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2. |
Ih nhjfme_ sx = vxt. |
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3. |
Ijb ijyfhebg_cghf jZ\ghf_jghf ^\b`_gbb |
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4. |
Wlh \b^gh ba jbk mq_[gbdZ |
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5. |
Hgb ^\b`mlky jZ\ghf_jgh \ jZaguo gZijZ\e_gbyo kh kdhjhklyfb |
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jZ\gufb ih fh^mex b df q |
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1. |
D g_jZ\ghf_jghfm ^\b`_gbx |
§5. |
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2. |
Kdhjhklv l_eZ \ ^Zgghc lhqd_ \ ^Zgguc fhf_gl \j_f_gb |
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3. |
Mkdhj_gb_f jZ\ghmkdhj_ggh]h ^\b`_gby l_eZ |
a |
gZau\Z_lky |
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\ ebqbgZ jZ\gZy hlghr_gbx baf_g_gby kdhjhklb v d ijhf_`mldm |
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\j_f_gb t aZ dhlhjuc wlh baf_g_gb_ ijhbahreh a = |
v = |
v − v0 |
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4. |
>\b`_gb_ k ihklhygguf mkdhj_gb_f |
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5. |
Hg ihdZau\Z_l [ukljhlm baf_g_gby fh^mey \_dlhjZ kdhjhklb |
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6. |
< kbkl_f_ KB f k2. |
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7. |
M\_ebqb\Z_lky ijb iheh`bl_evghf mkdhj_gbb |
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wlhf kemqZ_ |
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\ dlhj kdhjhklb b \_dlhj mkdhj_gby khgZijZ\e_gu mf_gvrZ_lky² |
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ijb hljbpZl_evghf \ wlhf kemqZ_ |
\_dlhj kdhjhklb b \_dlhj |
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mkdhj_gby ijhlb\hiheh`gh gZijZ\e_gu |
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§6. |
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1. |
Z vx = v0x + axt [ vx = axt. |
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2. |
< h[hbo kemqZyo ijyfZy \ kemqZ_ ©Zª ²ijhoh^ysZy q_j_a gZqZeh |
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kbkl_fu dhhj^bgZl |
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3. |
Wlb ^\b`_gby jZ\ghmkdhj_ggu_ h^gZdh \ |
i_j\hf kemqZ_ |
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mkdhj_gb_ iheh`bl_evgh Z \h \lhjhf²hljbpZl_evgh |
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§7. |
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1. |
Ijh_dpby \_dlhjZ i_j_f_s_gby \uqbkey_lky ih nhjfme_ |
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sx = v0 x t + |
axt 2 |
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Ih^klZ\bf \ wlm nhjfmem \ujZ` gb_ ^ey ijh_dpbb mkdhj_gby |
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2 |
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ax = |
vx − v0 x |
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Ihemqbf |
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sx |
= v0 xt + |
vx − v0 x |
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t 2 |
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= |
v0 x + vx |
t . |
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8
LZd dZd v0x = |
AO, vx = BC, t = OB kf jbk Z mq_[gbdZ lh fu |
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ihemqZ_f qlh ijh dpby \_dlhjZ i_j_f_s_gby sx |
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AO + BC |
OB |
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jZ\gZ iehsZ^b nb]mju OACB ²ijyfhm]hevghc ljZi_pbb k |
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2 |
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hkgh\Zgbyfb AO, BC b \ukhlhc OB. |
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2. sx = v0 x t + |
axt 2 |
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. |
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2 |
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§8.
1. |
Ih nhjfme_ sx |
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2 |
²^ey ijh_dpbb i_j_f_s_gby s = |
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— |
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ax t |
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at 2 |
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^ey fh^mey \_dlhjZ i_j_f_s_gby |
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2 |
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2. |
< n2 jZa ihkdhevdm s ~ t2 |
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s |
n |
= |
a(nt )2 / 2 |
= n2 . |
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3. |
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1 |
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at 2 / 2 |
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4. |
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st |
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DZd jy^ ihke_^h\Zl_evguo g_q_lguo qbk_e |
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1 |
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5. |
>ey hij_^_e_gby jZ\ghmkdhj_ggh]h ^\b`_gby |
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< jZaguo kbkl_fZo hlq_lZ wlb \§9_ebqbgu. bf_xl jZagu_ agZq_gby b ih1. jZaghfm hjb_glbjh\Zggu
RZjbd iZ^Zxsbc gZ ihe ^\b`ms_]hky Z\lhfh[bey g_ bf__l ]hjbahglZevghc2. kdhjhklb hlghkbl_evgh g_]h Hlghkbl_evgh A_feb hg bf__l kdhjhklv jZ\gmx kdhjhklb Z\lhfh[bey
Kdhjhklv imlv ljZ_dlhjby b l ^ jZaebqgu \ jZaguo kbkl_fZo hlkq3. _lZ
=_ebhp_gljbq_kdZy kbkl_fZ k\yaZgZ k Khegp_f ]_hp_gljbq_kdZy ²4. k A_fe_c
5. Kf_gZ ^gy b ghqb h[tykgy_lky \jZs_gb_f A_feb \hdjm] k\h_c hkb
JZ\ghf_jgh b ijyfhebg_cgh §10beb.ihdhblky 1. G_l
2. L_hjby :jbklhl_ey aZdexqZxsZyky \ lhf qlh ijb hlkmlkl\bb \g3. _rg_]h \ha^_ckl\by l_eh fh`_l lhevdh ihdhblvky
L_f qlh ih =Zebe_x l_eZ fh]ml jZ\ghf_jgh ^\b]Zlvky \ hlkmlkl\bb4. \g_rgbo kbe
Hiul bah[jZ`_gguc gZ jbk mq_[gbdZ ^hdZau\Z_l lh qlh ihfbfh5. bg_jpbZevguo kbkl_f hlkq_lZ \ dhlhjuo \uihegy_lky i_j\uc aZdhg GvxlhgZ kms_kl\mxl kbkl_fu bgh]h oZjZdl_jZ Hg
9
khklhbl \ ke_^mxs_f GZ l_e_`d_ h^bg rZjbd e_`bl gZ ]hjbahglZevghc ih\_joghklb Z \lhjhc ih^\_rb\Z_lky gZ gblb KgZqZeZ l_e_`dZ ^\b`_lky ijyfhebg_cgh b jZ\ghf_jgh b \ wlhf kemqZ_ h[Z rZjbdZ gZoh^ylky \ ihdh_ hlghkbl_evgh l_e_`db Klhbl lhevdh ijb^Zlv l_e_`d_ mkdhj_gb_ eb[h __ ijblhjfhablv eb[h ih^lhedgmlv dZd rZjbdb ijb^ml \ ^\b`_gb_ k mkdhj_gb_f hlghkbl_evgh l_e_`db LZdbf h[jZahf hlghkbl_evgh l_e_`db i_j\uc aZdhg GvxlhgZ g_ \uihegy_lky
Kms_kl\mxl kbkl_fu hlkq_lZ hlghkbl_evgh dhlhjuo l_eZ khojZgyxl6. k\hx kdhjhklv g_baf_gghc _keb gZ gbo g_ ^_ckl\mxl \g_rgb_ kbeu beb bo ^_ckl\b_ kdhfi_gkbjh\Zgh LZdb_ kbkl_fu gZau\Zxlky bg_jpbZevgufb
Bg_jpbZevgu_ kbkl_fu m^h\e_l\hjyxl i_j\hfm aZdhgm GvxlhgZ g7._bg_jpbZevgu_²g_l
Fh`gh 8. G_l
9.
Ijbeh`_ggZy d l_em kbeZ
§11.
1. Q_f [hevr_ fhsghklv Z\lhfh[bey Z khhl\_lkl\_ggh _]h kbeZ ly]b2. l_f [uklj__ hg m\_ebqb\Z_l k\hx kdhjhklv
Hiul bah[jZ`_gguc gZ jbk mq_[gbdZ ^hdZau\Z_l lh qlh ijbeh`3. _ggZy d l_em kbeZ y\ey_lky ijbqbghc mkdhj_gby >ey ijh\_^_gby ^Zggh]h hiulZ gZ^h \aylv l_e_`dm mklZgh\blv gZ g_c ^\Z h^bgZdh\h jZ[hlZxsbo \_glbeylhjZ b dZi_evgbpm >ey dhfi_gkZpbb kbeu lj_gby ijbdj_ibf d l_e_`d_ h^bg ba dhgph\ gblb i_j_dbgmlhc q_j_a [ehd Z d ^jm]hfm dhgpm gblb ih^\_kbf ]jma AZl_f hldjh_f djZg dZi_evgbpu b \dexqbf h[Z \_glbeylhjZ Ih^ ^_ckl\b_f kbeu \_glbeylhjh\ l_e_`dZ ijb^_l \ ^\b`_gb_ Ijb wlhf gZ klhe [m^ml iZ^Zlv dZieb q_j_a h^bgZdh\u_ ijhf_`mldb \j_f_gb L_i_jv _keb baf_jylv jZkklhygby f_`^m khk_^gbfb dZieyfb lh fh`gh m[_^blvky qlh wlb jZkklhygby [m^ml hlghkblvky dZd jy^ ihke_^h\Zl_evguo g_q_lguo qbk_e LZdbf h[jZahf fh`gh aZdexqblv qlh l_e_`dZ ^\b]ZeZkv jZ\ghmkdhj_ggh kf § IhkqblZ_f mkdhj_gb_ ih nhjfme_ a = 2s aZf_jb\ ijhc^_ggh_ l_e_`dhc jZkklhygb_ s b \j_fy __ ^\b`t 2gby ?keb mf_gvrblv kbem ^_ckl\mxsmx gZ l_e_`dm \ ^\Z jZaZ \udexqt _gb_f h^gh]h ba \_glbeylhjh\ b kgh\Z ihkqblZlv mkdhj_gb_ lh hgh ihemqblky \ ^\Z jZaZ f_gvrbf q_f i_j\uc jZa ?keb l_i_jv m\_ebqblv fZkkm l_e_`db \ ^\Z jZaZ ^h[Z\e_gb_f d l_e_`d_ ]jmaZ fZkkhc jZ\ghc fZkk_ l_e_`db b kgh\Z ihkqblZlv
10
mkdhj_gb_ lh hgh ihemqblky \ ^\Z jZaZ f_gvrbf q_f i_j\uc jZa LZdbf h[jZahf aZdexqZ_f qlh mkdhj_gb_ l_e_`db ijyfh ijhihjpbhgZevgh ijbeh`_gghc d g_c kbe_ b h[jZlgh ijhihjpbhgZevgh __ fZkk_
Mkdhj_gb_ l_eZ ijyfh ijhihjpbhgZevgh jZ\gh^_ckl\mxs_c ijbeh`4. _gguo d g_fm kbe b h[jZlgh ijhihjpbhgZevgh _]h fZkk_
a = |
F |
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6. G 1 |
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5. Hgb khgZijZ\e_gu |
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2 |
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§12.
Hiulu bah[jZ`_ggu_ gZ jbk mq_[gbdZ ih^l\_j`^Zxl lj1. _lbc aZdhg GvxlhgZ <h \k_o wlbo hiulZo ijb ihfhsb ^\mo ^bgZfhf_ljh\ baf_jyxlky kbeu k dhlhjufb ^\Z l_eZ ^_ckl\mxl ^jm] gZ ^jm]Z < i_j\hf hiul_ \aZbfh^_ckl\b_ l_e ijhbkoh^bl ijb bo g_ihkj_^kl\_gghf dhglZdl_ \h \lhjhf ² gZ jZkklhygbb \ lj_lv_f ² \ ijhp_kk_ ^\b`_gby Ijb wlhf \ dZ`^hf kemqZ_ ihdZaZgby ^bgZfhf_ljh\ hdZau\Zxlky h^bgZdh\ufb LZdbf h[jZahf fh`gh k^_eZlv \u\h^ qlh ^\Z l_eZ ^_ckl\mxl ^jm] gZ ^jm]Z k kbeZfb jZ\gufb ih fh^mex b ijhlb\hiheh`gufb ih gZijZ\e_gbx
Kbeu k dhlhjufb \aZbfh^_ckl\mxl ^\Z l_eZ jZ\gu ih fh^mex b ijhlb\hiheh`gu2. ih gZijZ\e_gbx
Wlh mkdhj_gb_ \\b^m [hevrhc fZkku A_feb ij_g_[j_`bl_evgh fZeh 3. GZijbf_j Khegp_ b EmgZ \aZbfh^_ckl\mxl ihkj_^kl\hf ]jZ\blZpbhgguo4. kbe
5. Wlb kbeu ijbeh`_gu d jZaguf l_eZf
>\b`_gb_ ih^ ^_ckl\b_f kbeu§13ly`. _klb
1. GZ^h baf_jblv jZkklhygby dhlhju_ rZjbd ijhoh^bl aZ ihke2. _^h\Zl_evgu_ h^bgZdh\u_ ijhf_`mldb \j_f_gb b m[_^blvky \ lhf qlh ^Zggu_ jZkklhygby hlghkylky dZd jy^ ihke_^h\Zl_evguo g_q_lguo qbk_e Wlh b [m^_l y\eylvky ^hdZaZl_evkl\hf lh]h qlh k\h[h^gh_ iZ^_gb_ l_eZ y\ey_lky jZ\ghmkdhj_gguf ^\b`_gb_f kf
§8)K. p_evx ihdZaZlv qlh mkdhj_gb_ k\h[h^gh]h iZ^_gby h^bgZdh\h ^ey3. \k_o l_e
Mkdhj_gb_ \ua\Zggh_ ^_ckl\b_f kbeu ly`_klb
4. Ba aZ kbeu khijhlb\e_gby \ha^moZ
5.
11
6. =Zebe_c
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§14. |
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1. |
>Z hgZ ij_iylkl\m_l _]h ih^t_fm |
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2. |
K mkdhj_gb_f Ijb ^\b`_gbb |
l_eZ \\_jo _]h kdhjhklv |
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mf_gvrZ_lky ih aZdhgm v(t) = v0 |
– gt < \_jog_c lhqdb ljZ_dlhjbb |
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kdhjhklv l_eZ jZ\gZ gmex b |
hgh |
gZqbgZ_l ^\b]Zlvky \gba |
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m\_ebqb\Zy kdhjhklv ih aZdhgm v(t) = gt ^h l_o ihj ihdZ g_ miZ^_l |
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gZ a_fex |
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3. |
Hl \_ebqbgu gZqZevghc kdhjhklb |
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4. |
?keb gZijZ\blv hkv \\_jo lh ijh_dpby \_dlhjZ kdhjhklb gZ wlm |
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hkv iheh`bl_evgZ Z ijh_dpby mkdhj_gby k\h[h^gh]h iZ^_gby ² |
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hljbpZl_evgZ |
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§15. |
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1. |
<aZbfgh_ ijbly`_gb_ \k_o l_e <k_e_gghc ]jZ\blZpbhggh_ |
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\aZbfh^_ckl\b_ l_e |
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2. |
=jZ\blZpbhggufb |
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3. |
BkZZd Gvxlhg \ ;9,,\_d_ |
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4. |
>\Z l_eZ ijbly]b\Zxlky ^jm] d ^jm]m k |
kbehc ijyfh |
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ijhihjpbhgZevghc ijhba\_^_gbx bo fZkk |
b h[jZlgh |
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ijhihjpbhgZevghc d\Z^jZlm jZkklhygby f_`^m gbfb |
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5. |
F = G |
m1m2 |
]^_ F ² fh^mev ]jZ\blZpbhgghc kbeu m1, m2 — |
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fZkku \aZbfh^_ckl\mxsbo l_e r ² jZkklhygb_ f_`^m gbfb G — |
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r 2 |
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]jZ\blZpbhggZy ihklhyggZy jZ\gZy 10-11 G f2 d]2. |
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6. |
AZdhg \k_fbjgh]h ly]hl_gby kijZ\_^eb\ \ ke_^mxsbo kemqZyo |
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^ey ^\mo l_e jZaf_ju dhlhjuo ij_g_[j_`bfh fZeu k jZkklhygb_f r |
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f_`^m gbfb _keb h^gh ba l_e bf__l nhjfm rZjZ jZ^bmk b fZkkZ |
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dhlhjh]h \h fgh]h jZa [hevr_ q_f m \lhjh]h l_eZ ijhba\hevghc |
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nhjfu ^ey ^\mo h^ghjh^guo l_e rZjhh[jZaghc nhjfu ijb |
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ex[uo bo jZaf_jZo |
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7. |
>Z |
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1. |
<_jgh 2. Mf_gvrZ_lky 3. Fl = mg. |
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§16. |
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4. |
KbeZ ly`_klb [hevr_ gZ ihexkZo l d A_fey g_fgh]h kiexkgmlZ |
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m ihexkh\ |
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5. |
Hgh ijb[ebabl_evgh \ jZa f_gvr_ a_fgh]h |
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12