Page 1
Name:
Unit 3 - Motion
Chapter 9 AccelerationDAY OUTLINE KEY TERMS
1 Read 9.1 summaries (p. 193 in pckg)Assignment:Key Terms (9) (p. 192)Velocity & Acceleration w.s. (p. 194)Positive, negative and zero Acceleration (p. 194)
2 9.1 notes (p. 195-196) 1. Change in velocityAssignment: Read p.380-391 (text) 2. Acceleration
p. 391 # 1,3,8,9 (p. 198) 3. DecelerationCalculating change in velocity w.s. (197)
3 9.1 QUIZ 4. Velocity-time graph9.2 Notes (slides 1 -5) (p. 199) 5. Constant AccelerationAssignment: Read 9.2 Summary (p. 201 in pckg) 6. Average Acceleration
Read p. 392-395 textbookp. 405 # 11-13 (p. 202)9.2 Describing motion w.s. (p. 203)
4 9.2 Notes (slides 6-9) (p. 199-200) 7. GravityAssignment: Read p.396-405 (text) 8. Acceleration due to
Calculating Acceleration (p.204) gravityAnalyzing vel-time graphs (p.205) 9. Air resistanceMotion match up w.s. (p. 205)
5 Acceleration lab (9-2d) p.402-403 — Due this class
6 Assignment:Ch.9 Review: Assessment 9.1, 9.2 (p. 208)
p. 406-407 # 4, 6, 7, 1 1-14, 16-21 (p.
206-207 in pckg)Physics Unit w.s. (209)
7 Unit 3 Review: p. 413- 417 #4, 8-12, 14, 18-20, 24-26, 29, 3 1-33, 36-5 1 (answers only for MIC Q.’s) (p.210-211 inpckg)
8 Chapter 9 package dueUnit 3 Test
1011
Page 2
Chapter 9: Acceleration KEY TERMS
Key Term Definition ExampleChange in velocity
Acceleration
Deceleration
Velocity-time graph
Constant acceleration
Average acceleration
Gravity
Acceleration due togravity
Air resistance
1°(L
Page 3
Des
crib
ing
Acc
eler
atio
n
How
can
you
calc
ula
tea
chan
ge
inve
loci
ty?
Ach
ange
inve
loci
ty()
occu
rsw
hen
the
spee
dof
anob
ject
chan
ges,
orits
dire
ctio
nof
mot
ion
chan
ges,
orbo
th.
Cha
nges
inve
loci
tyca
nbe
eith
erpo
siti
veor
nega
tive.
To
find
ach
ange
inve
loci
ty,
subt
ract
the
initi
alve
loci
ty(i
)fr
omth
efi
nalv
eloc
ity(i
).V
V
How
dosi
gns
ind
icat
ech
anges
inve
loci
ty?
Nor
th,
east
,up,
and
righ
tare
cons
ider
edpo
sitiv
e(-i
-)an
dso
uth,
wes
t,do
wn,
and
left
are
nega
tive
C—).I
fyou
slow
dow
nfr
om9
zn/s
forw
ard
(pos
itive
)to
2rn
/sfo
rwar
d(p
ositi
ve),
your
chan
gein
velo
city
isas
follo
ws:
1W=
—
=+2
in/s
—(+
9m
/s)
=—
7rn
/sY
our
chan
gein
velo
city
is7
rn/s
oppo
site
the
forw
ard
mot
ion.
You
rini
tialf
orw
ard
dire
ctio
nis
po,ri
tive,
soyo
urch
ange
inve
loci
tyis
nega
tive
whe
nyo
usl
owdo
wn.
Wh
atis
acce
lera
tion?
Acc
eler
atio
nis
the
rate
atw
hich
the
velo
city
ofa
mov
ing
obje
ctch
ange
s.A
chan
gein
velo
city
can
bea
chan
gein
eith
ersp
eed
ordi
rect
ion.
Thu
s,ac
cele
ratio
noc
curs
whe
nth
esp
eed
ofan
obje
ctch
ange
s,or
itsdi
rect
ion
ofm
otio
nch
ange
s,or
both
.A
ccel
erat
ion
isa
rate
ofch
ange
.Thi
sm
eans
ital
sota
kes
into
acco
unth
owqu
ickl
yth
eve
loci
tych
ange
s.
Rec
all
that
forw
ard
mot
ion
isde
fine
das
posi
tive
and
back
war
dm
otio
nis
defi
ned
asne
gativ
e.D
iffe
rent
fact
ors
can
help
you
deci
deif
anob
ject
’sac
cele
ratio
nis
posi
tive
orne
gativ
e,as
show
nin
the
tabl
ebe
low
:
Fact
orV
eloc
ityA
ccel
erat
ion
incr
ease
insp
eed
while
+(p
ositi
ve)
1-(p
ositi
ve)
trave
lling
forw
ard,
e.g.
,ac
cele
ratin
gaf
tery
ouha
vest
oppe
dat
ast
opsig
n
decr
ease
insp
eed
while
+(p
ositi
ve)
—(n
egat
ive)
trave
lling
forw
ard,
e.g.
,ap
ply
ing
the
brak
eson
abi
cycl
e
incr
ease
insp
eed
while
-—
(neg
ativ
e)—
(neg
ativ
e)tra
velli
ngba
ckw
ard,
e.g.
,aba
gfa
lling
toea
rthno
chan
gein
spee
d,co
nsta
nt0
e.g.
,ru
nnin
gat
aco
nsta
ntsp
eed
Not
eth
atan
obje
ctth
atis
slow
ing
dow
nis
chan
ging
itsve
loci
ty;
ther
efor
e,it
isac
cele
ratin
g.A
ccel
erat
ion
ina
dire
ctio
nth
atis
oppo
site
the
dire
ctio
nof
mot
ion
isso
met
imes
calle
dde
cele
rati
on.
Text
book
page
s38
0—39
1
Bef
ore
You
Rea
d
Are
you
acce
lera
ting
ifyo
uar
esl
owin
gdo
wn?
Exp
lain
your
answ
eron
the
lines
belo
w.
How
dosi
gns
indic
ate
chan
ges
inaccele
rati
on
?R
eadi
ngC
heck
2.W
hati
s the
acce
lera
tion
ofan
obje
cttra
velli
ngat
aco
nsta
ntve
loci
ty?
Cre
ate
aQ
uiz
Afte
ryou
have
read
this
sect
ion,
crea
tea
five-
ques
tion
quiz
base
don
wha
tyo
uha
vele
arne
d.R
epea
tth
equ
izun
tilyo
uge
tall
the
answ
ers
corre
ct.
0R
eadi
ngC
heck
1.D
efin
eac
cele
ratio
n.
164
MH
R•
Sec
tion
9.1
Des
crib
ing
Acc
eler
atio
n©
2008
McG
raw
-ItO
Rye
rson
lim
ited
©20
08M
cGra
w-H
illR
yers
onL
edite
dS
ecti
on9.
1D
escr
ibin
gA
ccel
erat
ion
•M
HR
165
Page 4
Dat
e
Use
with
text
book
page
s38
0—38
6.
Vel
ocit
yan
dac
cele
rati
on
Use
the
term
sin
the
voca
bula
rybo
xto
fill
inth
ebl
anks
.Y
oum
ayus
eea
chte
rmon
lyon
ce.
1.S
ince
velo
city
isa
,it
isd
epen
den
ton
the
__
__
______________
ofth
eob
ject
and
the
dire
ctio
nin
whi
chth
eob
ject
ism
ovin
g.
2.A
chan
gein
velo
city
is
__________________
whe
nan
obje
ctsp
eed
sup
.
3.A
chan
gein
velo
city
is
___________________
whe
nan
obje
ctsl
ows
dow
n.
4.A
nob
ject
has
__________________
whe
nit
istr
avel
ling
with
unif
orm
mot
ion.
5.A
ccel
erat
ion
isth
era
teof
chan
gein
___________________
6.A
nob
ject
has
a
____
____
____
____
____
____
____
____
____
_
whe
nits
spee
dis
incr
easi
ng.
7.A
nob
ject
has
a
____
____
____
____
____
____
____
____
____
_
whe
nits
spee
dis
decr
easi
ng.
8.If
anob
ject
’sac
cele
rati
onis
inth
e
____
____
____
____
____
____
____
____
____
_
asits
velo
city
,th
eob
ject
’ssp
eed
incr
ease
s.
9.If
anob
ject
’sac
cele
rati
onis
inth
e____
____
____
____
____
____
____
____
____
___
asits
velo
city
,th
eob
ject
’ssp
eed
dec
reas
es.
10.
Acc
eler
atio
nth
atis
oppo
site
toth
edi
rect
ion
ofm
otio
nis
call
ed
Use
with
text
book
page
385-
386.
Pos
itiv
e,n
egat
ive,
and
zero
acce
lera
tion
1.In
each
situ
atio
nde
scri
bed
belo
w,
iden
tify
whe
ther
the
obje
ctor
pers
onha
spo
sitiv
eac
cele
rati
on,
nega
tive
acce
lera
tion
,or
zero
acce
lera
tion
.
a)an
airp
lane
taki
ngof
f____
____
____
____
____
____
____
____
____
b)a
pers
onst
andi
ngst
illat
abu
sst
op
c)a
bus
brak
ing
asit
appr
oach
esa
red
light
d)a
pers
onsl
idin
gdo
wn
aw
ater
slid
ew
ithco
nsta
ntve
loci
ty
2.In
each
illu
stra
ted
exam
ple
show
nbe
low
,id
enti
fyw
heth
erth
eob
ject
orpe
rson
has
posi
tive
acce
lera
tion
,ne
gati
veac
cele
rati
onor
zero
acce
lera
tion
.
b)
Voc
abul
ary
cons
tant
veloc
itypo
sitiv
eac
cele
ratio
nde
cele
ratio
nsa
me
dire
ctio
nne
gativ
esp
eed
nega
tive
acce
lera
tion
vect
orop
posi
tedi
rect
ion
velo
city
posit
ive
acce
lera
tion
Ave
loci
ty
acce
lera
tion
velo
city
—
I0
-
=+
2O
rn!s
*6
mIs
d)=
—4m
/sj=
-1m
Is
t=O
st=
lst=
2s
t=3s
t=4
0t=
ts
,,
,,
0cm
20cm
40cm
60cm
80cm
100c
m
)
166
MH
R•
sect
ion
9.1
Des
crib
ing
Acc
eler
atio
n02008
McG
raw
-Ha
Rym
son
Uni
ited
168
MH
R•
Sec
tion
9.1
Des
crib
ing
Aoc
eler
atio
n©
2008
McG
raw
-FO
IlR
yars
onLF
nfte
d
Page 5
9.1 Describing Acceleration — Student Notes
+ An object travelling with
______________________
+ An object travelling with non-uniform motion will:
‘have different
______________________________
‘take different
__________________________________
•have a continuously
__________________________
has equal displacements in equal time intervals.
during equal time intervals.
to travel equal displacements.
Changes in Velocity
• A change in velocity (z) occurs when the
+ A change in______________________
+ If the change in velocity is
of an object changes, or its
______
changes, or both.
can be calculated by: A = —
, the object is travelling with
Positive Changes in Velocity
• If the change in velocity is the (+, -) as the initial velocity, the speed of the object is
Example: i = Vf — +9mIs - (+6mIs) = + 3mIs
Negative Changes in Velocity
• If the change in velocity is the
______________________
object is
Example: i = — = + 2mIs - (+9mIs) = - 7mIs
Acceleration
• isthe
.
(+, -) of the initial velocity, the speed of the
the change in
_____________________
can be due to a change in
_______________________
a change in
_____________________________,
or both.
• two objects with the
__________________________
can have
_________________________
> this is because acceleration describes
_______________________________________________
• Example: Suppose both of these vehicles, starting from rest, speed up to 60 knilh. They will have
the
___________________________
but since the dragster can get to 60 1cm/h faster than the old
car, the
Page 6
Positive Acceleration• The is the same as the
acceleration
velocity
Example#1: A car in the
________________________
direction.
If we designate the forward direction as
_________
(+) then the change in velocity is
____________________
therefore the acceleration is
________________
(+).
____________________________direction.
If we designate the forward direction as
__________________________________________
therefore the acceleration is —
Positive and Negative Acceleration *Remember positive (+) and negative (-) refer to directions.*
• Example#3: A
___________________________
in the
_____________________
direction.
> If we designate the backward direction as
_________________________
then the change in
velocity is
____________________________
therefore the acceleration is negative (-) even
though the car is increasing its speed.
Av =i — =z(—4m/s)—(—lm/s)=—3m/s=
ma’s
• Example#4: A
_________________________
in the
> If we designate the backward
____________________________as
negative (-) then the
__________________________________is
positive (+), therefore the
___________________
is
positive (+) even though the car is
_________________________
its speed.
=f—I=(—1mIs)—(—4m/s)=+3m/s=
vf——lm!s v1=—4mts-
Negative Acceleration
• Acceleration that is
_________
of motion is sometimes called
• Example#1: A car_____
the directionacceleration
oci +in the
(+) then the change in velocity is
direction.
Page 7
ApplyingName Date Knowledge
Use with textbook page 382.
Calculating change in velocity1. Complete the following table by calculating the missing quantities. Positive (+)
represents the forward motion. Use the formula A7 = — . In the last column,describe the change in velocity (e.g. object is slowing down, object is speeding up,or object is in uniform motion),
V V1 Description of Ai+ 14 mIs + 5 rn/s object is slowing down+BmIs Om/s
+25 mIs +12m/s+20m/s —3Dm/s—38m/s —1Dm/s
—16m/s Om/s—3m/s +22m/s
2. Use the following data table to calculate the change in velocity for each time interval.Suppose motion toward north is positive (+).
Time (s) Velocity (mis)0 0
10 1520 2830 2840 2250 12
a) Os—lOs.
b) lOs—20s
c) 20s—30s
d) 30s—40s
e) 40s—50s
© 2008 McGraw-Hill Ryerson Limited Section 9.1 Describing Acceleration • MHR 167
Page 9
9.2 Calculating Acceleration — Student Notes
Calculating Acceleration:The
_____________________
of an object depends onthe
________________________________and
the
_____________required
to change the velocity.When stopping a moving object, the relationship between time and acceleration is:
•
_________________________
the stopping time
_________________________
the acceleration
• the stopping time
_________________________
the acceleration
Velocity-Time Graphs:
• The motion of an object with
________________________________
is best represented by a
The motion of an object with
graph.
is best represented by a
________
graph.
Velocity vs. Time
Time (s)
The slope of a velocity-time graph is
. is measured in
_______
Determining Motion from a Velocity-Time Graph:
. slope (in the
acceleration) object’s velocity is
_____
direction.
0
‘a
to0
.
.
______________
slope(______________
_____________________slope
(________
in the
acceleration) — object’s velocity is
______________
— acceleration) — object’s velocity is
— direction or the object’s velocity is
40
30
20C,0
10
slope riserun
= 50m/s—25m(s4.0s — 2.0 5
- 25 mIs2.Os
= 13m1s2
:..............z.:..z.:::
1 2 3 4
increasing in the negative direction.
Velocity vs. Time
0
During which time interval was
• The acceleration zero?
• The acceleration negative?
• The acceleration positive?
• The object increasing it’s velocity north?• The object decreasing it’s velocity north?• The object moving at a constant velocity north?
Time (s)
qC
Page 10
-
Cal
cula
ting
Acc
eler
atio
n:a
Av
=(a
)(&
)&
=—
c--
‘“
V
_____
&a
.
Exa
mpl
e1:
Apo
olba
lltr
avel
ing
at2.
5m
Is,
tow
ards
the
cush
ion
boun
ces
offa
t1.
5ni
’s. I
fthe
ball
Gra
vity
and
Acc
eler
atio
n.
__________________
IV
inco
ntac
t wit
hth
ecu
shio
nfo
r0.
20s,
wha
tis
the
ball’
sac
cele
ratio
n?(A
ssum
eto
war
dsth
ecu
shio
nis
Gra
vity
isa_
__________________
.:V
the
posi
tive
dire
ctio
n.)
____
____
____
__th
at
acts
betw
een
d
____
____
____
____
____
____
____
____
__
isa
fric
tion-
like
forc
eth
atop
pose
sth
em
otio
nof
obje
cts
that
mov
eth
roug
hth
eai
r.
Exa
mpl
e2:
Aca
rac
cele
rate
sfr
omre
stat
3.0
mJs
2fo
rwar
dfo
r5.
0s.
Wha
t is
the
velo
city
ofth
eca
rat
Igno
ring
airr
esis
tanc
e,al
lobj
ects
will
____
____
____
____
____
____
____
___
tow
ards
the
Ear
that
th
een
do
f5
.O
s?
____________________
V
Cal
cula
ting
Mot
ion
Due
toG
ravi
ty:
Exa
mpl
e:Su
ppos
ea
rock
falls
from
the
top
ofa
clif
fW
hati
sth
ech
ange
inve
loci
tyof
the
rock
afte
r
itha
sfa
llen
for
1.5
s?(A
ssig
n“d
own”
asne
gativ
e(-)
)
Exa
mpl
e3:
Atr
ain
istr
avel
ling
east
at14
ni/s
.H
owlo
ngw
ould
toin
crea
seits
velo
city
to22
ni/s
east
,V
ifit
acce
lera
ted
at0.
50m
Is2
east
?(a
ssig
nea
stdi
rect
ion
posi
tive
(+)).
Mor
ePr
actic
e:I.
Wha
tis
the
chan
gein
velo
city
ofa
bric
kth
atfa
llsfo
r3.
5s?
Mor
ePr
actic
e:1.
Atr
uck
star
ting
from
rest
acce
lera
tes
unif
orm
lyto
18m
/s[W
jin
4.5
s.W
hati
sth
etr
uck’
s
acce
lera
tion?
2.A
ball
isth
row
nst
raig
htup
into
the
air
at14
rn/s
. How
long
does
itta
kefo
rth
eba
llto
slow
dow
nto
anup
war
dve
loci
tyof
6.0
mIs
?
2.A
tobo
ggan
mov
ing
5.0
rn/s
forw
ard
dece
lera
tes
back
war
dsat
-0.4
0m
Is2
for
10s.
Wha
t is
the
tobo
ggan
’sve
loci
tyat
the
end
ofth
e10
a?
3.A
rock
isth
row
ndo
wnw
ards
with
anin
itial
velo
city
of8.
0m
Is.
Wha
tis
the
velo
city
ofth
ero
ckaf
ter
1.5
s?
3.H
owm
uch
time
does
itta
kea
car,
trav
ellin
gso
uth
at12
ni’s
, to
incr
ease
itsve
loci
tyto
26m
/s
sout
hif
itac
cele
rate
sat
3.5
nifs
2so
uth?
Page 11
Text
book
page
s39
2—40
5
Bef
ore
You
Rea
d
Sum
mar
y
How
isac
cele
rati
on
det
erm
ined
ona
velo
city
-tim
egra
ph?
Ave
loci
ty-t
ime
grap
hre
pres
ents
the
mot
ion
ofan
obje
ctw
ithch
angi
ngve
loci
ty.
The
slop
eof
ave
loci
ty-t
ime
grap
hgi
ves
the
obje
ct’s
acce
lera
tion,
whi
chis
mea
sure
din
rn/s
2.W
hen
abe
st-f
itlin
epa
sses
thro
ugh
all
data
poin
ts,
the
obje
ct’s
velo
city
isch
angi
ngat
aco
nsta
ntra
tean
dit
expe
rien
ces
cons
tant
acce
lera
tion
.H
owev
er, s
ince
not
all
the
velo
citie
sm
aybe
dire
ctly
onth
ebe
st-f
itlin
e,th
esl
ope
isre
ferr
edto
asav
erag
eac
cele
rati
on(a)
.If
nort
his
cons
ider
edpo
sitiv
e,fo
rlin
esab
ove
the
x-ax
is:
•a
posi
tive
slop
e(a
)re
pres
ents
the
aver
age
acce
lera
tion
ofan
obje
ctth
atin
crea
ses
spee
dat
aco
nsta
ntra
tew
hile
trav
ellin
gno
rth.
Acc
eler
atio
nis
cons
tant
and
posi
tive.
•ze
rosl
ope
(b)
repr
esen
tsan
obje
cttr
avel
ling
nort
hat
aco
nsta
ntsp
eed.
Itis
not
acce
lera
ting.
•a
nega
tive
slop
e(c
)re
pres
ents
anob
ject
that
decr
ease
ssp
eed
ata
cons
tant
rate
whi
letr
avel
ling
north
.A
ccel
erat
ion
isco
nsta
ntan
dne
gativ
e.V
eloc
ityis
posi
tive.
Vel
ocity
vs.T
ime
tito
tTh
ee(of
Alin
ebe
low
the
x-ax
is(d
)re
pres
ents
incr
easi
ngsp
eed
ata
cons
tant
rate
tow
ard
the
sout
h.A
ccel
erat
ion
isco
nsta
ntan
dne
gativ
e.V
eloc
ityis
nega
tive.
Rec
all
that
aver
age
acce
lera
tion
isth
esl
ope
ofa
velo
city
-tim
egr
aph:
Slop
e=
rise
1:v
=
Thi
ste
xtbo
okon
lyco
nsid
ers
situ
atio
nsw
here
acce
lera
tion
isco
nsta
nt. T
his
mea
nsav
erag
eac
cele
ratio
nis
actu
ally
the
sam
eas
acce
lera
tion
atan
yin
stan
t.-
1wa=
OT
his
equa
tion
can
bere
arra
nged
toca
lcul
ate
velo
city
ortim
e.Fo
rve
loci
ty:
For
time:
Wha
tis
the
rela
tion
ship
bet
wee
ngr
avit
yan
dac
cele
rati
on
?
Whe
nan
obje
ctfa
llsne
arE
arth
’ssu
rfac
e,th
efo
rce
ofgr
avit
ypu
llsit
dow
nwar
d.C
onsi
der
aba
llbe
ing
thro
wn
stra
ight
upin
toth
eai
r,w
here
“up”
ispo
sitiv
e.•
On
the
way
up,
the
ball’
sve
loci
tyis
decr
easi
ng.
The
ball
issl
owin
gdo
wn,
soits
acce
lera
tion
isne
gativ
e.•
At
itsm
axim
umhe
ight
,th
eba
ll’s
velo
city
isze
rofo
ran
inst
ant
sinc
eth
edi
rect
ion
ofth
eba
llis
chan
ging
.(B
ecau
seth
eba
ll’s
velo
city
isst
illch
angi
ng,
the
ball
isac
cele
ratin
gal
thou
ghits
velo
city
isze
rofo
ran
inst
ant.)
•W
hen
the
ball
star
tsto
com
edo
wn,
itssp
eed
incr
ease
s.H
owev
er,
itsve
loci
tyis
nega
tive
beca
use
the
ball
ishe
adin
g“d
own.
”T
heba
ll’s
acce
lera
tion
isne
gativ
e.
How
does
air
resi
stan
cein
flue
nce
acce
lera
tion
due
togr
avit
y?
Obj
ects
fall
atdi
ffer
ent
rate
sbe
caus
eof
air
resi
stan
ce,
afr
ictio
n-lik
efo
rce.
Inth
eab
senc
eof
air
resi
stan
ce,
all
obje
cts,
rega
rdle
ssof
thei
rw
eigh
t,fa
llw
ithth
esa
me
cons
tant
acce
lera
tion
of9.
8m
/s2
dow
nwar
d.T
his
isac
cele
rati
ondu
eto
grav
ityCs
).In
man
ysi
tuat
ions
,th
eai
rre
sist
ance
actin
gon
afa
lling
obje
ctis
sosm
all
that
we
can
assu
me
the
obje
ctha
sa
cons
tant
acce
lera
tion
of—
9.8m
/s2,
whe
reup
isp
osi
tiv
e.
Nam
eD
ate
Cal
cula
ting
Acc
eler
atio
n
How
doyo
uth
ink
ave
loci
ty-t
ime
grap
hm
ight
diff
erfr
omth
epo
sitio
n-tim
egr
aph
you
lear
ned
abou
tin
the
prev
ious
chap
ter?
Wri
teyo
uran
swer
onth
elin
esbe
low
.
How
isac
cele
rati
on
calc
ula
ted
wit
hout
usin
ga
velo
city
-tim
egr
aph?
Dra
wa
Gra
ph
Draw
ave
loci
ty-ti
me
grap
hfo
ran
obje
ctex
perie
ncin
gpo
sitiv
e,ze
ro,a
ndne
gativ
eac
cele
ratio
n.
0R
eadi
ngC
heck
1.W
rite
the
equa
tion
tnac
cele
ratio
n.
t C >
Rea
ding
Che
ck
2.W
hat i
sth
eva
lue
ofac
cele
ratio
ndu
eto
grav
ityon
Earth
?
170
MH
R•
Sec
tion
9.2
Cal
cula
ting
Acc
eler
atio
n02008
F4cG
raw
-HiII
Ryo
rson
Um
Ced
©20
08M
cOra
WH
iUR
yers
cnL
imite
dS
ecti
on
92
Cal
cula
ting
Acc
eler
atio
n•
MH
R17
1
Page 13
Nam
e:__
____
____
____
____
____
__B
lock
:___
___
Dat
e:__
____
____
___
Scie
nce
10C
h.9.
2—D
escr
ibin
2M
otio
nA
ssig
nmen
t
Posi
tion
vs
Tim
e
30
25
120
02
46
8T
ime
(5)
The
slop
eof
the
line
is2.
5m
is.
Sinc
eth
esl
ope
isco
nsta
nt,t
heco
rres
pond
ing
velo
city
time
grap
h
wou
ldbe
aho
rizo
ntal
line
draw
nat
2.5
m/s
.
Vel
oci
tyvs
Tim
e t-0
24
Tim
e(s
)8
10
1.D
escr
ibe
the
mot
ion
ofth
efo
llow
ing
velo
city
-tim
egr
aphs
.Inc
lude
the
dire
ctio
nof
trav
el,
whe
ther
the
obje
ctis
acce
lera
ting
orde
cele
ratin
g,an
dan
ytim
esw
here
the
obje
ctst
ops
mov
ing
alto
geth
er.
a.Sl
opes
:0-
4s:
Vel
ocity
vsT
ime
b.V
eioci
tyvs
Tim
eSl
opes
:I
0-2s
:
-
12
;--
;--
-6-
lOs:
Tim
e(s)
d.Sl
ope:
0-lO
s:
Exa
mpl
e1:
The
follo
win
gpo
sitio
ntim
egr
aph
show
san
obje
cttr
avel
ling
wit
hun
ifor
mm
otio
n,
10
c.V
elo
city
vs
Tim
eSl
opes
:
I4
:6::
0!
IN8
10
6-8s
:
Tim
e(s)
S—lO
s:
HT
ime(
s)
t4
68
10
Tim
eis
)
Page 14
ApplyingName Date Knowledge
Use with textbook pages 396—400.
Colculafing acceleration1. What is the formula for each of the following quantities?
(a) acceleration (b) change in velocity (c) time interval
2. Complete the following table. Use the motion formula to calculate the missing
quantities. Show all your work and use the correct units.
Change in Time Acceleration Formula Used andVelocity Calculation Shown140 rn/s 8s 17.5 rn/s2
t 8
—60km/h 4hV
120 km/h 48 km/h2
15s —3.5 rn/s2V 12m/s 2.5s
—25 m/s —1 2.5 rn/s2
• 9.6 h 5 km/h2
3. Solve each problem using the appropriate motion formula. Show all your work anduse the correct units.
a) A car moving north goes from 5.56 rn/s to 63.9 rn/s in 7.5 s. What is theacceleration?
b) If a sprinter starts a race and has an acceleration of 2.4 m/s2 in 2.5 s, what is hisfinal velocity, assuming the initial velocity is 0 m/s2?
c) A rock accelerates at —9.8 rn/s2 when falling. How long does it take to change itsvelocity from —4.5 rn/s to —19.4 m/s?
d) A satellite released from a stationary space shuttle accelerates to +68 rn/s2 in25 s. What is its change in velocity?
172 MHR • Section 9.2 Calculating Acceleration © 2008 McGraw-Hill Ryerson Limited
2cL..
Page 15
NA
Ma
04
1012
Tim
e(s)
2.C
ompl
ete
the
foll
owin
gta
ble
.D
escr
ibe
the
slop
e,ac
cele
rati
on,
and
velo
city
ofth
eba
ll(e
.g.
posi
tive
,ne
gati
ve,
orze
ro).
MOT
ION
OFA
BALL
Tim
eIn
terv
alSl
ope
Acc
eler
atio
nV
eloc
ity
Os—
2s2s
—6s
6s-8
s
8s—
12s
3.D
escr
ibe
the
mot
ion
ofth
eba
llat
each
tim
ein
terv
al.
(a)
0s
—2
s
____
____
____
____
____
____
____
____
__
Goa
l•
Rev
iew
your
unde
rsta
ndin
gof
term
sth
atde
scri
bem
otio
n.
Mat
chea
chst
atem
ento
nth
ele
ftw
ithth
eco
rrec
tter
mon
the
righ
t.W
rite
the
term
’sle
tteri
nth
eap
prop
riat
esp
ace.
You
will
notn
eed
tous
eev
ery
term
.
1.—
mot
ion
with
noch
ange
insp
eed
ordi
rect
ion
2.—
aph
ysic
alqu
antit
yth
atha
sm
agni
tude
but n
odi
rect
ion
3.de
scri
bes
how
muc
han
obje
ct’s
posi
tion
has
chan
ged
4.th
eto
tall
engt
hof
ajo
urne
yth
atan
obje
ctta
kes
5.—
desc
ribe
sho
wfa
stan
obje
ctis
mov
ing,
but n
otits
dire
ctio
n6.
diff
eren
cebe
twee
nin
itial
time
and
final
time
7.—
the
loca
tion
ofan
obje
ctas
seen
byan
obse
rver
8.qu
antit
yw
ithbo
thm
agni
tude
and
dire
ctio
n
9.fr
ictio
n-lik
efo
rce
10.
9.8
m/s
3
11.—
can
bea
smoo
thcu
rve
orsc
raig
htlin
e
12.
allo
ws
usto
pict
ure
orvi
sual
ize
mot
ion
13.—
desc
ribe
sth
esp
eed
and
dire
ctio
nof
mot
ion
14.—
occu
rsw
hen
the
spee
dof
anob
ject
chan
ges,
orits
dire
ctio
nof
mot
ion
chan
ges,
orbo
th
15.—
acce
lera
tion
that
isop
posi
teto
the
dire
ctio
nof
mot
ion
16.—
the
chan
gein
anob
ject
’sve
loci
ty(i
ncre
ase
orde
crea
se)
ina
give
npe
riod
oftim
e
17.—
rate
ofch
ange
inpo
sitio
nfo
ra
time
inte
rval
18.
whe
nan
even
tocc
urs
19.
the
rise
ofa
grap
hov
erits
run
20.—
repr
esen
ted
byth
esl
ope
ona
velo
city
-tim
egr
aph
(b)
2s
—6
5—
(c)6
s—8s_
(d)
8s
—12
S.
0zo
stMG,
,,-HA
IL
Anh
d.cm
,.55
dgbe
m.yhe.
9dd
f,edem
ae
by
dp
pebA
,k.
Use
with
text
book
page
s39
4-39
6.
CH
APT
ER
9M
otio
nM
atch
-up
I’l!
,I’3
I3I
Anal
yzi
ng
vel
oci
ty-t
ime
gra
phs
1.W
hat
isth
em
eani
ngof
each
ofth
efo
llow
ing
feat
ure
sof
ave
loci
ty-t
ime
grap
h?
(a)
the
slope
ofth
elin
e
____
____
____
____
____
____
____
____
____
_
(b)
alin
eab
ove
the
x-ax
is
____
____
____
____
____
____
____
____
____
_
(c)
alin
ebe
low
the
x-ax
is
____
____
____
____
____
____
____
____
____
_
(d)
alin
ew
ith
apo
siti
vesl
op
e
____________
(e)
alin
ew
itha
nega
tive
slo
pe
(ia
hori
zont
alse
ctio
nof
the
gra
ph
(g)
apo
int
whe
reth
elin
ecr
oss
esth
ex-
axis
____
____
____
____
____
____
____
____
__
Use
the
foll
owin
gve
loci
ty-t
ime
gra
ph
repr
esen
ting
the
mot
ion
ofa
ball
mov
ing
toth
eri
gh
ton
ata
ble
toan
swer
ques
tion
s2
and
3.
n4 >1
A.
acce
lera
tion
B.
acce
lera
tion
due
togr
avity
C.
air
resi
stan
ceD
.av
erag
eac
cele
ratio
nE
.av
erag
eve
loci
tyF.
best
-fit
line
G.
chan
gein
velo
city
H.
cons
tant
acce
lera
tion
Lde
cele
ratio
n
J.di
stan
ceK
.gr
avity
Lve
loci
tyM
.uni
form
N.
mot
ion
diag
ram
0.
posi
tion
P.
posi
tion-
time
grap
h
Q.t
ime
R.
time
inte
rval
S.sc
alar
T.
spee
dU
.sl
ope
V.
disp
lace
men
tW
.vec
tor
X.
velo
city
-tim
egr
aph
@20
08M
cGra
w-H
illR
yers
onU
nite
dS
ecti
on
9.2
Cal
cula
ting
Acc
eler
atio
n•
MI-
IR17
3
Page 18
II.ç=
45km
lhjn
orth
l;c=6
Okn
vb(n
orth
l
Ill.i=
15rn
/s[ri
ghtj;
i=10
rn/s
pefti
I.W
hen
anob
ject’s
spee
dis
cons
tant
, the
obje
ctha
sze
roac
cele
ratio
n.
II.W
hen
anob
ject
’ssp
eed
isin
crea
sing,
the
obje
ctha
sa
posit
ive
acce
lera
tion,
Ill.W
hen
anob
ject
’ssp
eed
isde
crea
sing,
the
obje
ctha
sa
nega
tive
acce
lera
tion.
Use
the
foll
owin
gve
loci
ty-t
ime
grap
hto
answ
erqu
esti
on7.
4....
..
Tim
e(s
)
7.W
hich
line
repre
sents
anob
ject
with
the
gre
ates
tac
cele
rati
on?
B.B c.C
D.l
)
Use
the
foll
owin
gve
loci
ty-t
ime
grap
hto
answ
erqu
esti
on8.
Tim
e(s
)
8.W
hat
isth
eob
ject
’sac
cele
rati
onbe
twee
nth
eti
me
inte
rval
2s
and
4s?
A.-
j-lr
n/s
2 B.+1
0in
/s2
C.+2
0rn
/s2
D.+4
0ni/
s2
Use
with
text
book
page
s38
2—38
6.
Des
crib
ing
acce
lera
tio
nC.
the
obje
ctre
mai
nsat
rest
Nam
e
Mat
chth
eTe
rmon
the
left
with
the
best
Des
crip
tor
onth
eri
ght.E
ach
Des
crip
tor
may
beus
edon
lyon
ce.
Dat
esm
eJ
Use
with
text
book
page
s39
2-40
0.
Cal
cula
ting
acce
lera
tio
nM
atch
the
Des
crip
tor
onth
ele
ftw
ithth
ebe
stV
eloc
ity-T
ime
Gra
phon
the
righ
tTh
eV
eloc
ity-
lim
eG
raph
sre
pres
ent t
hem
otio
nof
aca
rhea
din
gno
rth.E
ach
Vel
ocity
-Tim
eG
raph
may
beus
edon
lyon
ce.
1._
acce
lera
tion
A.r
ate
atwh
ichan
obje
ct2.
dece
lera
tion
chan
ges
itsve
locit
y3.
cons
tant
velo
city
B.an
obje
cttra
velli
ng4.
chan
geIn
with
unifo
rmm
otio
nin
velo
city
astr
aigh
tline
C.ac
cele
ratio
nin
adi
rect
ion
that
isop
posit
eto
the
dire
ction
ofec
tico
D.ch
ange
that
occu
rsw
hen
the
spee
dof
anob
ject
chan
ges,
orits
dire
ction
ofm
otio
nch
ange
s,or
both
I,=
3.5m
/s[e
ast]
;=7.
5rnl
s[ea
st}
1.Th
eca
rIs
stopp
ed.
2..._
......
.The
car i
sac
cele
ratin
g.3.
The
car i
sslo
wing
down
.4.
The
cari
stra
velli
ngat
cons
tant
velo
city.
D.no
thin
gha
ppen
sto
the
obje
ct
7.Su
ppos
ean
obje
ctm
ovin
gfo
rwar
dch
ange
sits
velo
city
from
15rn
/sto
6m
/s.W
hat i
sth
ech
ange
inve
loci
ty?
A.—
21m
/s
B.—
9rn/
s
C.9
rn/s
D.2
1rn/
s
8.W
hich
ofth
efo
llow
ing
have
anac
cele
ratio
nin
the
sam
edi
rect
ion
asth
eob
ject
’sm
otio
n?
A.I
andll
on.l
y
B.I
andll
lonly
C.f
landli
lonly
D.I
,II,
and
ffl
9.W
hich
ofth
efo
llow
ing
are
true
abou
tac
celis
ratio
n?
A.I
andfl
on
ly
D.I
,IJ,
andff
l
The
Is) N
C.
lime
(ci
0.
a.
rena
Is
Cir
cle
the
lett
erof
the
bes
tan
swer
.
5.T
heto
rtoi
sem
oved
slow
lyan
dst
eadi
ly.
The
hare
ran
quic
lcly
,th
enfe
llas
leep
near
the
fini
shlin
e.Id
enti
fyth
efo
llow
ing
quan
titie
sas
scal
aror
vect
or,
resp
ectiv
ely:
the
aver
age
velo
city
ofth
eto
rtoi
sedu
ring
the
entir
era
ce,
the
acce
lera
tion
ofth
eha
redu
ring
the
firs
t2
min
utes
ofth
era
cean
dth
etim
eit
take
sfo
rth
eto
rtoi
sean
dth
eha
reto
fini
shth
era
ce.
A.
vect
or,
vect
or,
scal
ar
B.sc
alar
,sc
alar
,ve
ctor
C.ve
ctor
,sc
alar
,ve
ctor
0.sc
alar
,ve
ctor
,sc
alar
6.If
the
acce
lera
tion
ofan
obje
ctis
inth
eop
posi
tedi
rect
ion
asth
eve
loci
ty,
whi
chof
the
follo
win
gha
ppen
s?
)A.
the
obje
ctsp
eeds
up
B.th
eob
ject
slow
sdo
wn
B.la
ndif
ion
ly
C.R
and
III
only
5.A
ccel
erat
ion
isre
pres
ente
dby
the
slop
eof
a
A.
velo
city
-tim
egr
aph
B.po
sitio
n-tim
egr
aph
C.di
stan
ce-t
ime
grap
h
D.ac
cele
ratio
n-tim
egr
aph
6.A
met
eor
goes
from
+1.0
kin/
sto
÷2.2
km/s
in0.
04s.
Wha
t is
itsac
cele
ratio
n?
A.0.
031c
m/s
2
B.3
0k
m/s
2
C.55
km
/s2
D.8
0k
m/s
2
©20
08M
cGra
w-H
illR
yecs
onL
imite
dS
ecti
on9.
1D
escr
ibin
gA
ccel
erat
ion
•M
HR
169
176
MH
R•
Sect
ion
9.2
Cal
cula
tin
gA
ccel
erat
ion
©20
08M
cGra
w-H
HIR
ye,s
onLi
mite
d
Page 19
Physi
csU
nit(r
no
çoc.
Ao
ua()
1.(a
)A
car
mov
esea
stal
ong
ahi
ghw
ayat
90.0
krnl
hfo
rI
han
d15
mm
.Wha
tis
the
car’
sdi
spla
cem
ent?
(b)
How
long
will
itta
kefo
ra
pers
onw
alki
ngat
3.8
rn/s
nort
hto
mov
e12
5m
?
2.A
car
star
tsfr
omre
stan
dac
cele
rate
sat
ast
eady
rate
,re
achi
nga
fina
lve
loci
tyof
24.0
rn/s
in1
2s.
(a)
Cal
cula
teth
eac
cele
rati
onof
the
car.
(b)
Cal
cula
teth
eav
erag
eve
loci
tyof
the
car.
6.H
owm
any
seco
nds
will
itta
kea
spee
dboa
ttr
avel
ling
at70
.0km
/h[S
]to
cove
ra
dist
ance
of5.
0km
?
7.D
onov
anB
aile
yse
tthe
wor
ldin
door
trac
kre
cord
in19
96by
runn
ing
forw
ard
50m
inju
st5.
56s.
Wha
t was
Bai
ley’
sav
erag
eve
loci
ty?
8.A
boat
trav
els
acro
ssa
450
mla
kew
ithan
aver
age
forw
ard
velo
city
of5.
0rn
/s.
How
muc
htim
edo
esit
take
for
this
boat
tocr
oss
the
lake
?
9.T
hem
otio
nof
anel
evat
oris
repr
esen
ted
byth
epo
sitio
n-tim
egr
aph
belo
w.
Des
crib
e,us
ing
wor
ds,
the
mot
ion
ofth
eel
evat
ordu
ring
the
30s
time
inte
rval
.
0-l
os:
10-2
0s:
20-3
0s:
Posi
tion
vs.T
ime
(c)
Wha
tis
the
tota
ldi
spla
cem
ent
ofth
eca
r?
3.A
sing
le-e
ngin
eai
rpla
nele
aves
anai
rpor
tan
dfl
ies
toan
othe
rai
rpor
t85
0km
nort
h.It
take
s4.
0h
toco
mpl
ete
the
flig
htW
hat
isth
eve
loci
tyof
the
airp
lane
?
4.A
truc
ktr
avel
sfr
omC
ityA
due
wes
tto
City
B,a
dist
ance
of21
0km
.T
heto
tal
tim
efo
rth
etr
ipis
two
hour
san
dfi
ftee
nm
inut
es.
Wha
tis
the
aver
age
velo
city
ofth
etr
uck?
5.A
bus
trav
els
from
City
Xdu
eea
stto
war
dC
ityY
.If
the
bus
trav
els
atan
aver
age
velo
city
of90
km/h
[Ej,
wha
t will
beth
edi
spla
cem
ent
ofth
ebu
s4.
5h
late
r?
..:
L.
::7..
-
-4E
i-4
-•.
--
-.-
-
------
7.
.-
-_
4../..
..
‘-
-
--
-.
--
:1:-
:sL: :
:i
,.
20
...
-
10. A
syo
uap
proa
cha
tow
nw
hile
you
are
driv
ing,
you
take
your
foot
off t
heac
cele
rato
r.T
heca
rsl
ows
dow
nfr
om90
km/h
[S]
to50
km/h
[S)
in8.
0s.
Wha
tis
the
acce
lera
tion
ofth
eca
r?
11.
Aro
ckfa
llsfr
omth
eto
pof
ahi
ghcl
iff.
How
long
wou
ldit
take
this
rock
tore
ach
ave
loci
tyof
25rn
/sdo
wnw
ard?
(Hin
t:ac
cele
rati
ondu
eto
grav
ityis
9.8
m/s
2do
wn)
Page 20
Ph ictr t 0 q i ‘419__‘-_-?-- LI I*-) zq -‘i-—j
3,31
z’o
