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Unformatted text preview: EM311M  Dynamics
Exam 1 Monday, Sep 25, 2006, WEL 3.502 33’!” £145" “715? (4.4% a—l" w. ¥.w4wrfmx".* P‘V‘V 1. A particle is moving in a straight line with a constant acceleration a. At some time to > 0, the
corresponding position and velocity are $0 and 00, respectively. Derive the formulas for position
m(t) and velocity v(t) at any time t (5 points) Va 5 a : 1/ O ,‘0 If
1/ D
"5 ’ V ‘ Mb“ ) + “Va / fair" f {o‘ , " 1"
X40 4 CE“ 7‘ '4 *1/59 xKo w J '1'
x .53; . 4: (1‘ "7‘ £450 {’4‘ W f a {
ix :3, a 7",.» ., if! 2,15," 1 7,... X0 3‘ 3
x e W“ ‘mmlﬂmvﬂiﬂm‘l 2. The large and small hands of a clock meet at noon. What time will they meet next again? Give the answer in terms of a fraction (no decimal round off, please...) (5 points) v ./
’ " ’ ' e "' w. 3"” _
Q? n .5 .3 .j‘ if" . \f‘ 4/“ ‘ “mi *1 r‘ ‘ ’5“ A 5"? Van" a.» a; if It.
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6.
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13: x a f {.1
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1 N " 4 Q) @ 3. Give examples of motions in which: a/ at 76 0, an 2 0, b/ at = 0, an # 0. (5 points) a) ﬂiaﬁ‘ou .c 'at J ft ‘ ,r‘ f“ _ L? :3: ,4 {a as c" 6.: (3&0.ch  A ) ﬂan16.1.?“ «1!. u 4. £761.45; t d ML" 4' C h 5'" é ‘ V
I (CM: 4/; my {(4 / #6619736) :2" I ”
f 4. Derive the formula for acceleration vector components or and (L9 in the polar system of coordi—
nates (5 points) 0(3" cf:
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,V m. !" O
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a a .
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a.
r a 9' 5. A particle moves along a parabola y2 = a: with a constant speed 1). Determine the Cartesian
components of the velocity vector as a function of coordinate 1:. (5 points) C’oaaﬁm heal" rid0790a 5 raw «'3 l“ 5‘ X
Z n s“ 2;
‘2 i? L W g“; L,» a w V a...
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V l/
v + ~~~~ « 4‘ W,
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f7 "' f If 7 3+ 1 f i’éxw
1/ :r f .2, X 6. A projectile is launched at 100 ft/s at 600 above the horizontal. The surface on which it lands is
described by the equation shown. Determine the :1: coordinate of the point of impact. (25 points) /00 0635001 1‘ 2’ 50¢" X .127
... ’ I o z
y _._. .. 52.1,» :49? + Ioo 5.3m 56’ wt. : ——/6,/z‘ 74 596605
142:" ﬁv/WC Zf‘ Mag, W‘ac ‘fd'o/Jtcﬁi/C [a f: “fat? jroamyf (5) y I: 'ﬂlﬂait x /
Z. X = 5753's? iii] 6‘; r « lo/.‘i’/ 3 64.1524 ; :r w a i x ~ m 5% 53 8,6? «mm 7. The car increases its speed at a constant rate from 40 mi/ h at A to 60 mi /h at B. What is the
magnitude of its acceleration 2 s after it passes point A ?? (25 points)
' 7 #
y as+o%~g stew [T]
l 120a ‘ if; '— ﬁ I ‘ B w
A ‘ o go‘ft_._I—x 041.3%“; 151,9“, x4 +0 3 a 3’0 S r; «S’sz + Jﬁ’hgﬁ'rwa r3“? ~2F'/00 35:0
x 150 +£2.93 r52.3é=r.2752,z)4~4/ ~_u ‘ a 5:357
W, m? r
Q :5“ "2': "‘ «pl/.26 3'
59.57 H—
. 4f : 7g/[ [3—] @
M
2
V 5 4k i
0 ,__ ‘ﬂ
V—— 51? 67«— 736/54, ~==> V5 7"“ 30 Z J] @
%41ﬁoa (bf/6t. 3° 3 QtL =r 247/6 8. A point P moves along the spiral path 7‘ = (0.1)6 ft, where 0 is in radians. The angular position
0 = 2t rad, where t is in seconds, and r = 0 at t : 0. Determine the magnitudes of the velocity
and acceleration vectors of P at t = 1 s. (25 points) P A r: 0/ 6 :7 <94" [7‘47 0 Q r .1.“ J 69 r 0'1 [if F: m a = o u “mwumm m— MW"? m V: 02:“"+ m“ “' 0””? 5‘2"?”
WWW” M, if“ m s n z «~27 ...
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This note was uploaded on 11/03/2009 for the course EM 311 M taught by Professor N/a during the Spring '08 term at University of Texas at Austin.
 Spring '08
 N/A
 Dynamics

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