NCERT Textbook - सरल रेखा में गति | NCERT Textbooks in Hindi (Class 6 to Class 12) - UPSC PDF Download

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vè;k;     3
ljy js[kk esa xfr
3.1 Hkwfedk
fo'o dh izR;sd oLrq izR;{k ;k vizR;{k :i ls xfreku jgrh gS A gekjk
pyuk] nkSM+uk] lkbfdy lokjh vkfn nSfud thou esa fn[kkbZ nsus okyh fØ;k,¡
xfr osQ oqQN mnkgj.k gSa A bruk gh ugha] funzkoLFkk eas Hkh gekjs isQiQM+ksa eas ok;q
dk izos'k ,oa fu"dklu rFkk gekjh /efu;ksa ,oa f'kjkvksas eas #f/j dk lapj.k
gksrk jgrk gS A ge isM+ksa ls fxjrs gq, iÙkksa dks rFkk ck¡/ ls cgrs gq, ikuh dks
ns[krs gSa A eksVjxkM+h vkSj ok;q;ku ;kf=k;ksa dks ,d LFkku ls nwljs LFkku dks ys
tkrs gSa A i`Foh 24 ?kaVs eas ,d ckj viuh v{k osQ ifjr% ?kw.kZu djrh gS rFkk
o"kZ eas ,d ckj lw;Z dh ifjØek iwjh djrh gS A lw;Z vius xzgksa lfgr gekjh
vkdk'kxaxk uked eankfduh eas fopj.k djrk gS] rFkk tks Lo;a Hkh LFkkuh;
eankfdfu;ksa osQ lewg eas xfr djrh gS A
bl izdkj le; osQ lkis{k oLrq dh fLFkfr eas ifjorZu dks xfr dgrs gSa A
le; osQ lkFk fLFkfr oSQls ifjofrZr gksrh gS \ bl vè;k; eas ge xfr osQ ckjs
eas Ik<+asxs A blosQ fy, geas osx rFkk Roj.k dh /kj.kk dks le>uk gksxk A bl
vè;k; eas ge viuk vè;;u oLrq osQ ,d ljy js[kk osQ vuqfn'k xfr rd gh
lhfer j[ksaxs A bl izdkj dh xfr dks ljy js[kh; xfr Hkh dgrs gSa A ,dleku
Rofjr ljy js[kh; xfr osQ fy, oqQN ljy lehdj.k izkIr fd, tk ldrs gSaA
varr% xfr dh vkisf{kd izo`Qfr dks le>us osQ fy, ge vkisf{kd xfr dh
/kj.kk izLrqr djsaxs A
bl vè;;u eas ge lHkh xfreku oLrqvksa dks vfrlw{e ekudj fcanq :i eas
fu:fir djsaxs A ;g lfUudVu rc rd ekU; gksrk gS tc rd oLrq dk vkdkj
fuf'pr le; varjky eas oLrq }kjk pyh xbZ nwjh dh vis{kk i;kZIr :i ls de
gksrk gS A okLrfod thou eas cgqr&lh fLFkfr;kas eas oLrqvksa osQ vkeki (lkb”k)
dh mis{kk dh tk ldrh gS vkSj fcuk vf/d =kqfV osQ mUgas ,d fcanq&oLrq ekuk
tk ldrk gS A
'kq¼xfrdh eas] ge oLrq dh xfr osQ dkj.kksas ij è;ku u nsdj osQoy mldh
xfr dk gh vè;;u djrs gSa A bl vè;k; ,oa vxys vè;k; eas fofHkUu izdkj
dh xfr;kas dk o.kZu fd;k x;k gS A bu xfr;kas osQ dkj.kksa dk vè;;u ge ik¡posa
vè;k; eas djsaxs A
3.2 fLFkfr] iFk&yackbZ ,oa foLFkkiu
igys vkius i<+k gS fd fdlh oLrq dh fLFkfr esa ifjorZu dks xfr dgrs gSaA
fLFkfr osQ fu/kZj.k osQ fy, ,d lanHkZ fcanq rFkk v{kksa osQ ,d leqPp; dh
3.1 Hkwfedk
3.2 fLFkfr] iFk&yackbZ ,oa foLFkkiu
3.3 vkSlr  osx rFkk vkSlr  pky
3.4 rkR{kf.kd osx ,oa pky
3.5 Roj.k
3.6 ,dleku Roj.k ls xfreku oLrq dk
'kq¼xfrdh laca/h lehdj.k
3.7 vkisf{kd osx
lkjka'k
fopkj.kh; fo"k;
vH;kl
vfrfjDr vH;kl
ifjf'k"V 3.1
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vè;k;     3
ljy js[kk esa xfr
3.1 Hkwfedk
fo'o dh izR;sd oLrq izR;{k ;k vizR;{k :i ls xfreku jgrh gS A gekjk
pyuk] nkSM+uk] lkbfdy lokjh vkfn nSfud thou esa fn[kkbZ nsus okyh fØ;k,¡
xfr osQ oqQN mnkgj.k gSa A bruk gh ugha] funzkoLFkk eas Hkh gekjs isQiQM+ksa eas ok;q
dk izos'k ,oa fu"dklu rFkk gekjh /efu;ksa ,oa f'kjkvksas eas #f/j dk lapj.k
gksrk jgrk gS A ge isM+ksa ls fxjrs gq, iÙkksa dks rFkk ck¡/ ls cgrs gq, ikuh dks
ns[krs gSa A eksVjxkM+h vkSj ok;q;ku ;kf=k;ksa dks ,d LFkku ls nwljs LFkku dks ys
tkrs gSa A i`Foh 24 ?kaVs eas ,d ckj viuh v{k osQ ifjr% ?kw.kZu djrh gS rFkk
o"kZ eas ,d ckj lw;Z dh ifjØek iwjh djrh gS A lw;Z vius xzgksa lfgr gekjh
vkdk'kxaxk uked eankfduh eas fopj.k djrk gS] rFkk tks Lo;a Hkh LFkkuh;
eankfdfu;ksa osQ lewg eas xfr djrh gS A
bl izdkj le; osQ lkis{k oLrq dh fLFkfr eas ifjorZu dks xfr dgrs gSa A
le; osQ lkFk fLFkfr oSQls ifjofrZr gksrh gS \ bl vè;k; eas ge xfr osQ ckjs
eas Ik<+asxs A blosQ fy, geas osx rFkk Roj.k dh /kj.kk dks le>uk gksxk A bl
vè;k; eas ge viuk vè;;u oLrq osQ ,d ljy js[kk osQ vuqfn'k xfr rd gh
lhfer j[ksaxs A bl izdkj dh xfr dks ljy js[kh; xfr Hkh dgrs gSa A ,dleku
Rofjr ljy js[kh; xfr osQ fy, oqQN ljy lehdj.k izkIr fd, tk ldrs gSaA
varr% xfr dh vkisf{kd izo`Qfr dks le>us osQ fy, ge vkisf{kd xfr dh
/kj.kk izLrqr djsaxs A
bl vè;;u eas ge lHkh xfreku oLrqvksa dks vfrlw{e ekudj fcanq :i eas
fu:fir djsaxs A ;g lfUudVu rc rd ekU; gksrk gS tc rd oLrq dk vkdkj
fuf'pr le; varjky eas oLrq }kjk pyh xbZ nwjh dh vis{kk i;kZIr :i ls de
gksrk gS A okLrfod thou eas cgqr&lh fLFkfr;kas eas oLrqvksa osQ vkeki (lkb”k)
dh mis{kk dh tk ldrh gS vkSj fcuk vf/d =kqfV osQ mUgas ,d fcanq&oLrq ekuk
tk ldrk gS A
'kq¼xfrdh eas] ge oLrq dh xfr osQ dkj.kksas ij è;ku u nsdj osQoy mldh
xfr dk gh vè;;u djrs gSa A bl vè;k; ,oa vxys vè;k; eas fofHkUu izdkj
dh xfr;kas dk o.kZu fd;k x;k gS A bu xfr;kas osQ dkj.kksa dk vè;;u ge ik¡posa
vè;k; eas djsaxs A
3.2 fLFkfr] iFk&yackbZ ,oa foLFkkiu
igys vkius i<+k gS fd fdlh oLrq dh fLFkfr esa ifjorZu dks xfr dgrs gSaA
fLFkfr osQ fu/kZj.k osQ fy, ,d lanHkZ fcanq rFkk v{kksa osQ ,d leqPp; dh
3.1 Hkwfedk
3.2 fLFkfr] iFk&yackbZ ,oa foLFkkiu
3.3 vkSlr  osx rFkk vkSlr  pky
3.4 rkR{kf.kd osx ,oa pky
3.5 Roj.k
3.6 ,dleku Roj.k ls xfreku oLrq dk
'kq¼xfrdh laca/h lehdj.k
3.7 vkisf{kd osx
lkjka'k
fopkj.kh; fo"k;
vH;kl
vfrfjDr vH;kl
ifjf'k"V 3.1
HkkSfrdh
40
vko';drk gksrh gSA blosQ fy, ,d ledksf.kd funsZ'kkad&fudk;
dk pquko lqfo/ktud gksrk gSA bl fudk; esa rhu ijLij
yEcor v{k gksrs gSa ftUgsa x-, y- rFkk z-v{k dgrs gSaA bu
v{kksa osQ izfrPNsn fcanq dks ewy fcanq (O) dgrs gSa rFkk ;g
lanHkZ fcanq gksrk gSA fdlh oLrq osQ funsZ'kkad (x, y, z) bl
funsZ'kkad fudk; osQ lkis{k ml oLrq dh fLFkfr fu:fir djrs
gSaA le; ukius osQ fy, bl fudk; esa ,d ?kM+h j[k nsrs gSaA
?kM+h lfgr bl funsZ'kkad&fudk; dks funsZ'k ra=k (frame of
reference) dgrs gSaA
tc fdlh oLrq osQ ,d ;k vf/d funsZ'kkad le; osQ lkFk
ifjo£rr gksrs gSa rks oLrq dks xfreku dgrs gSaA vU;Fkk oLrq dks
ml funsZ'k ra=k osQ lkis{k fojkekoLFkk esa ekurs gSsaA
fdlh funsZ'k ra=k esa v{kksa dk pquko fLFkfr fo'ks"k ij fuHkZj
djrk gSA mnkgj.k osQ fy,] ,d foek esa xfr osQ fu:i.k osQ
fy, gesa osQoy ,d v{k dh vko';drk gksrh gSA nks@rhu
foekvksa eas xfr osQ fu:i.k osQ fy, nks@rhu v{kksa dh
vko';drk gksrh gSA
fdlh ?kVuk dk o.kZu blosQ fy, pqus x, funsZ'k&ra=k ij
fuHkZj djrk gSA mnkgj.k osQ fy,] tc ge dgrs gSa fd lM+d
ij dkj py jgh gS rks okLro esa ^dkj dh xfr* dk o.kZu ge
Lo;a ls ;k tehu ls layXu funsZ'k ra=k osQ lkis{k djrs gSaA ;fn
ge dkj esa cSBs fdlh O;fDr ls layXu funsZ'k ra=k osQ lkis{k
dkj dh fLFkfr dk o.kZu djsa rks dkj fojkekoLFkk esa gksxhA
,d ljy js[kk esa fdlh oLrq dh xfr osQ fooj.k gsrq ge
,d v{k (eku yhft, x&v{k) dks bl izdkj pqu ldrs gSa
fd og oLrq osQ iFk osQ laikrh gks A bl izdkj oLrq dh fLFkfr
dks ge viuh lqfo/kuqlkj pqus x, fdlh ewy fcanq (eku
yhft, fp=k 3.1 eas n'kkZ, x, fcanq O) osQ lkis{k fu:fir
djrs gSa A fcanq O osQ nk;ha vksj osQ funsZ'kkad dks ge /ukRed
rFkk ck;ha vksj osQ fLFkfr&funsZ'kkad dks Í.kkRed dgsaxs A bl
i¼fr osQ vuqlkj fp=k 3.1 eas fcanq P vkSj Q osQ fLFkfr&funsZ'kkad
Øe'k% $360 m vkSj $240 m gSa A blh izdkj fcanq R dk
fLFkfr&funsZ'kkad &120 m gS A
iFk&yackbZ
dYiuk dhft, fd dksbZ dkj ,d ljy js[kk osQ vuqfn'k
xfreku gS A ge x&v{k bl izdkj pqurs gSa fd ;g xfreku
dkj osQ iFk osQ laikrh gks A v{k dk ewy fcanq og gS tgk¡ ls
dkj pyuk 'kq: djrh gS vFkkZr le; t =0 ij dkj x = 0
ij Fkh (fp=k 3.1) A eku yhft, fd fHkUu&fHkUu {k.kksa ij
dkj dh fLFkfr fcanqvksa P, Q rFkk R ls O;Dr gksrh gS A ;gk¡ ge
xfr dh nks fLFkfr;kas ij fopkj djsaxs A igyh eas dkj O ls P
rd tkrh gS A vr% dkj }kjk pyh xbZ nwjh OP = +360
m gS A  bl nwjh dks dkj }kjk pyh xbZ iFk&yackbZ dgrs
gSa A nwljh fLFkfr eas dkj igys O ls P rd tkrh gS vkSj fiQj
P ls Q  ij okil vk tkrh gS A xfr dh bl vof/ eas dkj
}kjk pyh xbZ iFk&yackbZ = OP + PQ = 360 m + (+120
m) = +480 m gksxhA D;ksafd iFk&yackbZ eas osQoy ifjek.k
gksrk gS fn'kk ugha] vr% ;g ,d vfn'k jkf'k gS (vè;k; 4
nsf[k,) A
foLFkkiu
;gk¡ ;g izklafxd gksxk fd ge ,d nwljh mi;ksxh HkkSfrd jkf'k
foLFkkiu dks oLrq dh fLFkfr eas ifjorZu osQ :i eas ifjHkkf"kr
djsa A dYiuk dhft, fd le; t
1
 o t
2 
 ij oLrq dh fLFkfr
Øe'k%  x
1
 o x
2 
  gS A rc le; ?t (= t
2
–t
1
) eas mldk
foLFkkiu] ftls ge ?x ls O;Dr djrs gSa] vafre rFkk izkjafHkd
fLFkfr;kas osQ varj }kjk O;Dr fd;k tkrk gS %
?x = x
2
–x
1
(;gk¡ ge xzhd v{kj MsYVk (?) dk iz;ksx fdlh jkf'k eas
ifjorZu dks O;Dr djus osQ fy, djrs gSa)A
;fn x
2
 > x
1 
rks ?x  /ukRed gksxk] ijarq ;fn x
2
 < x
1 
rks
?x  Í.kkRed gksxk A foLFkkiu eas ifjek.k o fn'kk nksuksa gksrs
gSa] ,slh jkf'k;ksa dks lfn'kksa }kjk fu:fir fd;k tkrk gS A vki
lfn'kksa osQ fo"k; eas vxys vè;k; eas i<+saxs A bl vè;k; eas ge
,d ljy js[kk osQ vuqfn'k ljy xfr (ftls ge js[kh; xfr
dgrs gSa) osQ fo"k; eas gh i<+saxs A ,d&foeh; xfr eas osQoy
nks gh fn'kk;as gksrh gSa (vxzorhZ ,oa i'pxkeh vFkok v/ksxkeh
,oa ÅèoZxkeh) ftueas oLrq xfr djrh gS A bu nksukas fn'kkvksa
dks ge lqxerk osQ fy, $ vkSj & laosQrkas ls O;Dr dj ldrs
gSa A mnkgj.k osQ fy,] ;fn dkj fLFkfr O ls P ij ig¡qprh
gS] rks mldk foLFkkiu
?x = x
2
 – x
1
 =  (+360 m) – 0 m = +360 m
gksxk A bl foLFkkiu dk ifjek.k 360 m gS rFkk bldh fn'kk
x dh /ukRed fn'kk eas gksxh ftls ge $ laosQr ls fpfÉr djsaxs A
blh izdkj dkj dk P ls Q rd dk foLFkkiu 240 m –
360 m = –120 m gksxk A Í.kkRed fpÉ foLFkkiu dh fn'kk
dks bafxr djrk gS A vr,o] oLrq dh ,d&foeh; xfr
osQ fooj.k osQ fy, lfn'k laosQr dk mi;ksx vko';d ugha
gksrk gS A
fp=k 3.1 x&v{k] ewy fcanq rFkk fofHkUu le;kas eas dkj dh fLFkfr;k¡ A