,
Questionsand ExampleProblemsfrom Chapter 2
Question I
You aredriving down the road at a constantspeed.Another car going a bit faster catchesup witlr
you andpassesyou: Drast a poshielttgrryh fer botl vehieleson 1*lesameset of axes,arld rote
the point on the graphwherethe other vehicle passesyou.
)9u au?^.5A'
#h
8rt t,=o -ple"An @ pz"ao
c24ttJ tr
6-r.
p^^4 frt ^'ra^i rr}t" &Jh Jm;o f, a"d paaau ryat A.ir;o
Sdtca.r
"r-^
Question2
The figure below showsthe position versus-timegraphsfor two objects,A and B, that are
moving along the sameaxis.
a) At the instant t : I s, is.tbe speedof A. greaierthaa, lgssrh.an, or squal to the speedof B?
Explain.
b) Do objectsA and B everhave tle samespeed?If so, at what time or times? Explain.
a)
et
t=ts)-^prlA"i
A'-
,d A. 5e" il4Prd
2i^, 4 ala*
b) O)*-l)
1
V-3;
euestions3 ))4P24
Ac B,&r',^,?
fua^r-u"S
5fn - \p4r\ At'rQ 4t^''T"f 3"'"t
4'
Ball 1 is throm straight up in the air and.,at the same
instant,ball 2 is reieasedfrom rest and allowed to fal1.
Which velocity graph in the figure to the right best
representsthe motion of the two balls?
M)^r{ A
"1
.A)qA rd b"e
K;,wet c
/r\r,a*-tx- Q't'"'1e'
f-t
n'otllt(v^);
/ = 7s tt atur-llq
nsa\ )-erl4 al N'a -6,*,
I (s.)
"!-r
$o*
>a
-hdtaA: (v-); o
l,
I
S
B mr'-9'4
Problem I
For the velocity-versus-timegraphof frgure below:
a) Draw the correspondingposition-ve$us{ime graph.Assumethat x
b) What is th€ obk4fs positi on at r = 12 s?
c) Describea moving object that could havethesegraphs.
= 0 m at l = 0 s'
r'. (m/s)
J
it
2
I
I
0
246
-l
t (s)
4;f* hn"*,,Jfi^t IA. Al4.,t1"t b" ?"4i"rn l a- fu;e ?'$
p"fuay!, )^ry'm
\-,/
12
I
I
-2
A)
l0
}i
t-bE
)-'t
1-*lt.
rtWa b*
f=o }. t-Llst NqV p - 3 n,ls,-l.o,t t'*4s
\ a-p4,e.,u3mls, * d *",-", t-
Gsf-
t= lls i9,o4-Q4T-\
x (.)
-1
-q
-b
*a
-lr
(U)
V" *-Aa'fi Y"+\
#)CI" pr4rfir" tue rh^nJfr-61*a^r''-l.o.,
(o,.*^ b'I!'^^ ,tr\' y- d44 ia aua'e-cil ) " 51,u" a^e l?.n-,a$ CLLIA
))&r,, frw x -aln (6aat"-',u) -^a ta 'n r$ at t^. aL"n* lt"o *4,
5,
-+--
{>YrruDq
(.)
A
3^f s,
Problem 2
ln a 5.00 km race,one runnerruns at a steady12.0km/h and anotherruns at 14.5kn/h. How
lone doesthe fasxerrunnerhaveto wait at the frnish line to seethe slower runner cross?
'rn)b"i r Vx = oYat ---+ A t= bYrl*
*"q.-r
4-
oA
=4 At =
4^ n'n-q t
.$.crr
zur,'vna
\ -"+ a t =
+"e
5.oolq
=
O.gt?
hc
r a.o x -/h.
,"= o.3eshc
ffi
I
)"r-A
lr'^^t" n h
n &,".,;Ag;
O.o't?ho
Ir"b,4$rt +;aX
^tl/fwu1
=
t ,-e 2 =A.Dt? n. ( qH
/u-vv't!^
)
4-3 n,n
Problem 3
' A car startsftom x1= 10 m at t; :0 s and moveswith the velocity graphshown in the figure below.
a) What is the object'spositionat I : 2 s, 3 s, and4 s?
b) Does this car ever changedirection? Ifso, at what time?
1,.{m/s)
4)
t2
-8;v*^" );4+l--r'"a^*.,g.e+t'60
jfu
a,^4a r^n\DU-lg, MtqatJt'U ?,.'^,p4
-,.C; a-d tq , M c2{"{$,r,iJ F' c-r^a--a
8
4
t)
$."^,
-4
o^J
W^fr^\ &"a'r lb.r""--it"!
lj*
= |orn
:
-t o,rr-.r -i,vtwltr /cJ.lrl\re btfux;nq
)Dr'' +
lOn, *
Os tJ
U'Jrn< futfrt)et\
OS
(u)
Xs
3E
",^^^tJ'
\/a(lr^/s)(3s)=
t@
r.ls
xqs . Xrr . o^",..s.lac*vue *y:.--J
=
l'"liilrlZ"'{&
(Lt-/3)( r*) * t/)( s./.) ( as) -w
Xas = IDnr + a^t q ),"^)'4
=
F'uh"l
a^94 -
Xg = Xi r a^ra rt p4.-*t?*"t4
X1,
i,r )9"
;^5r'r + 7r(-et*/e )( tt) =llG'^
59v c*'t t9,&,y34 f,LL\t*fr$L "t@l--"-
/
N'94-hd*e'oane4
Problem 4
(a) What is the magnitudeof the averageaccelerationofa skier who, starting ffom rest, reachesa
speedof 8.0 rnls when going down a slope for 5.0 s? (b) How far doesthe skier travel in this
time?
,.o
a) (v*)+ --(v*),-*a*at ---'-"-,
(v* )+ . A* 6t
(v*;,.- on/s
(v")+=8.on'l>
Ax ='?'
d; ^ - (Vx)a <- :---+
8.onla
__---2
t>t
6t=5'Os
9.45
/. O -
Xr'=oto
7.O
Xt= X; * (v*);ot* [:.4x(ot)a
x,4- i/tex ( or) r : ,A(r .t n/s") (s.rrf . lo,or,
K^-e,rgn'"
/., \
"\^Ary
( vr/r
b)
x+=?-
> a" = 1.6r,'fue
),^* F^
4
/.r
\a = /.r r)
(Vr)+
(Vr); +lq,6x
----+ (A, v, \
= --------"ln
4,\e\X
tto
ax=
/ \).
( ; . r".,,f'rl
.r
\
probfems
5,/ .
fufirtu xi =ofq )
, = )0.o r\ -)
:=::!
ae,l,ra/5,)
Xs--M'on
a) What constantacceleration,in SI units, must a car haveto go from zero to 60 mph in 10 s?
b) What Fraction
of gis this?
c) How far hasthe car traveledwhen it reaches60 mph? Give your answerboth in SI units and rn
feet.
,
,^-,/
= tun'/
-1
ha"/Ige-3-tr\/4)r
\
nr ) \-?r"oos )=
,
Co nl / lt.
c\) (v-), . omls
(v' )+' \L-s-15
rlf = los
(v")*
O.x= ?
,t \
D)
o,/o
Ab.e*fs
_-=:j::::=:.
= (v*); + q* at
cx= !_Y-)t:(',^)t- 7!.s:JS:_a:tg
lo:
,r.r-
.'= \-GEq/s'
"
q .8D n/s"
D. ^'13 ---.
lA-=e"dr'7
a^" )77" oi I
.o
w)
( V"),. = on/:
(V,.)q' 3.u.z',ls
Af ' tos
a.^ = l.6t-/sl
Xi.."o
X5= ?
lloo
I-----.'
d\: -a '?.ii/9i
A=\rII,_
Problem 6
restat 1.1m/s2for 20 s. lt thenproceedsat constaatspeedfor 1100m beforeslowingdown at
2.2 rnls"rrtll 1tstopsat the statlon.
a) What is the distancebetweenthe stations?
b) Hory much time doesit take the train to go betweenthe stations?
+.-)
( v Y \J r '-=n0 t -^// s
^r j - ' t , 't -f r/ )\ 1 5
x:
xa= Taax[*){
.=
Kr= Za.(r,1"/s^)taoe)r
3ry-
at=)os^
X " ' ' d x + =?
.-o
-- 4"at
(v*)r-(V*)i+qrbt
LV*)+ = La to/5
(V*)+.?
tn--+t o
,-o
tea
(. - { " (vi)r a/ r r/2gx(at)\ -)
/\r
f^
= (t.l'F/r)X)os)
.-o
- x, :LV,); af+ '/;ar( o*) *
X
,
/ K - (v{).-At --= a t= bY(^)t
,4x=,Jry
Vx = A).r/s
Qx'o
Af.
6t= 3
\,/
U9,-
1t f{\/5
SDs
1==:;
\_,/
..
F^-oble^\3 * -
-^c,offivwad{
Probfem7
Startingfrom rest, a speedboatacceleratesat *10.5 rnls' for a distanceof 525 m. The engineis
then tumed off and the speedboatslows down at a rate of 5.00 m/s'. How long doesit take for
the speedboatto cometo rest?
fu" A4\*) "4f,4r5a5.
(V.)i- (V-),1*)4^ax ----) (V* )r'= aq^aY
=> 4^^".t;^,*r -J )^ N
X;=o*
Xg = 515."
(V*); - o.,r/s
(v")+' ?
a
Q" = +1b.5 n/5
(vx), = / o 5 , o 1 s
(v*)+- o ^ls
Qx=-
Ot= ?
5. o", nr/S*
tto
(v*)+
(v,)+
'
/o>n/s
:::-
--4
(V")+ - (V"); * q ^ D t
o
Af
O = (V*);+a''abt
( v' ).."
. - -....--.
Qy
/) t = - / 65 nls
'5.o" oluo'
l--- ,--- -L"-..---
--l
Problem $
A dragncer, startingfrom rest,speedsup for 402 m with an accelerationof+17 -0 n/s2.A
parachuiethenopens,slowingtle car down with an acceleration
of -6.10 m/s2.How fastis tbe
.^.>
opens?
racermovfurg
3.50x I 0' m aflertheparachute
I
o----_)a ----)c.-------r
!A
--
a(
qx
l' \
------)
) --------J
, , v^ * 11. 11 s
--r
c, <*-t.
q ->r----t---+--+,r.-r.
--,
,
4 X =_ \ / , ^
r Q
q
bolOm/s:'
,
P^t"j"k'+e'{a
)ft 4jrA o$fr u^j'b^'oIr'vg
$ 4otn
$zto dt,p;a,vo
t>
? "ts^t ,il
"'
Xi-orq
(V*)+"= (v*).'" Ao, (\-
\z : zrn4_
(v").=
(vy);= or"/s
-(vr)f.?
$
A
= 2..arx;
2..q"X.-
01 = l],orr/5\
v
)
4a,ilJ[,]&.^J 6'a;f4-e Wfuprnr tII./s',0(V*);
AX= ) , 5 0 K l 6 a m
(v *)+= (v*) j * )_q*ax
( v*),'= l \ ' / m , i s
r-}
(V*)t = 1V,,yra*jaa1
ul
(V*)q
dx=
- a,ro.7r.
(v* )+= I ?. l.o/.
A^)t = 2'l*15
( V*)*--lV*)i. a.xAf --- tt=-!J)i
At_ _ 1extu)/.
(t),1)r=0n19
Qx=-)-A.nlse
\t= ?.
\
l/r(-r,4-}r,r
ax = (vr); af .'/.rq.{ at) } = (ra,"/e!,o,;*
A\=?
l--r-
^
.r" /sn)
o( -jgs
r
'{-
-)'a\Nt dtatuovt\<o
frt"9 h,tu =
0-AOrr+ \lDoq +
irorq= [4;;l
CDsr- FOe+ los
=Ffr-
Problem 9
At the beginning ofa basketballgame,a refereetossesthe ball straightup with a speedof 4.6 m/s.
A player cannottouch the ball until after it reaehesits maximum height and begim to fall down.
What is the minimum tirne that a player must wait before touching the bail?
:e"-ffi
dWAffiryr
-'i)d"ntuq"n
ry-f**@
B.
fd,
V = o nls $o7" ^4'b* r\a)^'L
( V,,\, - (\ Vu\,
+d,t bt
t/L
\
I Jl
(Vv); = Ll.6n/s
l\f
.
-
=
/
r/
.\
t vY/(
...--
t
4,.1
0y= -q.sanp
bt --o "1'ls
bt=?
- q"sor'',ha
Problem 10
An astronauton a distantplanet wants to determineits accelerationdue to gravity. The astronaut
tlrows a rock straightup with a velocity of +15.0 m/s and measuresa time of 20.0 s before the
rock retums to his hand.What is the acceleration(magnitudeand direction) due to gravity on this
plaaet?
=
Yr" Otn
Y{"o(V,'r),': |S"ar"'/s
61 = 3o.oofr
ay=?
V - = Y . - * (vr)r bt +'lto.t (at)"
1;O
O = (Vy); at *
e1=- 91,)i"!
t/e
=
'/aqt (n/)t
- i(Vr)i
(at )*
er= - att5-o.ls') =
at
rl
ro/5
2o.on f s
( vr ); = lS'oo/e
(Vj)a. o.,,/s
bt' !o"o> A,l= ?
(vr)+ = (Vr);* ay of ---) oy = - (tJ))'/Yt
o
u, .l ,- -
- 1
' - t- s
' -.-a " / s )
lo"o5
Problem 11
A studentstandingon the groundtlrows a ball straightup. The ball leavesthe student'shand
with a speedof 15 m/s when the hand is 2.0 m abovethe ground. How long is the ball in the air
before it hits the ground?(The studentmovesher hand out of the way.)
l?
,i!i
iir l
:/^ A ' q
,tt
A1
tl
I
I
J
I
/./
\
=
(Vy
)i l5 */s
0y = - ?,7on/sq
Yt
)+
= 0'on
= ); * (v)); ot' laay(o*)i
(r*)"+(Vr;,ot + | t = o
7aa.r
!.=O
It
\-/
o
/z
\
v"
At= ?
4teAot-b*
%AdAr,,l^'<.
at'+Lx+C =o
-b
X -- ! 'l bl-9'c
(-,t.1o./s') otq +ll5nls) AD+A.ore'= 0
l\
q=-4,9oVs\
b = l5vfe
LL=
5 (-u,ao,ls)
C = ]"ory1
+ tG,3 n/s
- 't "8 o m/sa
^
L
./-l(
--
t'\
1,'(S
fuvn 2
Problem 12
upward
A 200kg weatherrocket.isloadedwith 100kg of fue1andfired straightup. It accelerates
resistance
effects.
any
air
runs
out
of
fuel.
Ignore
at 30.0m/sr for 30.0s, then
a) \44ratis the.rockel'smaximumaltitude?
b) How long is the rocket in the air?
c) Draw a velocity-versus-timegraphfor the rocket from liftoff until it hits the ground.
)
.u.-qo AX;-^f u'^J4 o
f^r€
=> fr,s" c/\o 3 F4"& /U;tlu TYnabn :
{,|t:D
FFr,ii
H'l
I
€' r''.rdr 1", i
t:
( .)
t r,;
I
---I-
i
I
A ,,"t
e
tl
fl H n c
I
o --i
i.,
t.
li
li
a, t )o.Dnlst ,ftc,ot=3D'0:
tv
A-r 3 ^,o,,s,A&&A 4.w,\A^XAt"*P-;J
A;^'^"4
I l'
la
ao
,.-\^t
-p)A N"^^a 6'n o^,^ q = - {'!Drn/5i
t-Al
-tJ^i* f-'*J "-f ^natuan:
A)t-"z
I
).= D-
Vr = ?
(vr)""o"/s
d.1: lD.oo/5
(v:),'?
At
3o.os
j, = Y" * (Vr)" l\t + t/^av (ut)\
= '/ritr (ot)' - t/)L3o.o"/s')(:o.os)'= lry
/,,
\vy,l'
--
t
/.r
=
ra, (at) = o) (ut) " (:a.o*7jXao'os)
W
\
\v)/o
'o
bor^r-y
'
,!-c.'J
f".d
,4 *.'Ft?"
uu-Qqg3r,Tr"^"4 'eJ
..o
i / rvr \ ) /\a2 . =
\
qoo.fe)a
9^ =
---r ot-= -*!'=
(v.,)r.=(vr),+ar(at)
/r\
(D/
Ya
-+ r-n
a'J--1s'
=
: ( v;) r Qoo"/s
(v1;r' o o/5
J^'?
) , = I 3 , s o a , ' , nta,=?
+-
AdLDr /-Tyg
= SlvsoDr'
',Jr= Dm
(vy)1 'D./s
'9'Zac'.194
Q \ 1=
x*:?
.
a\
Ya
\ e . = 5 1 , s o on
=
54.8 Kr.''
;gy"1t^)
-332_!.h, =
71"9s
_ 1 , g o n ft ^^
-=a'a=
= 3o.Ds + ?t"9 5 * ]*^;7. fult S{18aor,
= Ve * (Vr)" bt + '/sA) (at)A ,--) o =
Y^ " l.
af= /-3;.
-)'Cs{rga"q)
/ c > 5, 8 s
- g.8o-,/s"
14f", ts'- = 3o,os + g \.? s .+ lo5,Zs
=
rot