Velocity Answers NameSpeed md velocrty do not ha!e the sme meaning to scientists. Spee,l ts a sutltr tluun /irf. wfilcll mcans it can be completely describedbyitsmagnitude(orsize)'Ih€lnagnitudeisgiuenbyanunrberandaunit Forcxample.anoblecr'sspeedmaybemeasuredasl5meteLs pet second

Velocity is a rcclor r/uqt1li\ ln arder lo measure a lecior quantity, you must know the both its rnagnitude and tiirection. I he velocityofe object is detetrnined by nrasuring both the speed and ditec'li(r? in which an object is traveling.

. tfthe speed ofm object chuges, thcn its relocity also chmges.

. tfthe direction in rthich m object is lraaelin!! changes, thcn its velocity changes

r A chmete in either speed, direction, or both causes a oharge in relocity

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 problemsin 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. ThevelocitJ- ofen object ir motion is equal to the dirtanc€ it tr&vels per unit oltine in e givetr dircction.

Iixample l: What is the velocity of a car that travels 100.0 meters. northeast it) 4.65 seconds?

Exnmple 2: A boat travels witb a velocity equal to I 4.0 meters per second, east in 5. I 5 seconds, What distancein meters does the boat travel?

1. An airplane llies 525 kilorneters north in 1.25 hours. what is lhe airplane's vetocit-v?

i.ooLrngror --- I sorution --

l_\"f!uqitf . S25 Knr \()R t rr/ t.ZS hGiven rl=525 Krn \OR l'll: t = 1,25 h I * 42t) Klt/h NOIII H

r-LReratioushif ;;; ait -- -

r,__-..-,-_.-____:-.,-- I

2. Asoccerplayerkicksaball 6.5meters. I{owmuchtinreisneededtbrtheballtotravel ihisclistanceif i

velocity is 22 meters per second, south I 0.305

3. A cruise ship travels east across a river at 19.0 meters per minute. lfthe river is 4,250 tneters lvide, hoivIong does it take for the ship to reach rhe other side? 223.68 m in

4 Joaquin mows the lawn at his grandmother's home duriog the summer months. Joaquin measured thedistance across his grandmother's lawn as I 1..5 meters

a lf.Ioaquinmolvsonelengthacrosslhelawnt'romeasttowestinT.l0seconds,thenwhatislhevelocitv

7.

of the lawnrnorver? 1.62 m/s WEST

b. Once he reaches the edge ofthe lawn, Joaquin turns the larvnmower around. [{e morvs in the oppositedirection but maintains the same speed. what is the velocity of the lawnmower'.) I .62 m/s EAST

A family drives 88 1 miles from floustoo. T ex&s to Santa Fe. Nerv Mexico for vacation. How Iong will ittake lhe farnily to reach their destiuation ifthey travel at a velocit-v of55.0 miles per hour, northwesl?

16.02 h

A shopping cart is pushed I 5.6 meters west across a parking lo1 in 5.2 seconds. What is the velocilv oftheshopping cart? 3 m/s WEST

Katie and her best friend l,iam play tennis every Saturday nrorning. When Katie serves the ball to Lialn, ittravels 9.5 lneters south in 2. I seconds.

a. What is the vetocity of rhe tennis balt? 4.52rn/s SOUTH

b. lfthe tennls ball travels at constant speed, what is its velocity when l.iam retums Katie's serve? 4.S2ru/s]\OR"TH

A driver realizes lhat she is traveling in the wrong direction on a one-rvay street. She has already driven 3.5meters at a velocity of I 6 meters per second. east before deoiding to make a lJ-turn. How long did it take fbrthe driver to realize her error? 0.22 S

'luan's ntother drives I 2.5 miles southwest 10 her favorite shopping mall. What is the velocity ol herautomobile if she anives at lhe mall in 7.25 minutes? 1.72 mil rnin SW

l0Abusistravelingat79.7kilonrelersperhoureast,howt'ardoesthebustravel L4.5hours? I15.57Km1 l. A girl scout troop hiked 5.8 kilometers southeast in l.-i hours. What ivas the troop's velocity'l J,87Km/h SIi

I 2. A volcanologisl noted that a lahar rushed dorvn a mountain at 32.2 kilometers per hour, south. IIow far didthe mud l]ow in 17.5 minutes? 9.39 Km

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l,ooking for

Distance the boat travels

Given

Velocity .= 14.0 meters per second. east

'I'ime '. 5. l5 seconds

distance = vx!Rclationshlp

Solution

distrmci = v x,

'l'he boat travels 72. I meters.

- 14!m x5.15s=?31m

Acceleration Worksheet. Name:

Date:14.2 AccelerationAcceleration is the rate ofchange in the speed ofan object.'l'o detennine the rale oFacceleration, you use theformula below. 'Ihe units lirr acceleration are metels per second pet secontl or m,/s2.

Arcel':ration - Final speed-Beginning speed

Time

11-Yr

A positive value for acceleration sltorvs speeding up, and negalive value fbr acceleration shorvs slowing downSlowing 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

EXAMPLf,S

L Askaterincreaseshervelocityfiom2.0misto10.0m/sin3.0seconds.Whatistheskater'sacceleration?

Solution

.. 100m,'s-20rn./sArcetefallon = 2!n'.is.?s

'fhe acceleration ofthe skater is 2.7 meters pel secondper second.

2. A car accelerates itt a rate o[3.0 m/s2. lfits original speed is 8.0 m/s, how many secorrtls will it taleto reach a final speed oi25.0 rnJs?

\Vhile traveling aloug a highway a driver slorvs liom ?4 m/s to 15 m/s in l2 seconds. \\'hat is tlle automohile'sacceleration? (Reurembcr that a negative value indicates a slowing down tr deceleration.)

-0.75m/s/s

A parachute o1l fl raciilg dragster opens and changes tlre speed ofthe car frorn 85 m,/s tal 45 m/s in a period 0f4.5seconds. 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 delentrirethe acceleratioo ofthe rolling ball.

Acceleralion -!-5 nlsls "--_ ,__-

A car traveling ai a speed o{'30.0 l,r/s encouilters an energencv and oonres to a complete stop. l{ow much time will ittake for the car to stop ifil decelerates at -4.0 trl/s';? 7.5$

lf'a car can go fronl 0 t0 60 mi/lu ir 8.0 seconds, what tvould be its final speed afrer 5.0 seconds ilits starting speed

were 50 rni/lrr? {i7.5 milh

A cart rolling dowr an incline for 5.0 secr:nds has an acceleration of4.0 nr/s2. Ifthe cart has a beginning speeii of2.0m/s, what is its t'inal speedt 22 m/s

A helicoptel"s speed increases lronr 25 m1s to 60 n/s in 5 seconds. What is the acceleration ofthis helicopter? 7

mlsl$

Assheciimbsahill.aLJ,clistslowsdownfronr25ni/hrto6miflrrinl0seconds.Whatisherdeceleration? *1.9

mi/h/s

A motorcycle traveling at 25 rn,is accelerates at a rate of7.0 m/s: Iix 6.0 seconds. what is the final speetl ofthenrotorcycle? 67 m/s

A car starting from rest accelerates at a rate of8.0 m,/s/s. Whot is its tlnal speed at the end of4.0 seconds? 32mls

After traveling for 6.0 seconds, a nrnner reaches a speed of l0 m/s. What is the runner's acceleration? 1.61m/s/s

A cvclist accelerates at a rate of7.0 rn,/s2. How long will it teke the cyclist kr reach a speetl of 18 mis? 2.57

A skateboarder traveling at 7.0 lneters per second rolls to a stop at the top ofa raulp in 3.0 seconds. Whal ,s tl)e

skateboardor'sacceleration? -2.33 m/s/s

l

l

l

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the car

Solution

- :5Dm/s-80m./slrmi=-=)ir3 0 m!s"

-l'he time lor the car to reach its tinal speed is 5.7

l0

II

t2.

13.

l!!llc9-'r-]:ll.. :ls"ggltgj] ttetationship

v2*Yt

seconds