PHY111–Chapter2–Problems–MotioninOneDimension
1.Thespeedofanerveimpulseinthehumanbodyisabout100m/s.Ifyouaccidentallystubyourtoeinthedark,
estimatethetimeittakesthenerveimpulsetotraveltoyourbrain.
3.Apersontravelsbycarfromonecitytoanotherwithdifferentconstantspeedsbetweenpairsofcities.Shedrives
for30.0minat80km/hr,12.0minat100km/hr,and45.0minat40.0km/hrandspends15.0minuteseatinglunch
andbuyinggas.(a)Determinetheaveragespeedforthetrip.(b)Determinethedistancebetweentheinitialandfinal
citiesalongtheroute.
5.Twoboatsstarttogetherandraceacrossa60-km-widelakeandback.BoatAgoesacrossat60km/hr.BoatB
goesacrossat30km/hr,anditscrew,realizinghowfarbehinditisgetting,returnsat90km/hr.Turnaroundtimes
arenegligible,andtheboatthatcompletestheroundtripfirstwins.(a)Whichboatwinsandbywhatdistance?(Oris
itatie?)(b)Whatistheaveragevelocityofthewinningboat?
6.Agraphofpositionversustimeforacertainparticlemovingalongthex-axisisshownbelow.Findtheaverage
velocityinthetimeintervalsfrom(a)0to2.00s,(b)0to4.00s,(c)2.00sto4.00s,(d)4.00to7.00s,and(e)0to8.00
s.
7.Amotoristdrivesnorthfor35.0minutesat85.0km/hrandthenstopsfor15.0minutes.Hethencontinuesnorth,
traveling130kmin2.00hours.(a)Whatishistotaldisplacement?(b)Whatishisaveragevelocity?
9.Ajetplanehasatakeoffspeedof75m/sandcanmovealongtherunwayatanaverageaccelerationof1.3m/s2.If
thelengthoftherunwayis2.5km,willtheplanebeabletousethisrunwaysafely?Defendyouranswer.
11.Thecheetahcanreachatopspeedof114km/hr(71mi/hr).Whilechasingitspreyinashortsprint,acheetah
starts from rest and runs 45 m in a straight line, reaching a final speed of 72 km/hr. (a) Determine the cheetah’s
averageaccelerationduringtheshortsprint,and(b)finditsdisplacementatt=3.5s.
17. A graph of position versus time for a certain particle moving along the x-axis is shown below. Find the
instantaneousvelocityattheinstants(a)t=1.00s,(b)t=3.00s,(c)t=4.50s,and(d)t=7.50s.
19. Runner A is initially 4.0 mi west of a flagpole and is running with a constant velocity of 6.0 mi/hr due east.
RunnerBisinitially3.0mieastoftheflagpoleandisrunningwithaconstantvelocityof5.0mi/hrduewest.Howfar
aretherunnersfromtheflagpolewhentheymeet?
21.A50.g-gSuperBalltravelingat25.0m/sbouncesoffabrickwallandreboundsat22.0m/s.Ahigh-speedcamera
recordsthisevent.Iftheballisincontactwiththewallfor3.50ms,whatisthemagnitudeoftheaverageacceleration
oftheballduringthistimeinterval?
23.Acertaincariscapableofacceleratingatarateof0.60m/s2.Howlongdoesittakeforthiscartogofromaspeed
of55mi/hrtoaspeedof60mi/hr?
24. The velocity vs. time graph for an object moving along a straight path is shown below. (i) Find the average
acceleration of the object during the time intervals (a) 0 to 5.0 s, (b) 5.0 s to 15 s, and (c) 0 to 20 s. (ii) Find the
instantaneousaccelerationat(a)2.0s,(b)10s,and(c)18s.
25.Asteamcatapultlaunchesajetaircraftfromanaircraftcarrier,givingitaspeedof175mi/hrin2.50s.(a)Find
theaverageaccelerationoftheplane.(b)Assumingtheaccelerationisconstant,findthedistancetheplanemoves.
27. An object moving with uniform acceleration has a velocity of 12.0 cm/s in the positive x-direction when its xcoordinateis3.00cm.Ifitsx-coordinate2.00slateris–5.00cm,whatisitsacceleration?
29.Atruckcovers40.0min8.50swhileuniformlyslowingdowntoafinalvelocityof2.80m/s.(a)Findthetruck’s
originalspeed.(b)Finditsacceleration.
31. A Cessna aircraft has a liftoff speed of 120 km/hr. (a) What minimum constant acceleration does the aircraft
requireifitistobeairborneafteratakeoffrunof240m?(b)Howlongdoesittaketheaircrafttobecomeairborne?
36.Arecordoftravelalongastraightpathisasfollows:
(i)Startfromrestwithaconstantaccelerationof2.77m/s2for15.0s.
(ii)Maintainaconstantvelocityforthenext2.05minutes.
(iii)Applyaconstantnegativeaccelerationof–9.47m/s2for4.39s.
(a) Whatwasthetotaldisplacementforthetrip?(b)Whatweretheaveragespeedsforlegs1,2,and3ofthetrip,aswell
asforthecompletetrip?
37. A train is traveling down a straight track at 20 m/s when the engineer applies the brakes, resulting in an
accelerationof-1.0m/s2aslongasthetrainisinmotion.Howfardoesthetrainmoveduringa40-stimeinterval
startingattheinstantthebrakesareapplied?
39.Acarstartsfromrestandtravelsfor5.0swithauniformaccelerationof1.5m/s2.Thedriverthenappliesthe
brakes,causingauniformaccelerationof-2.0m/s2.Ifthebrakesareappliedfor3.0s,(a)howfastisthecargoingat
theendofthebrakingperiod,and(b)howfarhasthecargone?
41. In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a
straightaway at 71.5 m/s. The driver of the Thunderbird realizes that she must make a pit stop, and she smoothly
slowstoastopoveradistanceof250m.Shespends5.00sinthepitandthenacceleratesout,reachingherprevious
speedof71.5m/safteradistanceof350m.Atthispoint,howfarhastheThunderbirdfallenbehindtheMercedes
Benz,whichhascontinuedataconstantspeed?
45.Aballisthrownverticallyupwardwithaspeedof25.0m/s.(a)Howhighdoesitrise?(b)Howlongdoesittake
to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d)
Whatisitsvelocitywhenitreturnstothelevelfromwhichitstarted?
46.Aballisthrowndirectlydownwardwithaninitialspeedof8.00m/s,fromaheightof30.0m.Afterwhattime
intervaldoesitstriketheground?
47.Acertainfreelyfallingobject,releasedfromrest,requires1.50stotravelthelast30.0mbeforeithitstheground.
(a)Findthevelocityoftheobjectwhenitis30.0mabovetheground.(b)Findthetotaldistancetheobjecttravels
duringthefall.
49. Traumatic brain injury such as a concussion results when the head undergoes a very large acceleration.
Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an
accelerationgreaterthan1,000m/s2lastingforatleast1mswillcauseinjury.Supposeasmallchildrollsoffabed
thatis0.40mabovethefloor.Ifthefloorishardwood,thechild’sheadisbroughttorestinapproximately2.0mm.If
theflooriscarpeted,thisstoppingdistanceisincreasedtoabout1.0cm.Calculatethemagnitudeanddurationofthe
decelerationinbothcases,todeterminetheriskofinjury.Assumethechildremainshorizontalduringthefalltothe
floor.Notethatamorecomplicatedfallcouldresultinaheadvelocitygreaterorlessthanthespeedyoucalculate.
50.Asmallmailbagisreleasedfromahelicopterthatisdescendingsteadilyat1.50m/s.After2.00s,(a)whatisthe
speedofthemailbag,and(b)howfarisitbelowthehelicopter?(c)Whatareyouranswerstoparts(a)and(b)ifthe
helicopterisrisingsteadilyat1.50m/s?
51.Atennisplayertossesatennisballstraightupandthencatchesitafter2.00satthesameheightasthepointof
release.(a)Whatistheaccelerationoftheballwhileitisinflight?(b)Whatisthevelocityoftheballwhenitreaches
itsmaximumheight?Find(c)theinitialvelocityoftheballand(d)themaximumheightitreaches.
53. A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant
upwardaccelerationof2.00m/s2untilitsenginesstopatanaltitudeof150m.(a)Whatcanyousayaboutthemotion
oftherocketafteritsenginesstop?(b)Whatisthemaximumheightreachedbytherocket?(c)Howlongafterliftoff
doestherocketreachitsmaximumheight?(d)Howlongistherocketintheair?
56. ColonelJohnP.Stapp,USAF,participatedinstudyingwhetherajet pilot could survive emergency ejection. On
March19,1954,herodearocket-propelledsledthatmoveddownatrackataspeedof632mi/hr.Heandthesled
weresafelybroughttorestin1.40s.DetermineinSIunits(a)thenegativeaccelerationheexperiencedand(b)the
distancehetraveledduringthisnegativeacceleration.
57.Abulletisfiredthroughaboard10.0cmthickinsuchawaythatthebullet’slineofmotionisperpendiculartothe
faceoftheboard.Iftheinitialspeedofthebulletis400m/sanditemergesfromtheothersideoftheboardwitha
speedof300m/s,find(a)theaccelerationofthebulletasitpassesthroughtheboardand(b)thetotaltimethebullet
isincontactwiththeboard.
59.Astudentthrowsasetofkeysverticallyupwardtohisfraternitybrother,whoisinawindow4.00mabove.The
brother’soutstretchedhandcatchesthekeys1.50slater.(a)Withwhatinitialvelocitywerethekeysthrown?(b)
Whatwasthevelocityofthekeysjustbeforetheywerecaught?
62.Drawmotiondiagramsfor(a)anobjectmovingtotherightatconstantspeed,(b)anobjectmovingtotheright
andspeedingupataconstantrate,(c)anobjectmovingtotherightandslowingdownataconstantrate,(d)anobject
moving to the left and speeding up at a constant rate, and (e) an object moving to the left and slowing down at a
constantrate.(f)Howwouldyourdrawingchangeifthechangesinspeedwerenotuniform,thatis,ifthespeedwere
notchangingataconstantrate?
63. A ball is thrown upward from the ground with an initial speed of 25 m/s. At the same instant, another ball is
droppedfromabuilding15mhigh.Afterhowlongwilltheballsbeatthesameheight?
64.Topassaphysicaleducationclassatauniversity,astudentmustrun1.0miin12min.Afterrunningfor1min,
shestillhas500ydtogo.Ifhermaximumaccelerationis0.15m/s2,canshemakeit?Iftheanswerisno,determine
whataccelerationshewouldneedtobesuccessful.
68.Thedriverofatruckslamsonthebrakeswhenheseesatreeblockingtheroad.Thetruckslowsdownuniformly
withanaccelerationof–5.60m/s2for4.20s,makingskidmarks62.4mlongthatendatthetree.Withwhatspeed
doesthetruckthenstrikethetree?
70.Amountainclimberstandsatthetopofa50.0-mcliffthatoverhangsacalmpoolofwater.Shethrowstwostones
verticallydownward1.00sapartandobservesthattheycauseasinglesplash.Thefirststonehadaninitialvelocityof
–2.00 m/s. (a) How long after release of the first stone did the two stones hit the water? (b) What initial velocity
must the second stone have had, given that they hit the water simultaneously? (c) What was the velocity of each
stoneattheinstanteachhitthewater?
72.InBosnia,theultimatetestofayoungman’scourageusedtobetojumpoffa400-year-oldbridge(destroyedin
1993;rebuiltin2004)intotheRiverNeretva,23mbelowthebridge.(a)Howlongdidthejumplast?(b)Howfast
wasthejumpertravelinguponimpactwiththeriver?(c)Ifthespeedofsoundinairis340m/s,howlongafterthe
jumpertookoffdidaspectatoronthebridgehearthesplash?
75.Astuntmansittingonatreelimbwishestodropverticallyontoahorsegallopingunderthetree.Theconstant
speedofthehorseis10.0m/s,andthemanisinitially3.00mabovethelevelofthesaddle.(a)Whatmustbethe
horizontaldistancebetweenthesaddleandthelimbwhenthemanmakeshismove?(b)Howlongisheintheair?