Solutions

OneDimensionalKinematics
Problen 1
Startingfrom rest, a cm accelerates
at a constant4.00 m/s2for a distanceof425 m. The
car is then shiftedinto neutraland slowsdown at a ruteof 2.25 m/s2.How much time
elaosesbetweenwhenthe cm startsandwhen it stoos?
'. \t"a
4"^lr/o''
p
ir" Ayt"'M,y a
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2,).5
q+d\\d)t
oo
X-i"
\'=om
X = tl 15r")
)}"4
,,
l
ou
= V"t + Vxa.t^ --'--->X = '/sat
v= ?
Q . oD t/go
v-= ;:.- AoC*-
q= t4.oonfs^
v=
t=7
V
v
?4
_--_-_--=-+
Q = r/o+ al
V,n qt
V = O.q/r
q= -).a,5m/s)
a,\
= o\qx
=
---r
1),.4.x f e,(+.oo*,ls')(arS^) y=52"39
r
Vo = 5 s.?nfs
l
= l4.bs
f"1----.-'-
)(,,l15^)
L! q
(--
Yo = Ot"r/ S
t=
tr-n"^d)'"
-a+"A &,2,\ F-* 1 +4 fr, A*'^A P* 4e Yobb"''\
Yg
I
2'' 'uA^-L tt' '^z
^h 4.oo nf 9\ *',,J 4^,*
azlr/r\ ^t
)9" c,1
t= -u,A = _ * >v"3
t
n/5
/l
A.a-9n/5
5.1l
J},,i, = Z, * t.
= 14.t-s I5.\s
"
t= 4o"Es
---t
t
C=
^F
a
J>.1 9
Problem2
A hot-air balloon is rising upwardwith a constantspeedof 3.50 m/s. Whenthe balloon is
I 15m abovethe grormd,a passengertrying to takea pictwe accidentallydropshis cell
phoneover the sideof the balloon.Ignoring air resistance,how muchtime elapsesbefore
the cell phonehits the ground?
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lo
= ll5r.,
ri = Orn
U
V. = 3"5o r.'/9
lYe rcsq!
u
t-?
4
7t
-
,
\/ .
.t
--
tvt o (r--' -
L
VaC
/o
tt ,/ , , ^
/ r\ ,;.
(-1,tfi1c,*
) t''+
,)-
t/^q t'* Vot + Yo'o
--
t.2 -^ l"\/ L
15.>ornltr
= O
+I l 1 5 r r ;
"r'
'n
ALIJ-'
=
Jdui
,^a '
,lr*',fu*t fu
(-q.t "/s')t'
AXa+ bx* c=D'ra
' /\pn"a-^-f)\
4 = b r
fg''t
JPrc
r:;-;-
b'-tloc
{ b'-?qc
2.q
t.
r^
^ /-\+
' /,t ( 3.50 {/E )t. + //5 ',"r-* O
q = -4.1o nls^
6 = 3.so nls
c:
'4P'/dfiJa^
q-wo-\^afu
u,.'tlt,,''\r't
,t"'Il"*\
ril-tt*u.{
't t/ l q X
- r t//d, ^\I.\ v
'9"da Y\o
Pluc"t
lur*-rc\ aa J/v
nar*
q - -1'8nfta
Y-
o dA
J*, ,\^-h', ateld' c't l
'v:
O. Y'= ]'$omJ9
"uL
t'\r.E-:
---.--
- 3">v ^,/5:r J (:.so./r)',- '1(-t1.1o,115.)(
tte-)
f :
F^
/-
A (-q"9o,q/ee)
l/5 n
Ll,5os
t= 5"Als ot t'_=:--.
----
fi,QQ Fr\z'\o -Mtr D* ?,-,-'J
"{h
f = 5.1)s