Resoluções das Fichas 2 e 3. Cinemática de um ponto material

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An Vzy Mdadedunndo MondVane 
Facul dods d laugmkona 
C410 nqunhorno Civil Fon 
CadeiraiicaI 
T.eMO. Kue lucøo das hdhas 02 
e 03 
02- Mmabica de Mn
Voulo uatavial - I 
CiMmala eo. de waPonto natzn ol-T 
Dewnte 
03- 
imte 
batolomu QLine 
Mopulo, an 69 de yulo de 20 
Uwvar dade duardo Monddone 
Rese luepo da Frlho 0 
Cimemahca de um Youto Motanal 
- I 
Muhulo, a09 de zdlo de 2or 
ara apmokoda do wqmdo 
d 
Jemaborio das Veloudadn Mudion) 
Yara eamda mobude 
ara o reho 
d 
Cakaudando 
. t R 
M P 
A ,+ ho algohrtumo hra 0 cakoulo K3 
132 
bMeAuo ufoim 
eM-M- 
p-Xi 
Pavo Le2 
4-18 
M a3 (uano) A-0. O19 
= ty 
- arkaq (m) 
=Oreamg 3 
d m.t d ? 
d= 3. 
4.6 Augulo du indenau 
AS 
Voleei uode Madua 
ariVaudo o raio Vukor, tumn a Velovidoda 
PTelat) 
4EL]- 
d(8)1at) = a 
d 
=_b-2 bact lara hhar atleruo Vukoriol 
bosta dai var o vleudode 
6) idauia Per corida iub sodo de 
tomk 
Lintw galo de tm fo 
ikameia Percomida 
t-2 
At= bt-at) 
d= I7 = EE)- (2at 
2 
-at 
At=t-«t) 
9 tladn L)Veletidads Monima 
t20 Mox=C-0P
Cd 
CO 
CA 
X= 2,0 wax = 0,2 
1 M = 
Voeri dade iuntau 
ana = Vletidade medio 
dt 
JEO 
-B) (t-to)=X-Xo 
bo8-2 64 
to -Ko -t 
aquapo Pavamebrias 
9 2 * y-2(b4uazao da Traluloia) 
4T+ 46T
ds 
47 
Coust 
Rm hdo eqah vo day fava auhav @ Vlevidade a Oviqpma, tomn da obey Qnds 9= 0; X -0 
X 0x-bx=F0 
X=0 V (a-bx)=o 
E9vx= Qx-bx 
Xo (Dn X=0, tuon u Ponko ua Uviqewm t= (ax- b) 
vdoidade Ko -.bX, M Vy quueu Vdoi dade A&Ko 
Quaudo r-o 
=a -bo 
,NE =60 ku 
da ye=+da + d 
+ta+ b3 
SO+ 30+ 1L 
da ,ta 30k 
3 10 uú 
dg = .t = 10k 90 km 
9 ADkura ho TePo de Tandla i dade lov 
7Vi, tu,W 
- Na, ka caloudar o tmo 
t 
t 1-(0 
. 0p2 
10.t Lqt+R = sg (t*+att+¢*) 
H+R = 10.4t 5* 
A=10t b +SHR 
10t=+pR 
h.19 
o)o= (B)2 + (18tR4 7 7 
X-4t- a 
9ehar 7- (ra)ë + (e2t") 
l8= + (18-4) 
t i 
)- - Bti+ge ur)? dt 
d 
= 64 +e4 
= 206 
de 
= 8+(26t -4)F 7 
r = 2rb +4096 
l2= 43r2 c) farat 4 Alarauno 
lol= Ne4)-(844.4) 0=ax +0y 
=+l%1 -4) 
lal = 4o 
|el = %o0g 
Cy=y 4+ 36.4 
Jol = T48B7 tlal= 8+42-4 
al= 
t 
)= AMml 
Yo-3 by) = 0M/ Qy= 3 Co L) 
ax dt oy ds de 
Jb o 
Mm -Apn ( de 3 cn14) &E 
X=ent 
= 3 0n(t) B = ont- 0y dt 
= Cont 3 A0 (4 dx 
y-3-3 Cm t+3 
3 cot + 
oquaepi da Tvajucbori 
y--3 oma MNx)6 
-3 Cn t+ 6 y=-3.0nar nx) +b 
6 =(lo)* 
= LtAJA, n t 
l= Lt 
= A Cnt +t Mnt) + antQent)T 
d 
dE dt 
do (Ve Ox)+ (hy ay 
Po= cont ont -+[sn"tt cont)|=o - ust 
(1-t) =o, t- t4 
= 12M 
i duvan do q-984 
(120)t2 Y8813 9-4p 0.t+
= 144+/13h48 84,3= 41,t.t + 919t 
= 7 M/ 419t+47t 
- B13 =o 
tamo mmly Pouhi vo 
twalo da quwda i hbs 
=43 ku/k 
3 
t 
lya. 036 
ta=X t 129,6A 
Pamaro (ineo) 
Va 
02 hm = d 
LAchar0 wkaca do Fmonto 
X X XAOA utotanvo B + 
awaro Paaro 
pubocarob 
APA X.B+,t pamaro 
XAulocowro A = X4 t9at 
9 A- K. 
o nbr do efonke 
per dumada do mcoa tvo 
Xp AutocCANrO mn ro = Ytavo 2 Vi 
XMCOMlro -3 pp =d +#gt 
d X2 Mconto = Apt-Vat 
3Vst= 
3V 
Aabbi mdo 0 MUnO Vretamo tuM 
F Mcon to 
Xa mcom bro Kncadho-1/s) temPo de monho 
X3 ncontio X+X2+X,* +.Xn* = ditauua Par cotri da 4uieCarv0 A 
VALAt V= da V P+ X+X3* ... Xn = 
S at 
AS=2. -3 
e d -AS= d 
M 0, hogo 0 Vam da yolton imcaleulo.Vei 
+ 
ha on Ponuboy den Vuberan, Pora 
davem kr Mmebri c 
tliVar adade undo Momlaue 
Aese ucgo do Frdka 03 
Clunabco de um tonbo Mnakeniod 
hdvo Mrdalak 
MaPabo a 09 d yulho de 01 
MG MMUDMO imitante 
Ay putowovel= teamiao 
Aukuovl 
a-M/s mesefon bor 0 aro ullratamao 
Comia 
dintamia d B 
TXoOwOD =0 
Ahubowov l = - d 
Autova oVel = 0 
X CQMAO =0 XAutomow 
tmto de montroButrao caroo maD 
X=Km 
at= 2.H 
2 
X= at 8. 
t= 
C 
)Leckameia de larata ) 
= .E 
X-Xo 7std '2d=a.t2
Xe = st+4 
at 
(F+d)= 
A3P aminO- 
d 2 
at=s+d). 
-96tir88sTL"R b Piat = 9,b1 -22 
d dry , d o7 5.b mja 
de 
+ 
d de 
Bm =9.6i- 2tk 
Varo t= 
-Get 
Perat 3 
=b -2 rn96-23 
ASn = 
a dx 
a-d= (a0n)+(2t0) 
o 4 co)t 
- 2/mt
(4 ent) de+ (200t) dt quatm da 1rajokev,a 
=-4 0mt+ 4 -4 cnt= Xl4 
-4Cent 
lo y= Ment 2Rnt = y 
X=- 4 eønt +4 + mt tecony = (-r+4) Sont = (-Ku 
b) J= {uwn+}2 + (2c»mt 
a= cet4 sent 
= 23ent+L 
2/4wntpe 1= 
a2.40s- os 
81= a3. 
6= 3. 0S+ 
18 3,2 ml 4 M/ 
- HAE
A= m Ja 
a de 
AE dt 
JO +t 
= A.t 
4AtR +?t X= 
6= 99 
gdahjo 100Mm 
4ay0 
ma atima dasuua =* t Bog 2.4 (h+R) 
98-2.Dh+ o 
9o04=20(h + 100) 
2ok 9b04 -00 
6) Dtwto de ubi da 
oy M_604 
20 
t 
2802 m 
918 
420 0 
2mfo de quwdo 
2 00= J0,24 
AX 
t0,r 
a)uao de ubida 
Bt 9.8 
-2m B.ygt t= 0933 
Ujmax 
y-4 Det -49t* 
y=Dp- 
ny =(2 Nan 37)0,933 -
9,8.(0.953) 
Aleana Hori geu hb 
4u 2Y 
By GS3 4,3 
AY 423 m 
A QEU va MMawimo. 
Vhoudade da bla o belyo Chao 
p= poy-9t 
=2. Am 3- 
9,8.0,933 
g = S9L Ml 
pelo= Wo Mia (p.onf)E 
Tralaukevio. 
Y=rr oa0), w 
rO0 S 
aMha 
X= SSO M 
ViModa 
SC0 
taw 
t04 
s)&a 2 g(y4) 
LomY-
4hP 
302S+ 10000 7 
Ma Vethoa 
uaudo augë o 
MaVio 
yF-Voyy ogo 
-Vo pn=VAnn. 
- gt 
V AY= 9 
tmbo que Yatva. faka. akiuguo 
Naeio. 
amdo t=t V.CoAY 
V.conY 
den a=4(K1-k) 
plreo-o)_ 
a 100 
2- awa (016) 
9-Kv 
a dv 
-V d 
9-k kv 
y- 2 2-L 
3 
iquaad Trajueva
2- 
K j0.0m 
la = 
9 40 hm 
t 
20t-40t +6 yot 24t èA6t 
Jo 
404 - 24t+ 1t dr = 34 tt 
= 10t-8t+8t 
3 W 4ot - 24+*+ 16t 
Polo manno freuo, teme 
b Oc Kala t=4, 
W=22 
2 
e 7874/js 
A3 
t= t2t-1 (W- 
y= , Comtunke 
&2) = Yeni Contavute 
un= W t +2 
WiH = 2f+2 
Yara t= , tM qui 
W=6 
T. 637,0 
- W. 
le.R 
= K 463 MMJo 
T 463 Qe = 637.10 
c h3.i0 
Nenava 
toqt Vovradaoo) Vckuwa Bm/ 
V caro = sbhu»/k 
y chuva 
Vchu va dug (06) 
Varascaro 
31° 
Vaviabm Aelacao oð oi = 300kunl. 
Velo gyudb 9o km/& VA 
VAs Vdeidads do 
avno m Roloyovao noko Vas 
euh dey 
Vas (ar m Relaoo ao soo VAs 
VasVea + Vas 
Vs 619o 
Vss 8b,2 Kml& 
g1-) Tte)- (6t+ 4tl- 3t7 
el= (6t,3)7 - 3 3K 
18t-6t dt 
ee) = (12t t4)-6t 
V t (1t+4li -4t- 
18t+ Gt} 
V 13t +4-18t*)E 
a96 -6 Lm/ 
22.) 
bolo 
50 km/ 
100 Km/h 
4OD EnYh 50{m 
bola Comb Comb 
4DD Rmh 
50 kmh 
1 y V-V, - 00-50 = 50 Km 
-400 +50 = 150 
Km/h 
TL -vV +Vda > t: {00+ 50'= 411, 80 Km/h+ 
98 nf h = 55 m/ 
t t0o. 40 
> A = U.t A = 55.10 550m 
198 m/h = 59 mlb 
t Uy {0«|0 j00ml 
Oado
50 mlh- 13,89 mlb 
39 
-(19,39 
029 
16,023 
o 09,94 
r-9t t 
t 
h- t:o 
h = 5(0,33)= 0, 
5445, 
40 FTn/h 0, 
00112 Km/s 
4)= 80 Km lh 
= 0, 0112km / 
0 450,4 5b 
t ,02934 
t450,45b» 
0,0411 2,4686 10 mmlb° 
450,45 
a 2,4686 10m/n*, 
A6-)Gad 
Beet 2t-1
w = 2t+3 
olt 
du = nadl
18 
= 432 ya20 
2Knlh 
= 4,4t mlh 
b-d acty 
26,56