmYyEdlmanelxcab;BI0 dl; 20
dak; enAelIkþarexon ehIy[sisScMlgcUlesovePAlMhat;rbs;eK.
niyayeTAkan;sisSfa : RKUcg;[b¥ÚneRbIbnÞat;elx Edlb¥ÚneTIbnwgcMlgdak;kñúgesovePArbs;
b¥Ún rab;BI1dl; 9 bnÞab;mk rab; 6 EfmeTot. KUsrgVg;elIelxEdlb¥Únrab;eXIjenaH. :
1
8> TI4 KW RtUvsresrelx9 bUknwg 6 CaviFIbUktamCYredk. niyayR)ab;sisSfa {\T,ÚvenH
RKUcg;[b¥ÚnsresrcMeNaTdUcteTAenH} sresrcMeNaTmYyeTot EdlmanlkçN³RsedogenHKW
4 + 6 = 10. RKUR)ab;sisSfa {cUrb¥ÚnsresrcMeNaT XøI 9 RKab; bUknwgXøI 6 RKab;
dUclMnaMKMrUenHEdr} .
9> TI5 KW RtUvsresrelx 9 bUknwg 6 CaviFIbUktamCYrQr. RKU[]TahrN_ epSgeTotdak; elIkþar
exon edaysresrCaviFIbUkelxtamCYrQr. RKUR)ab;sisSfa :\T,ÚvenH cUrb¥ÚnsresrcMeNaT
XøI 9 RKab; bUknwgXøI 6 RKab; dUcKMrUenHEdr : .
KMrUkic©kar xageRkamenH KWCa]TahrN_sMeNrrbs;sisS eqøIytmeTAnwgkic©karEdlRKÚdak;[eFVIcMnYnBIr
nak; ³
sisS k sisS xrgVaytMél
xageRkamenHKWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisSnigkardak;BinÞúsisSmñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
karyl;BIviFIepSg² 5 5 3
cMelIyRtwmRtUv nigPaBs¥at 5 5 0
srub 10 10 3
2
mUlvicarN_ sisS kk sMerc)andl;kMritlT§plsikSa eday)anbgðajkaryl;dwgc,as;las;GMBIviFIedaHRsaynImYy²
ehIy)anpþl;cMelIy)anRtwmRtUvpgEdr.
sisS xx BuMsMerc)ankMritlT§plsikSaeT,Iy. sisSenHeFVI[mankMhusmYy enAeBlrab;Rmaméd ¬sisS
enHR)akdCaKitfa RtUvEtbgðajRmaméd6 enAeBlbUk6 nwg 9 eKKitfa cMnYnsrub KW16¦. nagKUrXøI
BuMRtwmRtUvnwgcMnYneT,Iy. karBit sisSenHKUrrUbXøIxVHehIysisSenH BuMmanTMnukcitþkñúgkarrab;Edr. sisS
enHGacrab;cMnYnenAelIbnÞat;elx)an EteKBuMyl;GMBIrebobeRbIbnÞat;elxedIm,IbUkBIrcMnYneT. cMeBaH
karbUkelxvij sisSenHRKan;EtcMlgelxBIRKU Edlsresrdak;enAelIkþarexonEtb:ueNÑaH. RKURtUv
elIkTwkcitþdl;sisSenH ehIyerobcM[eKeFVIkarCamYysisSepSgeTot b¤ CamYynwgRKU edIm,Ihat;rab;BI
elx1 dl;20 edayeRbIvtßútMNagtamry³KMnUr BI1 dl; 20. rYcmk sisSenHGaceronviFIrab;epSg²
eTot)an.
3
1 2 3
muxviC¢aKNitviTüa fñak;TI 2
lT§plsikSa
lMnaMKMrU-BICKNit ³ bMeBjlMnaMKMrU tamBN’ tamrag TMhM nig cMnYn .
kic©karvaytMél
1> kic©karenHRtUv)andak;[sisSbMeBj bnÞab;BIsisS)aneroncb;emeron CaeRcInTak;TgeTAnwglMnaM
KMrU nigbnÞab;BIhat;eFVIlMnaMKMrUepSg² CaeRcInelIkrYcmk.
2> RKUcMlglMnaMKMrUxageRkam dak;elIkþarexon. Bnül;sisSfa kñúgkic©karenH sisSRtUvbMeBjlMnaM
KMrUnImYy² bnþ enAkñúgcenøaHEdl[ tamrUb b¤KMrU b¤ cMnYn EdlsisSKitfa RtwmRtUv.
3> sisSRtUveFVIkarCabuKÁl.
KMrUkic©kar
xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn 2
nak; ³
sisS {k}
sisS {x}
4
rgVaytMélxageRkamenH KWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisSmñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
rUbTI1 2 2 0
rUbTI2 2 2 1
cMnYn 2 2 1
srub 6 6 2
mUlvicarN_ sisS k sMerc)andl;kMritlT§plsikSa. sisSenHyl;c,as;GMBIlMnaMKMrU eBleRbIrUb nigcMnYn.
sisS x BuMsMerc)andl;kMritlT§plsikSaeT. RKUKYrEtsesIrsisS eRBaHsisSenHmanbMNinrab;elx
)anl¥ EtRKURtUvcMNayeBlCamYysisS xx nigsisSdéTeTotEdlmanlT§pldUcsisS xx enHpg Edr.
RKUGacrkvtßúgay²mYycMnYn ¬dUcCa XøI RKYstUc² nigeQI¦ dak;TaMgbItMerobtamlMdab; ¬]> XøI RKYs
eQI¦ ehIyniyayfa : ebIeyIgerobvtßúenHeT,Igvij b¤ eFVICaKMrUmYyeTot tamlMnaMenH etIeyIgKYrEt
dak;GVIbnÞab;? bnÞab;BIsisS)anGnuvtþ rYcRKUGacniyayfa :cUrRkeT,kemIllMnaMKMrUTI 2. etImanrUbGVImun
eK? dUecñH etIeyIgKYrdak;rUbGVIenAkEnøgcenøaHTI1 ebIsinCaeyIgerobrUbTaMg3enHeT,Igvij? bnÞab;mk
segátemIllMnaMKMrUTI 3 etIeyIgKYrdak;elxGVII enAkEnøgcenøaHTI1ebIsinCaeyIgerobelxTaMg 3 enH eT,Ig
vij? RKUGacpþl;»kasdl;sisSeFVIkic©karenHeT,Igvij.
5
muxviC¢aKNitviTüa fñak;TI 3 {k :
lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦ cMnYn³ eRbIrUbiyvtßúú kñúgkarTijj lk;; nigGab;; edayeRbIRkdasR)ak;Rtwmm 10 000 erol..
kic©karvaytMél
1> kic©karenHRtUv)andak;[sisSeFVI bnÞab;BIsisS)aneronemeronGMBIrUbIyvtßú nigkareRbIR)as;RbmaNviFI
bUk nigdk Tak;TgeTAnwgrUbIyvtßú. kic©karenH sMrab;vaytMéleTAelIkic©karrbs;sisSCaRkum ¬kñúg1
RkummanbInak;¦. RKURtUvBinitüemIl rgVaytMéleTAelIlT§plsMerc)anrbs;smaCikRkumnImYy²
EdlRKUdak;[sisSeFVI bnÞab;BIkargarCaRkum etI)anRtwmRtUvEdrb¤eT?
2> sisSeFVIkarCaRkum EdlmancMnYn 3nak; kñúgmYyRkum.
3> sresrcMeNaTdak;elIkþarexon³
BUsuk)an[rgVan;CaTwkR)ak;cMnYn 8 000eroldl;k� ÜyRbus/RsIcMnYn3nak;. k� ÜyRbus/RsIcMnYn 3nak;
enaH)ansMercnaMKñaeTApSar edIm,ITijvtßú. BYkeKsMercfa RtUvTijvtßú1muxmñak;.
¬k¦ sresreQ�aHrbs;xøÜn rayeQ �aHvtßúEdlxøÜn)anTij nigtMél.
¬x¦ etIenAsl;R)ak;Gab;b:un �an?
4> Bnül;dl;sisSmYyRkum Edlman3nak; eday[eKedIrtYCabgb¥ÚnRbus b¤ bgb¥ÚnRsI.
5> sisSRtUvsMEdgqakenH CamYyRkummYyepSgeTot EdlmanbInak;dUcKña edayBYkeKsMEdgCaBUsuk
nigGñklk;enApSar.
6> muneBlsMEdg sisSRtUvbMeBjkic©karenAkñúgtaragKMrUxageRkay.
7> enAcugbBa©b;énkarsMEdg RkumsisSnImYy²RtUvpþl;cMelIytbeTAnwgkic©kar ¬k¦ nig ¬x¦xagelI
edaysegçb [sisSdéTeTotenAkñúgfñak;sþab;.
6
KMrUkic©kar xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karEdlRKÚdak;[eFVIcMnYn 3
nak; ³
sisSRkum {k} namm
nigeKatþnam
muxTMnij tMél
nIta b‘íc 2 2000erol
cinþa sMeBot 1 3 000erol
sn esovePA 1 1 500erol
srubR)ak;cMNay 6 500 erol
8 000- 6 500 = 1 500 erol
dUecñHR)ak;EdlenAsl; 1 500 erol
sisSRkum {x} eyIg[suCata nigEsn 3 000 erolmñak; nigsuvNÑ 2 000 erol.
suvNÑTijesovePAGs; 1 500 erol dUecñH suvNÑsl;luyGab; 500 erol.
EsnTijkatabGs; 3 000 erol dUecñH EsnBuMsl;luyGab;eT,Iy.
suCataTijb‘icBIredIm Gs; 2 000 erol dUecñH nagsl;luyGab;1 000erol.
dUecñH luyGab;EdlenAsl; srub³ 500 + 0 + 1000= 1500 erol
sisSRkum {K} eyIg[ lI 2 000erol. lITijeckGs; 1 500erol enAsl; 500erol.
[sn 3 000erol. snTijnMGs; 3 000erol dUecñHsnK�anR)ak;enAsl;;eT.
[m:a 3 000erol. ma:TijePsC¢³Gs; 2 000erol enAsl; 100erol.
dUecñH R)ak;enAsl;TaMgGs; 500 + 0 + 100 = 600erol.
7
rgVaytMélxageRkamenH KWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisS
mñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
sis
SS K
vicarc,as;las; 5 5 5 5
KNna)anRtwmRtUv 5 5 5 2
srub 10 10 10 7
mUlvicarN_ sisSRkum kk yl;c,as;GMBIcMeNaT eFVI)anelIsBIkMritsþg;dakm�viFIsikSa edayeFVIvicar)anc,as;las; nig
KNna)anRtwmRtUv.
siisSRkum xx )aneRbIviFIepSgBIsisSRkum kk b:uEnþ BYkeK)anQandl;kMritsþg;dakm�viFIsikSaEdr eday
eFVIvicar)anc,as;las; nig KNna)anRtwmRtUv.
sisSRkum KK eRbIviFIdUcKña eTAnwgRkum xx . kareFVIvicarrbs;eK)anc,as;las; EteFVI[mankMhusmYy kñúg
karKNna. BYkeK)anQandl;kMritsþg;dakm�viFIsikSa EtRKURtUvrMlwkBYkeK[eFVIkarRbugRby½tñ enA
eBleFVIkic©kar nig[]TahrN_bEnßmmYycMnYn Tak;TgeTAnwgkardkcMnYnKt;xÞg;Ban; ecjBIxÞg;Ban;.
8
muxviC¢aKNitviTüa fñak;TI 3 :x :
lT§plsikSa
FrNImaRtt ³ sg;RtIekaNedayeRbIbnÞat; EdkQan nig Ekg.
kic©karvaytMél
1> eKalbMNgd¾cMbgénkic©karenH KWpþl;skm �PaBrIkraymYy eday[RKUCaGñksegát faetIsisS
sÁal;rUbRtIekaNenAkñúgesovePAsisSEdrb¤eT? etIsisSGacKUrrUbRtIekaNedayxøÜnÉg)anEdr
b¤eT?
2> Cakarl¥Nas; ebIsinCasisSmñak;²manbnÞat; nigex �Aéd. ebIsinCasisSBuMmanbnÞat;RKb;KñaeT
BYkeKGaceRbIR)as;vtßúepSg² EdlRtg;dUcCabnÞat; edaykMNt;ykRtwmRbEvg 5 sm ¬]>ex�Aéd
EKmesovePA¦.
3> Bnül;sisSfa dMbUg sisSRtUvKUrkaerFMmYyenAkñúgesovePAlMhat; ¬TMhM 10sm�10sm¦.
RKURtUvTukeBlevla[sisSeFVIkic©karenH.
4> Bnül;sisSfa kic©kardMbUg RtUvKUrrUbRtIekaNmYy EdlmanRCugBIrRbEvg 5sm erogKña nigRCugTI3
ykRtwmRbEvgNamYy. sisSminRtUveFVIkic©karenHeT,Iy Tal;EtRKUR)ab;[eFVI. RKUGaceFVIbgðajGMBI
rebobdUcxageRkamdak;elIkþarexon³
� KUrbnÞat;mYyEdlmanRbEvg 5sm dak;Rtg;kEnøgNamYy
� KUrbnÞat; 5sm mYyeTot pÁúMCamYybnÞat;xagelI
enAcugbnÞat; begáIt)anCamuM
� KUsbnÞat;mYyeTotpÁúMCamYybnÞat;TaMgbI begáIt)anCaRtIekaN
5> Bnül;fa sisSRtUvKUrrUbRtIekaNenHdak;xagkñúgrUbkaer EdlBYkeKeTIb)anKUrdak;kñúgesovePAenaH.
9
6> bnÞab;mk Bnül;sisSfa kic©karTI2 RtUvKUrrUbRtIekaNCaeRcIn EdlmanRbEvgRCugb:un�ank¾)an dak;
enAkñúgrUbkaerEdleTIbnwg)anKUrkñúgesovePArYc Et rUbRtIekaNTaMgenaH eFVIy:agNakuM[KUrCab;Kña b¤
kat; ExVgKña. sisSRtUveRbIbnÞat; b¤vtßúepSg²CMnYsbnÞat; edIm,IKUrRtIekaNTaMgenH.
7> CacugeRkay RtUvR)ab;sisSfa enAsl;eBl1naTIeTot edIm,IbBa©b;kic©kar KWRtUvBinitüemIl nrNa
KUrRtIekaN)aneRcInCageK ¬bUkrYmTaMgRtIekaNEdlmanRbEvg 5sm pgEdr¦ enAkñúgrUbkaer
enaH. Bnül;sisSfa sisSnwg)an 4BinÞú ebIsinCaKUrRtIekaN EdlmanRCugRbEvg 5sm )an
RtwmRtUv 3BinÞú eTot ebIKUrRtIekaN)anRtwmRtUv nig 3BinÞúeTot ebIsinCakic©kareFVI)ans¥atl¥ ehIy
BuMmanRtIekaNNab:HKñaeT,Iy.
8> RKURtUvrMlwkeBlEdlenAsl; kñúgnaTIcugeRkay dUcCasl;30vinaTI eTot sl;15vinaTI eTotbnÞab;mk
R)ab;[sisSQb;. sisSTaMgGs;RtUvdak;bí‘ccuH ¬Qb;sresr¦ ehIyyk kic©kareTAdak;[RKU.
KMrUkic©kar xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karEdlRKÚdak;[eFVIcMnYn 2
nak;³
sisS {k} sisS {x}
10
rgVaytMélxageRkamenH KWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisS
mñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
sg;RtIekaNEdlmanRCug2 RbEvg
5sm )anRtwmRtUv4 4 4
cMnYnRtIekaNbEnßm 3 3 2
kic©kars¥at 3 3 1
srub 10 10 7
mUlvicarN_ sisSS k sMerc)anlT§plelIsBIkMritlT§plsikSa. sisSenHGacKUrrUbRtIekaN)anRtwmRtUv kic©kar
s¥at ehIyeFVI)anelOn.
sisS xx k¾GacQandl;kMritlT§plsikSaEdr. EteTaHbICa sisSenH)anKUrrUbRtIekaN)aneRcInCag
sisS kk k¾eday k¾rUbxøHminEmnCaRtIekaNeT eRBaHKUselOneBk eTIbeFVI[rUbRtIekaNxøHb:HKña
b¤kat;ExVgKña. eTaHCay:agNak¾ eyIgenAEtGacbBa¢ak;[eXIjfa sisSenHGacKUrrUbRtIekaN)anEdr.
11
muxviC¢aKNitviTüa fñak;TI 4 ________________________________________________________________
lT§plsikSa
rgVas;rgVal; ³ eRbI]bkrN_xñatÉkta nigeRCIserIsxñatsmRsbedIm,IkMNt; ³ RbEvgBI KILÚEm:t eTA
mIlIEm:t.
________________________________________________________________
kic©karvaytMél
1> Bnül;sisSfa eKalbMNgénkic©karenH KWeFVIkar)a:n;s�ancMgay[)ankan;EtCak;c,as; cMgay
BIpÞHeTAsala.
2> [sisSeRbIbnÞat; edIm,IKNnacMgayénCMhanmFüm KitCasg;TIEm:t Camunsin ¬sUmemIlKMrUskm�PaBeron nigbeRgon¦. sisSRtUvsresrcMgay KitCasg;TIEm:t ¬bgÁt;[eTACacMnYnKt;¦ enAkñúg
esovePAlMhat;.
3> [sisSrab;cMnYnCMhan EdleKedIrBIpÞHeTAsalaeron enAéf¶bnÞab;. [sisSsresrcMnYnenHenAkñúg
esovePAlMhat;.
4> RKUBnül;sisSfa kic©karenH sisSRtUvKNnarkcMgayBIpÞHeTAsalaeron edayeRbIcMnYnTaMgBIr
EdlrkeXIjxagelI KitCaKIT,ÚEm:t b¤CaEm:t.
KMrUkic©kar
xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karEdlRKÚdak;[eFVIcMnYn 2
nak;³
sisS k
mYyCMhanrbs;´ RbEvg 50 sm. ´edIr)an 1300 CMhan.
dUcenH cMgayBIpÞHeTAsalaeron KW 503001 � sm = 65 000 sm.
65 000sm = 650m.
sisS x
mYyCMhanrbs;´ RbEvg 47 sm. ´edIr)an 987 CMhan.
dUcenH cMgayBIpÞHeTAsalaeron KW 47987� sm = 46 489 sm.
46 489 sm = 46 m.
12
rgVaytMél xageRkamenHKWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúeGaysisSmñak;².
lkçN³vinicä½y
GRt
aBinÞúú
sis
SS kk
sis
SS xx
kareRbI]bkrN_sMrab;vas; 2 2 2
viFIKNna 2 2 2
bMNinkñúgkarKNna)anRtwmRtUv 2 2 1
karbþÚrxñatBIsg;TIEm:t eTAEm:t 2 2 0
srub 88 88 55
mUlvicarN_ sisS kk sMerc)ankMritlT§plsikSa edaysisSenH)aneRbIbnÞat;)anRtwmRtUv edIm,IKNnaCMhan ehIy
)anbgðajBIkareFVIvicarc,as;las; karKNna nigkarbþÚrxñat)anRtwmRtUv.
sisS xx mankMhuskñúgkarKuNcMnYnénCMhan RbEvgmFüm. sisSenHeFVsRbEhs kñúgkarbþÚrxñatBIsg;TI
Em:teTAEm:t. eTaHCay:agNak¾eday kareFVIvicarrbs;sisSenH)anl¥Nas;. RKURtUvbegáIt]TahrN_mYy
sMrab;[sisSenHeFVIeT,Igvij ehIyrMlwk[sisSenHykcitþTukdak; minRtUv[mankMhusdEdleT. krNI
ebIsisS x eFVIkarKNna)anRtwmRtUv enaHsisSenH GacQandl;kMritlT§plsikSaehIy.
13
muxviC¢aKNitviTüa fñak;TI 5 ________________________________________________________________
lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦sßiti³ sg;; nigbkRsayTinñn½yEdlbgðajenAkñúgtaragg RkabExSS Rkabssrr nigRkabpøitgay².
________________________________________________________________
kic©karvaytMél
1> kic©karenHvaytMéleTAelIsmtßPaBrbs;sisSkñúgkarsg;Rkabsrsrgay² tamTinñn½yEdl[.
kic©karenH RtUv)anvaytMéleTAelIRkabsrsrenAkñúgsþg;dakm�viFIsikSaEtmYycMNucb:ueNÑaH .
2> kic©karenHRtUv)andak;[sisSeFVI bnÞab;BIsisS)aneroncb;emeronTak;TgeTAnwgxøwmsarénRkab
srsr nigrebobsg;.
3> [sisSbMeBjkic©karxageRkam³
tamlT§plénEtsKNitviTüaf� I²enH sisSTTYl)anlT§pldUcxageRkam³
� sisS 20 nak; )anBinÞú 8/10
� sisS 7 nak; )anBinÞú 7/10
� sisS 1 nak; )anBinÞú 6/10
� sisS 3 nak; )anBinÞú 4/10
� sisS 1 nak; )anBinÞú 2/10
� sisS 8 nak; )anBinÞú 1/10
sg;RkabsrsrtamTinñn½yEdl[enH. sg;Rkab edayykG½kS x tagBinÞúrbs;sisS nig G½kS y
tagcMnYnsisS.
14
KMrUkic©kar xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karEdlRKÚdak;[eFVIcMnYn 2
nak; ³
sisS k
sisS x
rgVaytMél xageRkamenHKWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúeGaysisSmñak;².
15
lkçN³vinicä½y
GRt
aBinÞúú
sis
SS kk
sis
SS xx
karbkRsayTinñn½yenAkñúgtarag 5 5 3
karerobcMTinñn½yenAkñúgtarag)anRtwmRtUv 5 5 2
srub 10 10 5
mUlvicarN_ sisS kk )anbegáItRkab)anl¥ nigbkRsayTinñn½y)anRtwmRtUv. sisS xx BuM)aneFVItamkarENnaM
edaysg;Rkab dak;bRBa©asG½kS x nig G½kS y.
RKURtUvrMlwksisS xx GMBIsar³sMxan; énkarGankarENnaM[)anm:t;ct; nigBinitüeT,IgvijeTAelIkargar
Edl)aneFVI faetIRtwmRtUv tamkarENnaMb¤eT. eTaHCay:agenHk¾eday sisS kk nigsisS xx sMerc)an
kMritsþg;dakm �viFIsikSaEdr.
16
muxviC¢aKNitviTüa fñak;TI 6 ¬k¦ ___________________________________________________________________________
lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦cMnYn ³³ KNnatMélmFümm R)ak;cMeNjj xatt ehIysresrr nigepÞógpÞat;vikáybRt)anRtwmRtUv.. ___________________________________________________________________________
kic©karvaytMél
1> kic©karvaytMélenHRtUv)andak;[sisSbMeBj bnÞab;BIsisS)aneronGMBIGtßn½yénBakü {tMél}
{R)ak;cMeNj} nig {xat} nigbnÞab;BIsisS)anGnuvtþkñúgkarKNnatMél R)ak;cMeNj nigxat
rYcmk.
2> kic©karenHvaytMéleTAelIcMeNHdwgrbs;sisS GMBIBakü {tMél R)ak;cMeNj nigxat} nigeTAelI
smtßPaBénkarKNna)anRtwmRtUv. kic©karenHBuMvaytMéleTAelIsmtß PaBrbs;sisSkñúgkar
sresr nigkarepÞogpÞat;vikáyb½RteT,Iy.
3> RKUdak;cMeNaT[sisSeFVIdUcxageRkam³
suPaBeTIbEt)anTijtUbf�ImYyenApSar edIm,Ilk;mYk.
nagRtUvcMNayGs; 2 000erolkñúgmYyéf¶ sMrab;bg;PasIu.
enAedImExmInanag)anTijmYk 100 mkBIeragcRk EdlmantMél 700erol kñúgmYkmYy.
ebInaglk;mYkmYykñúgtMélmFüm 1 500erol etInagcMeNj b¤xatenAeBlnaglk;mYkGs;;enA
cugExmIna?
17
KMrUkic©kar xageRkamenHKWCa]TarN_BIsMeNrrbs;sisS eqøIytbeTAnwgkic©karRdlRKÚdak;[eFVIcMnYn 2
nak;³
sisS k
dMbUg ´KNnatMélCamunsin ³
ExmIna man31 éf¶ dUecñH tMélPasIu KW 000231� erol = 62 000erol
ebImYkmYytMél 700 erol enaHmYk100 tMél 70 000erol
dUecñH tMélsrub 62 000erol + 70 000erol = 132 000erol
\T,ÚvenH ´KNnarkéfølk;mYkTaMgGs;³
kñúgmYkmYy1 lk;)an 1 500 erol enaHmYk 100lk;)an 150 000 erol
R)ak;cMeNj b¤xat = éfølk; – éføedIm
dUecñH R)ak;cMeNj b¤xat = 150 000 erol –132 000 erol = 18 000 erol
dUecñH R)ak;cMeNjsMrab;ExmIna KW 18 000 erol .
sisS x
R)ak;cMeNj KWCaR)ak;Edl´lk;)an dkCamYynwgR)ak;Edl´cMNay.
dUcenH R)ak;cMeNj 1500 – 700
R)ak;cMeNjsrub 900.
rgVaytMél xageRkamenHKWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúeGaysisS
mñak;².
lkçN³vinicä½y
Gtib
rmaa
sis
Skk
sis
Sxx
vicar nigviFIedaHRsaycMeNaT 5 5 2
karKNna)anRtwmRtUv 5 5 1
srub 10 10 3
18
mUlvicarN_
sisS kk sMerc)antamkMritsþg;dakm�viFIsikSa eday)anbgðajBIbMNinvicar nigKNna)anRtwmRtUv.
sisS xx BuMsMerc)antamkMritsþg;dakm �viFIsikSaeT. sisSenHyl;BIGtßn½yénBakü EtBuMGaceFVIcMeNaT
)an ehIyeFVIvicaredIm,IedaHRsaycMeNaT)aneT. sisSenHeFVI[mankMhusmYy enAkñúgkarKNna. RKU
RtUvelIkTwkcitþdl;sisSenH eRBaHsisSenH)anyl;c,as;GMBIGtßn½yénBakü. RKURtUvCYyBinitüemIlkar
KNnarbs;sisS. RKURtUvniyayfa :cUreyIgeTABinitüemIlcMeNaTvij :. ebIeyIgcMeNj)an 800erol
kñúgmYkmYy etIeyIgcMeNj)anb:un�an ebIsinCaeyIglk;Gs;mYk100? cUrb¥ÚncMlgdak;kñúgesovePA.
\T,ÚvenH cUrb¥ÚnGancMeNaTeT,Igvij ehIyR)ab;RKU BIGVIxøHEdlb¥Ún)ancMNay. etIcMNayGs;b:un �an?
cUrb¥ÚncMlgdak;kñúgesovePA. etIenAsl;b:un�an ebIsinCaeyIgdkéføedImecjBIR)ak; éfølk;srubenaH? l¥
Nas; b¥ÚneqøIy)anRtwmRtUvehIy !
19
muxviC¢a KNitviTüa fñak;TI 6 ¬x¦
lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦ rgVas;rgVal;; ³ KNnary³eBll edaydwgel,ÓnmFümm nigcMgaycrr ..
kic©karvaytMél
1> kic©karenHRtUv)andak;[sisSeFVI bnÞab;BIsisS)aneroncb;emeronTak;TgeTAnwgrebobKNnary³
eBlcr edaydwgel,ÓnmFüm nigcMgaycr.
2> [sisSeFVIcMeNaTxageRkam. ENnaMR)ab;sisSfakareFVIcMeNaTenHsisScaM)ac;RtUveFVIkarbk
Rsay.
suxa)aneFVIdMeNIrtamrfynþBIPñMeBjeTAkan;extþesomrab cMgay 306Km edayel,ÓnmFüm
45Km/m:. Kat;ecjdMeNIrBIPñMeBjenAema:g10RBwk . ehIyenAtampøÚvKat;Qb;sMrakBisar)ayéf¶Rtg;
Gs;ry³eBl !ema:g. etIsuxaeTAdl;esomrabenAema:gb:unñan?
KMrUkic©kar
xageRkamKWCa]TahrN_BIsMeNrrbs;sisSeqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn2nak;³
sisS {k}
eRbIrUbmnþ ry³eBl= cMgaycr ÷ el,ÓnmFüm 306 ÷ 45 = 6.8
dUcenH ry³eBleFVIdMeNIr KW 6.8em:ag
0>1 m: = 6 naTI
0>8 m: = 8 x 6 = 48 naTI
naM[ 6>8 m: = 6 m: 48 naTI
ry³eBlCiHrfynþ KW 6m: 48 naTI. edayQb;Gs;mYyem:ag edIm,IRss;RsUbGaharéf¶Rtg;
ry³eBleFVIdMeNIrsrubKW ³ 6 em:ag 48 naTI + 1 = 7em:ag 48naTI. dUecñHsuxaeTAdl;esomrab
enAem:ag10RBwk + 7m:48naTI = 17em:ag48naTI RtUvnigem:ag 6nig 48naTIl¶ac.
20
sisS {x} ry³eBl= cMgaycr x el,Onénrfynþ KW 306 x 45
306
x 45
13770
dUecñH ry³eBlsrub KW 13m: 77 naTI
rgVaytMélxageRkamenH KWCalkçN³vinicä½yrgVaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisSmñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
vicar nigviFIedaHRsay cMeNaT RtwmRtUv 5 5 0
cMelIyRtwmRtUv 5 4 2
srub 10 9 2
mUlvicarN_ eTaHCa sisS kk BuM)anpþl;cMelIycugeRkay)anRtwmRtUvk¾eday k¾sisSenHGacQandl;kMritsþg;dakm �viFIsikSaEdr. kareFVIvicarrbs;sisSmanlkçN³c,as;las; ehIykarKNnak¾RtwmRtUvEdr. sisSenH
eFVI[mankMhusmYy KWbþÚr 24 em:ag eTA 12 em:ag. sisSenHenAEtGacbgðajTaMgcMeNHdwgénkar
KNnary³eBlcr nigbMNinKNnay:agl¥\tex©aH.
sisS xx BuM)ansMercdl;kMritsþg;dakm�viFIsikSaeT. RKURtUvbgðajdl;sisSenHfa kic©karEdlsisSenHeFVI
KW)anl¥Nas;CaBiess kareFVIviFIKuN.
RKURtUvrMlwksisSenH GMBIkareRbIR)as;rUbmnþ edIm,IKNnael,Ón cMgay nigry³eBl. RKURtUv[cMeNaT
gay²mYycMnYnedIm,I[sisSenHeFVIedayeRbIRtIekaN. rYcmk RKURtUvCYysisSenH b¤[sisSNamñak;
CYyrMlwkGMBIrebobbþÚrxñatBInaTIeTAem:ag.
RtIekaNenHeFVI[sisSgayRsYlkñúgkarcgcaMrUbmnþ
cMgaycr
el,ÓnmFüm ry³eBlcr
21
muxviC¢a KNitviTüa fñak;TI 7
lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦ FrNImaRt ³ edaHRsaycMeNaT KNnamuMM edayeRbIlkçN³muMrbs;RtIekaNN nigRbelT,ÚRkam..
kic©karvaytMél
1> kic©karvaytMélenHRtUv)andak;[sisSbMeBj bnÞab;BIsisS)aneronGMBIlkçN³muMénRtIekaNrYc.
kic©karenHepþatEteTAelIlkçN³muMénRtIekaNb:ueNÑaH minEmneTAelIRbelT,ÚRkameT.
2> Bnül;sisSfa PaKeRcInenAkñúgEts eKtMrUv[edaHRsaycMeNaT b¤ eqøIysMNYr. EtcMeBaHkic©karenH
vij RtUv)an[sisSbegáItcMeNaT nigsYrsMNYr edIm,I[sisSdéTeTot edaHRsay.
3> kic©karenH KWsisSRtUvKiteTAdl;sßanPaBRbcaMéf¶NamYy EdlBak;B½n§eTAnwgmuM RtIekaN nigbegáIt
cMeNaTsMrab;[sisSepSgeTot yklkçN³muMénRtIekaNmkedaHRsay. [sisSelIk]TahrN_
BIsßanPaBRbcaMéf¶NamYy EdlTak;TgeTAnwgclnaénvtßúEdlGacbegáIt)anCaRtIekaN ¬dUcCa
El,g CaBiess )al;Tat; b¤ b‘Íy:a¦.
4> bnÞab;mk sisSRtUvtak;EtgcMeNaT nigbegáItsMNYrmYycMnYn sMrab;[ sisSdéTedaHRsay.
5> RKUGac[sisSdUrcMeNaTKñaeTAvijeTAmk edIm,IBinitüemIlfaetIBYkeKGacedaHRsaycMeNaTrbs;
sisSepSgeTot)anEdrb¤eT. rgVaytMélelIkic©karenH KWEp¥keTAelIfaetIsisSGacbgðajcMeNH dwg
kñúgkarbegáItcMeNaT nigsMNYr)anl¥RtwmRtUvTak;TgeTAnwglkçN³muMénRtIekaN Edrb¤eT.
KMrUkic©kar
xageRkamKWCa]TahrN_BIsMeNrrbs;sisSeqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn2nak;³
sisS {k}
kILakrbukb‘Íy:amñak;)anbBa¢Ún
kUn)al;BITItaMg A[eTAb:HkUn)al;
BN’ex �AenATItaMg B edIm,I[kUn)al; TItaMg
B remolcUlrn§ enATItaMg C . edaydwg
famMuEdlpÁúMrvagknøHbnÞat; � �AB nig
22
AB
C
� �BC manrgVas;es� I nwg �130 ehIymMu EdlpúMÁrvagknøHbnÞat; � �AB nig � �AC manrgVas;es�I nwg �
21 .
cUrKNnamuMEdlbegáIteT,Igeday � �AC nig � �BC .
ebI cmAB 36� eRbIra:b:T½r nigbnÞat; edIm,Isg;RtIekaN xagelI edayeRbImaRtdæan cmmm 11 � .
cUrvas;tamrUbxagelI edIm,IrkRbEvg AC nig BC.
sisS {x} kILakr mñak;)anTat;bBa¢Ún)al;BITItaMg A
eTA[kILakrmñak;eTotenATItaMg B.
ehIykILakrTItaMg B enaH)anTat;)al;
bBa©úÚlTIRtg; TItaMg C .
eKdwgfamMu �� 80ˆCBA nig �� 75ˆACB
k> cUrKNna CAB ˆ .
x> ebIcMgayEdlkIT,akrenATItaMg A
bBa¢Ún)al;eTAkIT,akrTItaMg B manRbEvg 10 Em:t cUreRbIbnÞat; r:ab:T½r nigmaRtdæan mcm 11 �
edIm,IKUrRtIekaN EdlbegáIteT,Igeday cMNuc A , B nig C .
rgVaytMélxageRkamenH KWCalkçN³vinicä½yrgVaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisSmñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
begáItcMeNaT edaymankaryl;dwgc,as;
GMBIlkçN³muMénRtIekaN. 5 5 5
bMrab;nigsMNYr)anRtwmRtUv 5 5 5
srub 10 10 10
23
mUlvicarN_ TaMgsisS kk nigsisS xx )anbegáItcMeNaTl¥RtwmRtUv edaybgðajBIcMeNHdwgTak;TgeTAnwgkareRbIR)as;
lkçN³muMénRtIekaN edIm,IrkmuMEdlBuMsÁal;. sisSTaMgBIrenH)ansMercdl;kMritsþg;dakm�viFIsikSa.
sisSTaMgBIrenHcaM)ac;RtUvbgðajkaryl;dwgmYykMritepSgeTot EdlTak;TgeTAnwglkçN³muMénRbelT,Ú
Rkam edIm,I[GacQandl;kMritsþg;dakm�viFIsikSa)aneBjelj.
24
muxviC¢aKNitviTüa fñak;TI 8 ___________________________________________________________________________
lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦sißtii ³ rkmFümm emdüann m:Utt BITinñn½yEdl[[ rYmTaMgtaragbMENgEckeRbkg;; ehIyEjk[[
eXIjBIPaBxusKñaa rvagmFümm emdüann nigm:Ut.. __________________________________________________________________________
kic©karvaytMél
1> kic©karenH RtUv)anerobcMeT,Ig sMrab;dak;[sisSeFVIEtmYyEpñkxagedIménlT§plsikSa xagelI.
2> kic©karenH RtUv)anerobcMeT,IgsMrab;dak;[sisSeFVI bnÞab;BIsisS)aneronGMBIGtßn½yén Bakü mFümm
emdüann m:Ut nigBYkeK)anbMeBjlMnaMskm�PaBxageRkam enHrYc³
k> [sisSeFVIkarCaRkumEdlman 5 nak;
x> sisSeRbIbnÞat; Em:t b¤ rgVas;epSg²EdlminEmn]bkrN_sþþg;da ¬RbEvgéd eQI¦ edIm,IRbmUl
Tinñn½y Tak;TgeTAnwgkMBs;sisSnImYy² enAkñúgRkum.
K> [sisSeFVIkarCaRkum edIm,IKNnamFüm m:Ut emdüan BITinñn½yEdl[.
X> sisSeT,Igbgðajkic©karenAxagmuxfñak; edayBnül;GMBIGtßn½yénBakünImYy² nigGMBIrebob
KNnaedIm,IrkcMelIy.
3> bnÞab;mk dak;cMeNaTxageRkam[sisSedaHRsayerogxøÜn.
mþayrbs;ssuFaa )anlk;RCUkcMnYn5k,almanTMgn;dUcxageRkam ³ 77.5 kg ; 98 kg ; 77 kg ; 86 kg ; 93 kg
Bnül;GMBIGtßn½yénBakü mFüm emdüan nigm:Ut rYcrkmFüm emdüan nigm:Ut BITinñn½yenH.
KMrUkic©kar
xageRkamenHKWCa]TahrN_BIsMeNrrbs;sisSeqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn 3nak;
sisS {k}
mFüm³ mFümmann½ydUcCamFümPaKEdr. eyIgGacKNnarkmFüm)an edayRKan;EtbUkcMnYn
TaMgGs;ehIyEcknwgcMnYnénvtßú³
25
77>5 + 98 + 77+ 86 +93 = 431>5
mFüm = kg3.865
5.431�
dUcenHTMgn;mFüménRCUkKW kg3.86 .
emdüann ³ emdüan KWCacMNucéntMélkNaþl.
´GacKNnarkemdüan edayRKan;EterobcMnYntamlMdab;BITabeTAx<s; bnÞab;mkqUttMélEdlx<s;Cag
nig tMélEdlTabCagecal rhUtdl;tMélkNaþl³ 77 77.5 86 93 96
dUcenHemdüanKW ³ 86
m:Ut³³ m:UtKWCatMélNaEdldUcKña. enAkñúgenH K�antMélNadUcKñaenaHeT,Iy. dUecñHTinñn½yEdlRbmUl
pþúM)anK �anm:UteT.
sisS {x}
mFüm³ mFümKWmann½ydUcCamFüPaKEdr. eyIgGacbUkcMnYnelxTaMgGs; ehIyEcknwgcMnYnénvtßú³
mFüm= 77>5 + 98 + 77+ 86 +93 = 401>5
mFüm = kg3.805
5.401�
dUcenHTMgn;mFüménRCUkKW 83kg
emdüann ³ emdüan KWCacMnYnelxkNaþl.
eyIgGacrkemdüan edayqUttMélEdlx<s;Cag nigtMélEdlTabCagecal ³
77 77>5 86 93 96
dUcenHemdüanKW 86 .
m:Ut³³ m:UtKWCatMélNaeRcInCageK. 77 manBIrdg. elxepSgBIenHmanEtmYydg.
dUecñH Tinñ½yEdlRbmUl pþúM)anm:Ut 77.
sisS {K} Tinñ½yEdlRbmUlpþúM)anm:Ut 77.
26
mFüm = 77 + 77>5 + 86 + 93 + 98 = 401
emdüan = 7.812
5.163
2
865.77��
� .
rgVaytMélxageRkamenH KWCalkçN³vinicä½yrgVaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisSmñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
sis
SS K
yl;GMBIBakü nigbBaØtiþ 3 3 2 1
bMNinkñúgkarKNna 2 2 1 0
cMelIyRtwmRtUv nigkic©kars¥at 3 3 1 0
srub 8 8 4 1
mUlvicarN_ sisS kk yl;c,as;GMBIniymn½yénBakü nigGacGnuvtþcMeNHdwgrbs;xøÜn enAkñúgkaredaHRsaycMeNaT.
sisS kk )ansMercelIskMritsþg;dakm�viFIsikSa.
sisS xx yl;c,as;Biniymn½yénBaküb:uEnþmankMhuskñúgkarKNna nigeRCIserIs RKURtUvCYyBnül;ENnaM
GMBIBaküm:UteT,Igvijfa m:UtKWCatMélEdlekIteT,Igjwkjab;CageK ehIyvamantMéldUcKña BuMEmnman
tMélRbhak;RbEhlKñaenaHeT. RKURtUvCYyelIkTwkcitþ[sisSenH BinitüepÞogpÞat;emIlcMelIyeT,Igvij
ral;elIkEdl)aneFVI. RKURtUvdak;kic©karNaEdlRsedogKña [sisSeFVI ebIsinCasisSenH GaceqøIy
cMelIyenH)anRtwmRtUv enaHbBa¢ak;fa sisSenHsMerclT§plsþg;dakm�viFIsikSaehIy.
sisS KK BuMsMerc)andl;kMritsþg;dakm�viFIsikSaeT,Iy. sisSenHBuMyl;GMBIBakü nigbBaØtiþ nigmankMhus
kñúgkareRbIRbmaNviFITaMgbYn. RKURtUvcMNayeBledIm,ICYyBnül;BIbBaØtiþenHdl;sisS RKUGaceRbIrUbPaB
edIm,IbBa¢ak;BIGtßn½yénBaküTaMgenaH ]TahrN_ KUrrUb)al;tUc²EdlmanTMhMxusKña edaydak;tMerobKña
mYyCYr ehIyBnül;GMBIn½yénBaküm:Ut emdüan nigmeFüm tamrUbPaBenaH. RKUKYrEtCYysisS b¤[
sisSBUEkNamñak;CYYyrMlwkBIkarbUkcMnYntamlMdab;. RbkarenH KWCYy[sisSecHbUktamlMdab;)anRtwm
RtUv.
27
muxviC¢aKNitviTüa fñak;TI 9 ¬k¦
lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦ BICKNit³ edaHRsayRbB½n§smIkardWeRkTII 1manBIrGBaØat..
kic©karvaytMél
1> kic©karenHRtUv)aneFVIeT,IgbnÞab;BIsisS)aneronsMrYl nigBnøatkenSamBICKNitgay²rYcehIy.
2> sresrcMeNaTdUcxaeRkam³
ebIpløaTijsURtRbEvg 3Em:t nigRkNat;cMnYn 2 kI tMél 44 000 erol.
suPaTijsURt 5 Em:t nig RkNat; 3 kI tMél 72 000.
etIsURtmYyEm:téføb:un �annigRkNat;mYykIéføb:un �an?
3> sYrsisS[eqøIysMNYr edayBnül;tamdMNak;kardUcxageRkam.
KMrUkic©kar
xageRkamKWCa]TahrN_BIsMeNrrbs;sisSeqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn3nak;³
sisS {k}
tag x tMélsURtkñúg 1 Em:t KitCaerol nigtag y CaRkNat;kñúgmYykIKitCaerol eyIg)ansmIkar ³
pløaTijsURt m3 nig RkNat; 2 kI yx 23 � eyIg)an 0004423 �� yx
suPaTijsURt m5 nigRkNat; 3kI yx 35 � eyIg)an 0007235 �� yx
edaHRsay � �iiyx
iyx
0007235
0004423
��
��
KuN �i nig 3 ehIy �ii nig 2
� �ivyx
iiiyx
000144610
00013269
��
��
yk �iv – �iii naM[ 00012�x .
28
CMnYs x kñúg � �i eyIg)an 0044200036 �� y
00036000442 �y
0004�y
epÞogpÞat;kñúg � �ii eyIg)an 00072000120006000043000125 ������ RtwmRtUv
cMelIy³ sURttMél 12 000 erol kñúg 1m nigRkNat; 1kI tMél 4 000 erol.
sisS {x}
tag x tMélsURt 1Em:tKitCaerol nigtag y CaRkNat;kñúgmYykIKitCaerol eyIg)ansmIkar ³
pløaTijsURt m3 nig RkNat; 2 kI yx 23 � eyIg)an 0004423 �� yx
suPaTijsURt m5 nigRkNat; 3kI yx 35 � eyIg)an 0007235 �� yx
edaHRsaysmIkar � �� �iiyx
iyx
0007235
0004423
��
��
rktMél x kñúgsmIkar � �i eTACMnYskñúgsmIkar � �ii eyIg)an
3
200044 yx �
� � � �iiiyy000723
3
2000445��
KuN � �iii nwg 3 eyIg)an � �ivyy 000216910000220 ��
y�0004
CMnYskñúgsmIkar � �i eyIg)an
000123
00036
3
0004200044��
��x .
epÞogpÞat;kñúg � �ii eyIg)an 00072000120006000043000125 ������ RtwmRtUv
cMelIy³ sURttMél 12 000erol kñúg 1m nigRkNat; 1kI tMél 4 000 erol
sisS {K}
sURttageday x KittMélCaerol nigtagkMNat;eday y KittMélCaerol
pløaTijsURt 3m nig kMNat; 2kI yx 23 � eyIg)an 0004423 �� yx
suPaTijsURt 5m nigkMNat; 3kI yx 35 � eyIg)an 0007235 �� yx
29
edaHRsaysmIkar � �iiyx
iyx
0007235
0004423
��
��
cMelIy³ sURttMél 12000erol kñúg 1m nigRkNat; 1kI tMél 4 000 erol
rgVaytMélxageRkamenH KWCalkçN³vinicä½ysMrab;vaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisS
mñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
sis
SS K
vicarKNitviTüa nigsmIkar)anRtwmRtUv 5 5 5 2
bMNinedaHRsaysmIkar)anRtwmRtUv 5 5 5 0
cMelIyRtwmRtUv nigkic©kars¥at 2 2 2 2
srub 12 12 12 4
mUlvicarN_
eTaHbIsisS kk )aneRbIviFIbUkbM)at; edIm,IedaHRsaysmIkar nig sisS xx )aneRbIviFICMnYsedIm,IedaHRsay
smIkark¾edayBYkeKTaMgBIr)anrkeXIjcMelIyRtwmRtUvdUcKña . enHbBa¢ak;[eXIjfa BYkeKeFVIkic©kar
sMerc)anelIsBIkMritsþg;dakm �viFIsikSa.
sisS KK eFVI)ancMelIyRtwmRtUvk¾b:uEnþ sisSenHBuM)anQandl;kMritsþg;dakm�viFIsikSaeT,Iy. smIkar
sresr)anRtwmRtUv cMelIyk¾)anRtwmRtUvEdr EtkaredaHRsayBuM)aneFVItamsmIkarBIrGBaØat. sisSenH
GaccMlgcMelIyBIeKk¾fa)an . dUecñH RKURtUvrMlwksisSfa kareFVIkic©kar sMxan;KWRtUveFVItamkarENnaM.
RKURtUvdak;kic©karNamYyeTot EdlRsedogenH [sisSeFVI ehIy[sisSbgðajBIkareFVIvicar nigkaredaH
Rsay.
30
muxviC¢aKNitviTüa fñak;TI 9 ¬x¦
lT§plsikSa ¬manenAkñúgsþg;dakm�viFIsikSa¦³
BICKNit³³ edaHRsaysmIkardWeRkTII 1manmYyGBaØt..
kic©karvaytMél
1> kic©karenHmanlkçN³s� úKs�ajCagkic©karenAfñak;TI 9 Epñk kk. ebIsinCasisSGacbMeBjkic©kar
fñak;TI 9 Epñk kk )ansisSenaH)ansMercdl;kMritsþg;dakm�viFIsikSa niglT§plsikSaehIy. kic©kar
xageRkamenH sMrab;[EtsisSBUEkeFVI ehIyRKURtUvKitrkskm�PaBbEnßm edIm,I[sisSGacTTYl
)annUvGtßRbeyaCn_tamry³skm�PaBTaMgenaH.
2> RKUdak;cMeNaTdUcxageRkam³
m:UtUumYYyeRKOgecjdMeNIrBIPPñMeBjj eTATIrYmextþttaEkvv enAem:ag mnh308 RBwkedayel,Ón
mFüm hkm40 . knøHema:geRkaymanrfynþRkugmYyecjdMeNIrBIPñMeBjeTATIrYmextþtaEkv
edayel,Ón hkm60 .
k> sresrsmIkartagcMgaypøÚvBIPñMeBjeTAkEnøgEdlyanynþTaMgBIrCYbKña.
x> etIrfynþRkugtamTan;m:UtUuenAema:gb:un�an ?
K> cUrrkcMgayBIPñMeBjeTAkEnøgCYbKña.
3> sYrsisS[eqøIysMNYr edayBnül;tamdMNak;kardUcxageRkam.
KMrUkic©kar
xageRkamKWCa]TahrN_BIsMeNrrbs;sisSeqøIytbeTAnwgkic©karEdlRKUdak;[eFVIcMnYn 2nak;³
sisS {k}
k> sresrmIkartagcMgaypøÚvBIPñMeBjeTAkEnøgEdlyanynþTaMgBIrCYbKña. tag t ¬KitCaema:g ¦
ry³eBlm:UtUeFVI dMeNIr BIPñMeBjeTAkEnøgCYbKña. ehIy ¬t -1/2¦ CaeBlEdlrfynþRkug eFVIdMeNIr
BIPñMeBjeTAdl;kEnøgCYbKña.
31
xageRkamenH KWCataragmYy tagtMélxusKñaénel,On ry³eBl cMgaycrrbs;m:UtUnigrfynþRkug.
yanynþþ el,ÓnmFümm ry³eBll cMgayy
m:UtU 40km/h t(h) 40t km
rfynþRkug 60km/h (t -1/2 )h 60(t-1/2)km
tamtaragxagelIsmIkarcMgaypøÚvBIPñMeBjeTAkEnøgEdlyanynþTaMgBIrCYbKña ³ 40t = 60(t -1/2)
x> ´GaceRbIrUbmnþenH edIm,Irkry³eBlEdlyanynþTaMgBIrCYbKña ³ 40t = 60(t-1/2) 40t = 60t - 30 30 = 60t - 40t 30 = 20t t= 30/20 t = 3/2h = 1h30mn8h30mn + 1h 30mn = 9h60mn =10h
dUcenHyanynþTaMgBIrCYbKñaenAema:g 10 RBwk
K> ´GaceRbItarag edIm,IrkcMgayBIPñMeBjeTAkEnøgCYbKña³ d= vt (v = 40km/h ; t =3/2h )
dUcenH d =40 ×3/2= 60km
dUecñH d = 60km
sisS {x} k> ry³eBlm:UtUeFVIdMeNIrBIPñMeBjeTAkEnøgCYbKña 8h30h + 30m =9h
smIkartagcMgayBIPñMeBjeTAkEnøgCYbKña 40x = 60 x 9x = 540/40 x = 54/4x = 13.5h
x> ry³eBleFVIdMeNIrBIPñMeBjeTAkEnøgyanynþTaMgBIrCYbKña 13.5h + 30min = 15h30m
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K> rUbmnþcMgay d = vt
dUcenH d = 60 x13.5
dUecñH cMgayBIPñMeBjeTAdl;kEnøgCYbKña KW 810km
rgVaytMélxageRkamenH KWCalkçN³vinicä½yrgVaytMélelIkic©karrbs;sisS nigkardak;BinÞúsisSmñak;².
lkçN³vinicä½y Gtib
rma
sis
SS k
sis
SS x
vicarKNitviTüa nigsmIkar)an RtwmRtUv 6 6 1
bMNinedaHRsaysmIkar 4 4 4
cMelIyRtwmRtUv nigkic©kars¥at 2 2 0
srub 12 12 5
mUlvicarN_ sisS kk )aneRbIrUbmnþ nigGnuvtþ)anRtwmRtUv. sisSenHeFVIkic©karsMerc)andl;kMritsþg;dakm�viFIsikSa.
sisS xx GaceRbIrUbmnþ nigGnuvtþRbmaNviFITaMgbYn EtsisSenHBuMyl;BIrebobedaHRsaycMeNaTtam
rUbmnþeT,Iy. RKURtUvCYydl;sisSenH kñúgkarKUrtagcMeNaT edIm,I[sisSenHyl;BIcMeNaTenH. RKURtUv
R)ab;sisSfa sisSRtUvEterobcMBt’mandak;enAkñúgtaragdUcsisS kk Edr. BIeRBaH sisSenHeFVIkic©karBuM
)anl¥ BuMmann½yfa sisSenHBuMGacsMerc)andl;kMritsþg;dakm�viFIsikSaeT,Iy. eRBaHenHKWCakic©kar
EdlBi)ak s� úKs�ajCag kic©karfñak;TI9 Epñk kk eTAeTot. ebIsinCasisSenHGacbMeBjkic©karfñak;TI9
Epñk kk enaHbBa¢ak;[eXIjfa sisSGacsMerc)andl;kMritsþg;dakm�viFIsikSa)anehIy.
33