Velocity
Answers
1.
Name
md velocrty do not ha!e the sme meaning to scientists. Spee,l ts a sutltr tluun /irf. wfilcll mcans it can be completely described
byitsmagnitude(orsize)'Ih€lnagnitudeisgiuenbyanunrberandaunit
Forcxample.anoblecr'sspeedmaybemeasuredasl5
meteLs pet second
Speed
An airplane llies 525 kilorneters north in 1.25 hours. what is lhe airplane's vetocit-v?
i.ooLrngror
l_\"f!uqitf
Given rl=525
Krn \OR
---
l'll: t = 1,25 h
;;; ait -- r,__-..-,-_.-____:-.,--
--
I sorution
. S25 Knr \()R t rr/ t.ZS h
I * 42t) Klt/h NOIII H
I
r-L
rcclor r/uqt1li\ ln arder lo measure a lecior quantity, you must know the both its rnagnitude and tiirection. I he velocity
object is detetrnined by nrasuring both the speed and ditec'li(r? in which an object is traveling.
Velocity is
a
ofe
. tfthe speed ofm
2.
object chuges, thcn its relocity also chmges.
.
tfthe direction
r
A chmete in either speed, direction, or both causes a oharge in relocity
in rthich
3.
l:
What is the velocity of
a
I
A cruise ship travels
south
I
car that travels 100.0 meters. northeast it) 4.65 seconds?
ihisclistanceif i ts
0.305
east across a river at 19.0 meters per minute.
Iong does it take for the ship to reach rhe other
4
I
Asoccerplayerkicksaball 6.5meters. I{owmuchtinreisneededtbrtheballtotravel
velocity is 22 meters per second,
m object is lraaelin!! changes, thcn its velocity changes
You can use r r/ I to solte velocity problems in the same moner that you changed the fo.m ofthe equation to solve speed problems
in I'art A. The boldfaced v is rned to represant \elocity as a vector quantity. l he la'iables d and t re ured for distuce ad time. The
velocitJ- ofen object ir motion is equal to the dirtanc€ it tr&vels per unit oltine in e givetr dircction.
Iixample
Reratioushif
side? 223.68
lfthe river
m
is 4,250 tneters lvide, hoiv
in
Joaquin mows the lawn at his grandmother's home duriog the summer months. Joaquin measured the
distance across his grandmother's lawn as I 1..5 meters
a
lf.Ioaquinmolvsonelengthacrosslhelawnt'romeasttowestinT.l0seconds,thenwhatislhevelocitv
of the
lawnrnorver? 1.62 m/s WEST
ofthe lawn, Joaquin turns the larvnmower around. [{e morvs in the opposite
direction but maintains the same speed. what is the velocity of the lawnmower'.) I .62 m/s EAST
b. Once he reaches the edge
A family drives
88 1 miles from floustoo. T ex&s to Santa Fe. Nerv Mexico for vacation. How Iong will
take lhe farnily to reach their destiuation ifthey travel at a velocit-v of55.0 miles per hour, northwesl?
it
16.02 h
A shopping cart is pushed I 5.6
shopping
7.
Exnmple 2: A boat travels witb a velocity equal to I 4.0 meters per second,
in meters does the boat travel?
east
in
5. I
What is the vetocity of rhe tennis
b. lfthe tennls ball travels
l,ooking for
distrmci
'I'ime
'.
5.
14.0 meters per second. east
l5
seconds
distance
Rclationshlp
4.52rn/s SOUTH
at constant speed, what is its velocity when l.iam retums Katie's serve? 4.S2ru/s
A driver
realizes lhat she is traveling in the wrong direction on a one-rvay street. She has already driven 3.5
meters at a velocity of I 6 meters per second. east before deoiding to make a lJ-turn. How long did it take fbr
14!m x5.15s=?31m
= v x, -
the driver to realize her
Given
.=
balt?
]\OR"TH
Solution
Distance the boat travels
Velocity
ofthe
Katie and her best friend l,iam play tennis every Saturday nrorning. When Katie serves the ball to Lialn, it
travels 9.5 lneters south in 2. I seconds.
a.
5 seconds, What distance
meters west across a parking lo1 in 5.2 seconds. What is the velocilv
cart? 3 m/s WEST
'l'he boat travels 72. I meters.
error? 0.22
S
'luan's ntother drives I 2.5 miles southwest 10 her favorite shopping mall. What is the velocity ol her
automobile if she anives at lhe mall in 7.25 minutes? 1.72 mil rnin SW
l0Abusistravelingat79.7kilonrelersperhoureast,howt'ardoesthebustravel
= vx!
1
I
l. A girl
scout troop hiked 5.8 kilometers southeast
in l.-i hours. What
L4.5hours?
I15.57Km
ivas the troop's velocity'l J,87Km/h SIi
2. A volcanologisl noted that a lahar rushed dorvn a mountain at 32.2 kilometers per hour, south. IIow far did
the mud l]ow in 17.5 minutes? 9.39 Km
Acceleration Worksheet.
a highway a driver slorvs liom ?4 m/s to 15 m/s in l2 seconds. \\'hat is tlle automohile's
acceleration? (Reurembcr that a negative value indicates a slowing down tr deceleration.)
\Vhile traveling aloug
Name:
Date:
-0.75m/s/s
14.2 Acceleration
A parachute
Acceleration is the rate ofchange in the speed ofan object.'l'o detennine the rale oFacceleration, you use the
formula below. 'Ihe units lirr acceleration are metels per second pet secontl or m,/s2.
Arcel':ration
-
o1l fl
raciilg dragster opens and changes tlre speed ofthe car frorn 85 m,/s tal 45 m/s in a period 0f4.5
seconds. What is the acceleratiorl ofthe
dragster? -tt.9 m/slS
The table belo\ry includes data lbr a ball rolling down a trill, Fill in the lnissing data values in the tablc aud delentrire
the acceleratioo ofthe rolling ball.
Final speed-Beginning speed
Time
11-Yr
A positive value for acceleration
sltorvs speeding up, and negalive value fbr acceleration shorvs slowing down
Slowing down is also called deceleration.
I'he acceleration tbnnula oan be rearranged to solve for other variables such
..
as
linal speed (v:) and time (/).
l/-v.1
-..
)r-llr
a
Acceleralion
EXAMPLf,S
L
Askaterincreaseshervelocityfiom2.0misto10.0m/sin3.0seconds.Whatistheskater'sacceleration?
Solution
lf'a car can
l
l
were 50
l
..
Arcetefallon
100m,'s-20rn./s
= 2!n'.is.
?s
'fhe acceleration ofthe
skater is 2.7 meters pel second
l!!llc9-'r-]:ll.. :ls"ggltgj
] ttetationship
A
ir
complete stop. l{ow much time will it
8.0 seconds, what tvould be its final speed afrer 5.0 seconds
cart rolling dowr an incline for 5.0 secr:nds has an acceleration of4.0 nr/s2.
ilits
starting speed
Ifthe
of2.0
cart has a beginning speeii
22 m/s
A helicoptel"s speed increases lronr 25
I
m1s
to 60 n/s in 5 seconds. What is the acceleration ofthis helicopter? 7
mlsl$
l
Assheciimbsahill.aLJ,clistslowsdownfronr25ni/hrto6miflrrinl0seconds.Whatisherdeceleration?
I
A car accelerates itt a rate o[3.0 m/s2.
to reach a final speed oi25.0 rnJs?
go fronl 0 t0 60 mi/lu
a
I
I
v2*Yt
2.
"--_ ,__-
rni/lrr? {i7.5 milh
m/s, what is its t'inal speedt
I
per second.
-!-5 nlsls
A car traveling ai a speed o{'30.0 l,r/s encouilters an energencv and oonres to
take for the car to stop ifil decelerates at -4.0 trl/s';? 7.5$
lfits original
speed is 8.0 m/s, how many secorrtls
will it tale
the car
A motorcycle traveling at 25
nrotorcycle?
Solution
-lrmi=-=)ir:5Dm/s-80m./s
3 0 m!s"
-l'he
time lor the car to reach its tinal speed is 5.7
*1.9
mi/h/s
l0 A car starting from
rn,is accelerates at a rate
of7.0 m/s: Iix 6.0 seconds. what is the final speetl ofthe
67 m/s
rest accelerates at a rate of8.0 m,/s/s. Whot is its tlnal speed at the end of4.0
seconds? 32
mls
II
After traveling for 6.0 seconds,
a
nrnner reaches a speed of l0 m/s. What is the runner's
acceleration?
1.61
m/s/s
seconds
t2. A cvclist accelerates at
13.
a
rate
of7.0
rn,/s2.
How long will it teke the cyclist kr reach a speetl of 18
A skateboarder traveling at 7.0 lneters per second rolls to
skateboardor'sacceleration? -2.33 m/s/s
a stop at the
mis?
2.57
top ofa raulp in 3.0 seconds. Whal ,s tl)e