Chapter 2 Linear Mo on
|
|
|
- Ambrose Morris
- 5 years ago
- Views:
Transcription
1 Chper Lner M n
2 .1 Aerge Velcy The erge elcy prcle s dened s The erge elcy depends nly n he nl nd he nl psns he prcle. Ths mens h prcle srs rm pn nd reurn bck he sme pn, s dsplcemen, nd s s erge elcy s zer. Remrk: There s derence beween dsnce nd dsplcemen. Dsnce, sclr quny, s he cul lng he ph reled by prcle, bu dsplcemen, ecr quny, s he shres dsnce beween he nl nd he nl psns he prcle.
3 Speed s he mgnude he elcy. Ths mens h he speed cn neer be nege. The erge speed ders rm erge elcy n h cers he l dsnce rher hn he l dsplcemen, h s erge speed The SI un elcy s m/s. ldsnce.1 Insnneus Velcy The nsnneus elcy prcle s dened s lm d 0 d
4 In he psn-me grph sme nsn s he slpe he ngen h nsn. Le he psn prcle res wh me ccrdng he grph shwn The nsnneus elcy specc me A s he slpe he ngen h pn. he slpe hs ngen lne ges he nsnneus elcy A
5 Emple.1 The psn prcle res wh me ccrdng +3 wh n m nd n s. ) Fnd he erge elcy r he nerl 0 s b) Fnd he nsnneus elcy 1.5 s Slun nd nd, we he subsue r nd n he - reln, h s, nd ( ) + 3( ) 0 ( ) + 3( ) m m/ s 0 Nw we he r he erge elcy d And r he nsnneus elcy + 3 d The nsnneus elcy 1.5 s s bned by subsung r 1.5 s n he ls equn (1.5) m/ s
6 .3 Accelern When he elcy mng bdy chnges wh me, we sy h he bdy hs ccelern. The erge ccelern prcle s dened s The SI un elcy s m/s. The nsnneus ccelern prcle s dened s lm d 0 d d d
7 Emple. The elcy n bjec res wh me ccrdng V5-3 wh n m/s nd n s. ) Fnd he erge ccelern r he nerl 1 s s b) Fnd he nsnneus ccelern s Slun nd nd, we he subsue r nd n he - reln, h s, 5( ) m/s nd 5( ) m/s Nw we he r he erge ccelern And r he nsnneus ccelern d d 5m/s 7 1 5m/s Ne h he ccelern s ndependen me (cnsn).
8 Emple.3 The psn-me grph prcle mng lng he -s s gen n he gure. Fnd ) Fnd he erge elcy r he nerl s 5 s. b) Fnd he erge ccelern r he nerl 0.5 s.5 s. Slun ) As s cler rm he grph, 3 m, nd 0. Nw we ge m/s b) Snce ny pn s he slpe he - grph h pn, we he 0.5 s 6m/s, nd.5 s 0, s (m) (s) m/s -3
9 .4 Lner mn wh cnsn ccelern The smples ype lner mn s he unrm mn n whch he ccelern s cnsn. In such cse here we dene by, by, nd by, nd ke 0. The be equn nw s + Als, becuse s cnsn, we cn wre
10 Nw s ( ) +
11 Sregy r slng prblems wh cnsn ccelern: () Chse yur crdnes such h he prcle begns s mn rm he rgn ( 0). () Decde he sense he pse drecn. () Mke ls he knwn qunes. D n rge wre ny ecr quny (,,, ) h he drecn ppse yur pse sense s nege quny. () Mke sure h ll he qunes he he sme sysem uns. () () Accrdng wh s gen nd wh s requesed, yu cn esly decde whch equn r equns yu need sle r he unknwns.
12 Emple.4 A cr srs rm res nd mes wh cnsn ccelern. Aer 1 s s elcy becmes 10 m/s. Fnd, ) he ccelern he cr b) he dsnce he cr rels n he 1 s Slun Le he drecn mn be lng he pse -s, where he cr srs rm he rgn 0 ( 0). Nw + Bu 0, 10 m/s nd 1 s T nd he dsnce we use 10 m/s 1 ( 10)( 1) 70 m
13 .5 Free Fllng Bdes A reely llng bdy s ny bdy mng reely under he nluence gry regrdless s nl mn. Assumng h he grnl ccelern, dened by g, s cnsn, we cn cnsder he mn ree llng bdy s lner mn wh cnsn ccelern. Snce he mn s ercl we ke ur s be he y-s wh he +e snce s upwrd. S we replce by y nd he ccelern by -g The e sgn s becuse he grnl ccelern s lwys dwnwrd. g9.8 m/s 3 /s
14 y g 1 g gy Remrk: Remember h he grnl ccelern, g, s cnsn n mgnude nd n drecn nd hs mens h he nege sgn g n he ls equns wll n be chnged unless yu chnge yur pse sense, regrdless he drecn mn.
15 Emple.4 An bjec s hrwn erclly upwrd wh n nl speed 5 m/s. ) Hw lng des ke rech s mmum hegh? b) Wh s he mmum hegh? c) Hw lng des ke reurn he grund? d) Wh s s elcy jus bere srkng he grund? 5m/s Slun ) A he mmum pn 0. usng he equn h g s g 9.8
16 b) The mmum hgh s he ercl dsnce wh 0. usng he equn gy y ( 5) 0 h 31.9m g 9.8 ( ) c) When reurnng he grund, he l dsplcemen he bjec s zer (y 0). usng he equn y 1 g ( 9. 8) 5.1s 4.9 d) T nd he nl elcy he mn we use he equn g ( 9.8)( 5.1) 5m/s 5 The mnus sgn ndces h he drecn he elcy s dwnwrd Ne h we use he eq. sme resul. gy wh y 0 we ge he
17 Emple.6 Asuden, snds he edge he r buldng, hrws bll erclly upwrd wh n nl speed 0 m/s. The buldng s 50 mhgh, nd he bll jus mssed he edge he r n s wy dwn. Fnd, ) he me needed r he bll reurn he leel he r, b) he elcy nd he psn he bll 5 s, c) he elcy he bll jus bere hng he grund. 50 m 0m/s Slun ) When he bll reurns he leel he r, s dsplcemen, y, s zer. 1 y g 0 0 ( 9. ) s
18 b) Usng he equn g ( 9.8)( 5) 9 m/s And usng he equn y 1 g y ( 0)( 5) ( 9.8)( 5).5m c) Frm he equn 1 gy m/s ( 0) ( 9.8)( ) 50 The pse slun s rejeced becuse he bll hs he grund whle llng.
19 .5 RELATIVE MOTION Suppse h w persns wn bsere he mn prcle P. The rs persn Omer s snry wh respec he erh, whle he secnd persn, Ahmed s mng wh cnsn speed rele he erh. Le he reerence rme Omer be reerred by rme E (rme he erh) nd he reerence rme Ahmed by rme A. The dsplcemen he prcle w.r.. he erh s dened by PE, he dsplcemen he prcle w.r.. Ahmed s dened by pa whle AE s s he dsplcemen he A rele E. Frm he gure we cn wre + PE pa E AE AE A PA PE P Derene w.r.. we ge + PE pa AE
20 Emple.7 A mn, n cr, s drng n srgh hghwy cnsn speed 70 km/h rele he erh. Suddenly, he sps ruck relng n he sme drecn wh cnsn speed 60 km/h rele he erh. ) Wh s he elcy he ruck rele he cr? b) Wh s he elcy he cr rele he ruck? c) I he cr sps he ruck when hey re 1.5 km pr, hw lng des ke he cr erke he ruck? Slun ) Le TC denes he elcy he ruck rele he cr, nd TE nd CE dene, respecely, he elces he ruck nd he cr rele he erh. TC TE TC + CE TE CE km/h The mnus sgn ndces h he cr s mng n he ppse drecn rele he cr.
21 b) Agn he elcy he cr rele he ruck CT s CE CT + TE CT CE TE Ne h s ne shuld epec km/h c) The me needed r he cr erpss he ruck s 1.5 CT h 9mnues
Use 10 m/s 2 for the acceleration due to gravity.
ANSWERS Prjecle mn s he ecrl sum w ndependen elces, hrznl cmpnen nd ercl cmpnen. The hrznl cmpnen elcy s cnsn hrughu he mn whle he ercl cmpnen elcy s dencl ree ll. The cul r nsnneus elcy ny pn lng he prblc
Physics 201 Lecture 2
Physcs 1 Lecure Lecure Chper.1-. Dene Poson, Dsplcemen & Dsnce Dsngush Tme nd Tme Inerl Dene Velocy (Aerge nd Insnneous), Speed Dene Acceleron Undersnd lgebrclly, hrough ecors, nd grphclly he relonshps
2015 Sectional Physics Exam Solution Set
. Crrec answer: D Ne: [quan] denes: uns quan WYSE cadec Challenge 05 Secnal Phscs Ea SOLUTION SET / / / / rce lengh lengh rce enu ass lengh e a) / ass ass b) energ c) wrk lengh e pwer energ e d) (crrec
Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration
Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse
As we have already discussed, all the objects have the same absolute value of
Lecture 3 Prjectile Mtin Lst time we were tlkin but tw-dimensinl mtin nd intrduced ll imprtnt chrcteristics f this mtin, such s psitin, displcement, elcit nd ccelertin Nw let us see hw ll these thins re
Chapter 2. Motion along a straight line. 9/9/2015 Physics 218
Chper Moion long srigh line 9/9/05 Physics 8 Gols for Chper How o describe srigh line moion in erms of displcemen nd erge elociy. The mening of insnneous elociy nd speed. Aerge elociy/insnneous elociy
2010 Sectional Physics Solution Set
. Crrec nwer: D WYSE CDEMIC CHLLENGE Secnl hyc E 00 Slun Se y 0 y 4.0 / 9.8 /.45 y. Crrec nwer: y 8 0 / 8 /. Crrec nwer: E y y 0 ( 4 / ) ( 4.9 / ) 5.6 y y 4. Crrec nwer: E 5. Crrec nwer: The e rce c n
Average & instantaneous velocity and acceleration Motion with constant acceleration
Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission
PHUN. Phy 521 2/10/2011. What is physics. Kinematics. Physics is. Section 2 1: Picturing Motion
/0/0 Wh phyc Phy 5 Phyc he brnch o knowledge h ude he phycl world. Phyc nege objec mll om nd lrge glxe. They udy he nure o mer nd energy nd how hey re reled. Phyc he udy o moon nd energy. Phyc nd oher
1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor.
In Eercise 1, use sndrd recngulr Cresin coordine sysem. Le ime be represened long he horizonl is. Assume ll ccelerions nd decelerions re consn. 1. Consider PSA iniilly res in he beginning of he lef-hnd
Chapters 2 Kinematics. Position, Distance, Displacement
Chapers Knemacs Poson, Dsance, Dsplacemen Mechancs: Knemacs and Dynamcs. Knemacs deals wh moon, bu s no concerned wh he cause o moon. Dynamcs deals wh he relaonshp beween orce and moon. The word dsplacemen
Physics 20 Lesson 9H Rotational Kinematics
Phyc 0 Len 9H Ranal Knemac In Len 1 9 we learned abu lnear mn knemac and he relanhp beween dplacemen, velcy, acceleran and me. In h len we wll learn abu ranal knemac. The man derence beween he w ype mn
(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.
Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)
10.7 Power and the Poynting Vector Electromagnetic Wave Propagation Power and the Poynting Vector
L 333 lecmgnec II Chpe 0 lecmgnec W Ppgn Pf. l J. l Khnd Islmc Unves f G leccl ngneeng Depmen 06 0.7 Pwe nd he Pnng Vec neg cn be sped fm ne pn (whee nsme s lced) nhe pn (wh eceve) b mens f M ws. The e
i-clicker Question lim Physics 123 Lecture 2 1 Dimensional Motion x 1 x 2 v is not constant in time v = v(t) acceleration lim Review:
Reiew: Physics 13 Lecure 1 Dimensinal Min Displacemen: Dx = x - x 1 (If Dx < 0, he displacemen ecr pins he lef.) Aerage elciy: (N he same as aerage speed) a slpe = a x x 1 1 Dx D x 1 x Crrecin: Calculus
Physics Courseware Physics I Constant Acceleration
Physics Curseware Physics I Cnsan Accelerain Equains fr cnsan accelerain in dimensin x + a + a + ax + x Prblem.- In he 00-m race an ahlee acceleraes unifrmly frm res his p speed f 0m/s in he firs x5m as
R th is the Thevenin equivalent at the capacitor terminals.
Chaper 7, Slun. Applyng KV Fg. 7.. d 0 C - Takng he derae f each erm, d 0 C d d d r C Inegrang, () ln I 0 - () I 0 e - C C () () r - I 0 e - () V 0 e C C Chaper 7, Slun. h C where h s he Theenn equalen
WYSE Academic Challenge Regional Physics 2008 SOLUTION SET
WYSE cdemic Chllenge eginl 008 SOLUTION SET. Crrect nswer: E. Since the blck is mving lng circulr rc when it is t pint Y, it hs centripetl ccelertin which is in the directin lbeled c. Hwever, the blck
Lecture 4 ( ) Some points of vertical motion: Here we assumed t 0 =0 and the y axis to be vertical.
Sme pins f erical min: Here we assumed and he y axis be erical. ( ) y g g y y y y g dwnwards 9.8 m/s g Lecure 4 Accelerain The aerage accelerain is defined by he change f elciy wih ime: a ; In analgy,
PHYS 1443 Section 001 Lecture #4
PHYS 1443 Secon 001 Lecure #4 Monda, June 5, 006 Moon n Two Dmensons Moon under consan acceleraon Projecle Moon Mamum ranges and heghs Reerence Frames and relae moon Newon s Laws o Moon Force Newon s Law
Announcements. Formulas Review. Exam format
Annuncemens 1. N hmewrk due mrrw! a. Wuld be an ecellen eening sud fr and/r ake he eam. Eam 1 sars da! a. Aailable in Tesing Cener frm Tues, Sep. 16 10:15 am, up Mnda, Sep, clsing ime i. If u pick up ur
A 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m
PHYS : Soluions o Chper 3 Home Work. SSM REASONING The displcemen is ecor drwn from he iniil posiion o he finl posiion. The mgniude of he displcemen is he shores disnce beween he posiions. Noe h i is onl
DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
approaches as n becomes larger and larger. Since e > 1, the graph of the natural exponential function is as below
. Eponentil nd rithmic functions.1 Eponentil Functions A function of the form f() =, > 0, 1 is clled n eponentil function. Its domin is the set of ll rel f ( 1) numbers. For n eponentil function f we hve.
PHYSICS 1210 Exam 1 University of Wyoming 14 February points
PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry 2013 150 poins This es is open-noe nd closed-book. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher
Physics 15 Second Hour Exam
hc 5 Second Hou e nwe e Mulle hoce / ole / ole /6 ole / ------------------------------- ol / I ee eone ole lee how ll wo n ode o ecee l ced. I ou oluon e llegle no ced wll e gen.. onde he collon o wo 7.
a = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114
Lner Accelerton nd Freell Phyc 4 Eyre Denton o ccelerton Both de o equton re equl Mgntude Unt Drecton (t ector!) Accelerton Mgntude Mgntude Unt Unt Drecton Drecton 4/3/07 Module 3-Phy4-Eyre 4/3/07 Module
A Kalman filtering simulation
A Klmn filering simulion The performnce of Klmn filering hs been esed on he bsis of wo differen dynmicl models, ssuming eiher moion wih consn elociy or wih consn ccelerion. The former is epeced o beer
Motion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.
Moion Accelerion Pr : Consn Accelerion Accelerion Accelerion Accelerion is he re of chnge of velociy. = v - vo = Δv Δ ccelerion = = v - vo chnge of velociy elpsed ime Accelerion is vecor, lhough in one-dimensionl
Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!
Knemtc Quntte Lner Phyc 11 Eyre Tme Intnt t Fundmentl Tme Interl t Dened Poton Fundmentl Dplcement Dened Aerge g Dened Aerge Accelerton g Dened Knemtc Quntte Scler: Mgntude Tme Intnt, Tme Interl nd Speed
e t dt e t dt = lim e t dt T (1 e T ) = 1
Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie
The Components of Vector B. The Components of Vector B. Vector Components. Component Method of Vector Addition. Vector Components
Upcming eens in PY05 Due ASAP: PY05 prees n WebCT. Submiing i ges yu pin ward yur 5-pin Lecure grade. Please ake i seriusly, bu wha cuns is wheher r n yu submi i, n wheher yu ge hings righ r wrng. Due
4.8 Improper Integrals
4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls
( ) WYSE ACADEMIC CHALLENGE Regional Physics Exam 2009 Solution Set. 1. Correct answer: D. m t s. 2. Correct answer: A. 3.
YSE CDEMIC CHLLENGE Regnl hyscs E 009 Slutn Set. Crrect nswer: D d hrzntl v hrzntl 3 345 t s t 0.3565s t d d d ll ll ll gt 9.80 s 0.63 ( 0.3565s). Crrect nswer: (-70. 0 ) ( 3 /s) t ( 4. 0 /s ) ( 4. 0 /s
ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o:
R TE EVTE (dhd H Hdg) L / Mld Kbrd gú s v l m sl c m qu gs v nns V n P P rs l mul m d lud 7 súb Fí cón ví f f dó, cru gs,, j l f c r s m l qum t pr qud ct, us: ns,,,, cs, cut r l sns m / m fí hó sn sí
Displacement, Velocity, and Acceleration. (WHERE and WHEN?)
Dsplacemen, Velocy, and Acceleraon (WHERE and WHEN?) Mah resources Append A n your book! Symbols and meanng Algebra Geomery (olumes, ec.) Trgonomery Append A Logarhms Remnder You wll do well n hs class
K The slowest step in a mechanism has this
CM 6 Generl Chemisry II Nme SLUTINS Exm, Spring 009 Dr. Seel. (0 pins) Selec he nswer frm he clumn n he righ h bes mches ech descripin frm he clumn n he lef. Ech nswer cn be used, ms, nly nce. E G This
3 Motion with constant acceleration: Linear and projectile motion
3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr
Faculty of Engineering
Faculty f Engneerng DEPARTMENT f ELECTRICAL AND ELECTRONIC ENGINEERING EEE 223 Crcut Thery I Instructrs: M. K. Uygurğlu E. Erdl Fnal EXAMINATION June 20, 2003 Duratn : 120 mnutes Number f Prblems: 6 Gd
Motion in a Straight Line
Moion in Srigh Line. Preei reched he mero sion nd found h he esclor ws no working. She wlked up he sionry esclor in ime. On oher dys, if she remins sionry on he moing esclor, hen he esclor kes her up in
ENGR 1990 Engineering Mathematics The Integral of a Function as a Function
ENGR 1990 Engineering Mhemics The Inegrl of Funcion s Funcion Previously, we lerned how o esime he inegrl of funcion f( ) over some inervl y dding he res of finie se of rpezoids h represen he re under
Kinematics Review Outline
Kinemaics Review Ouline 1.1.0 Vecrs and Scalars 1.1 One Dimensinal Kinemaics Vecrs have magniude and direcin lacemen; velciy; accelerain sign indicaes direcin + is nrh; eas; up; he righ - is suh; wes;
ENGI 4421 Probability and Statistics Faculty of Engineering and Applied Science Problem Set 10 Solutions Chi-Square Tests; Simple Linear Regression
ENGI 441 Prbbly nd Sscs Fculy f Engneerng nd Appled Scence Prblem Se 10 Sluns Ch-Squre Tess; Smple Lner Regressn 1. Is he fllwng se f bservns f bjecs n egh dfferen drecns cnssen wh unfrm dsrbun? Drecn
EEM 486: Computer Architecture
EEM 486: Compuer Archecure Lecure 4 ALU EEM 486 MIPS Arhmec Insrucons R-ype I-ype Insrucon Exmpe Menng Commen dd dd $,$2,$3 $ = $2 + $3 sub sub $,$2,$3 $ = $2 - $3 3 opernds; overfow deeced 3 opernds;
ARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac
REVIEW OF ALGEBRA Here we review the bsic rules nd procedures of lgebr tht you need to know in order to be successful in clculus. ARITHMETIC OPERATIONS The rel numbers hve the following properties: b b
Wp/Lmin. Wn/Lmin 2.5V
UNIVERITY OF CALIFORNIA Cllege f Engneerng Department f Electrcal Engneerng and Cmputer cences Andre Vladmrescu Hmewrk #7 EEC Due Frday, Aprl 8 th, pm @ 0 Cry Prblem #.5V Wp/Lmn 0.0V Wp/Lmn n ut Wn/Lmn.5V
JEE-Physics. A body in translation motion can move on either a straight line path or curvilinear path.
J-hsics ricle Kinemics Kinemics In kinemics we sd hw bd mes wih knwing wh i mes. ll pricles f rigid bd in rnslin min me in idenicl fshin hence n f he pricles f rigid bd in rnslin min cn be sed represen
CHAPTER 2 LINEAR MOTION
0 CHAPTER LINEAR MOTION HAPTER LINEAR MOTION 1 Motion o an object is the continuous change in the position o that object. In this chapter we shall consider the motion o a particle in a straight line, which
Uniform Circular Motion
Unfom Ccul Moton Unfom ccul Moton An object mong t constnt sped n ccle The ntude of the eloct emns constnt The decton of the eloct chnges contnuousl!!!! Snce cceleton s te of chnge of eloct:!! Δ Δt The
Math 105: Review for Exam I - Solutions
1. Let f(x) = 3 + x + 5. Math 105: Review fr Exam I - Slutins (a) What is the natural dmain f f? [ 5, ), which means all reals greater than r equal t 5 (b) What is the range f f? [3, ), which means all
The Perceptron. Nuno Vasconcelos ECE Department, UCSD
he Perceprn Nun Vscncels ECE Deprmen, UCSD Clssfcn clssfcn prblem hs pes f vrbles e.g. X - vecr f bservns feures n he rld Y - se clss f he rld X R = fever, bld pressure Y = {dsese, n dsese} X, Y reled
Physics Worksheet Lesson 4: Linear Motion Section: Name:
Physics Workshee Lesson 4: Liner Moion Secion: Nme: 1. Relie Moion:. All moion is. b. is n rbirry coorine sysem wih reference o which he posiion or moion of somehing is escribe or physicl lws re formule.
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
11.2. Infinite Series
.2 Infinite Series 76.2 Infinite Series An infinite series is the sum f n infinite seuence f numbers + 2 + 3 + Á + n + Á The gl f this sectin is t understnd the mening f such n infinite sum nd t develp
SPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
element k Using FEM to Solve Truss Problems
sng EM t Slve Truss Prblems A truss s an engneerng structure cmpsed straght members, a certan materal, that are tpcall pn-ned at ther ends. Such members are als called tw-rce members snce the can nl transmt
Let s treat the problem of the response of a system to an applied external force. Again,
Page 33 QUANTUM LNEAR RESPONSE FUNCTON Le s rea he problem of he response of a sysem o an appled exernal force. Agan, H() H f () A H + V () Exernal agen acng on nernal varable Hamlonan for equlbrum sysem
PHYS 314 HOMEWORK #3
PHYS 34 HOMEWORK #3 Due : 8 Feb. 07. A unifrm chain f mass M, lenth L and density λ (measured in k/m) hans s that its bttm link is just tuchin a scale. The chain is drpped frm rest nt the scale. What des
AP Physics 1 MC Practice Kinematics 1D
AP Physics 1 MC Pracice Kinemaics 1D Quesins 1 3 relae w bjecs ha sar a x = 0 a = 0 and mve in ne dimensin independenly f ne anher. Graphs, f he velciy f each bjec versus ime are shwn belw Objec A Objec
Electrostatic/magnetostatic forces
Eecsc/gnesc ces spes ppc: eneg e ec eneg ce (vec) ve (vec) en ( eneg ) ( snce) ne s cn gve e O ce (n pessue) u cn en snge sp cne s pe e ce spe epe: pe pes eecsc: ppe vge gnesc: cuen I Den. Nekk 00, s upe
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).
Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)
https://goo.gl/eaqvfo SUMMER REV: Half-Life DUE DATE: JULY 2 nd
NAME: DUE DATE: JULY 2 nd AP Chemistry SUMMER REV: Half-Life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng
Asynchrnus Sequen Differentiation Applications 1: Related Rates
Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm
STA6E NO, LR. Council DeIegote Iouncit Seol. Dqte / / Re-centif. IounciI Delegote Iouncil Seol. Dqie. Sl-oging. This is noi o sionpd subdivision
S6, LR PL SBDVS ue ny D Pn umber PS5 4627 Lcqn Ln Pr PHLLP SLD 0WS wnp Secn rwn [[men 15(P, 16 & 17 rwn P e Reerence L Pn Reerence L PS524867K P re c me ubvn MG e n nnnv n n n n pn v01.1028 0L.85 SLM RD
Physics 123 Lecture 2 1 Dimensional Motion
Reiew: Physics 13 Lecture 1 Dimensinal Mtin Displacement: Dx = x - x 1 (If Dx < 0, the displacement ectr pints t the left.) Aerage elcity: (Nt the same as aerage speed) a x t x t 1 1 Dx Dt slpe = a x 1
CIRCLE YOUR DIVISION: Div. 1 (9:30 am) Div. 2 (11:30 am) Div. 3 (2:30 pm) Prof. Ruan Prof. Naik Mr. Singh
Frst CIRCLE YOUR DIVISION: Dv. 1 (9:30 am) Dv. (11:30 am) Dv. 3 (:30 m) Prf. Ruan Prf. Na Mr. Sngh Schl f Mechancal Engneerng Purdue Unversty ME315 Heat and Mass ransfer Eam #3 Wednesday Nvember 17 010
Waveshapping Circuits and Data Converters. Lesson #17 Comparators and Schmitt Triggers Section BME 373 Electronics II J.
Waeshappg Crcuts and Data Cnerters Lessn #7 Cmparatrs and Schmtt Trggers Sectn. BME 7 Electrncs II 0 Waeshappg Crcuts and Data Cnerters Cmparatrs and Schmtt Trggers Astable Multbratrs and Tmers ectfers,
Model Solutions to Assignment 4
Oberlin College Physics 110, Fll 2011 Model Solutions to Assignment 4 Additionl problem 56: A girl, sled, nd n ice-covered lke geometry digrm: girl shore rope sled ice free body digrms: force on girl by
Solutions to Problems. Then, using the formula for the speed in a parabolic orbit (equation ), we have
Slutins t Prblems. Nttin: V speed f cmet immeditely befre cllisin. V speed f cmbined bject immeditely fter cllisin, mmentum is cnserved. V, becuse liner + k q perihelin distnce f riginl prblic rbit, s
Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018
Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and
x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions
Knemtc Quntte Lner Moton Phyc 101 Eyre Tme Intnt t Fundmentl Tme Interl Defned Poton x Fundmentl Dplcement Defned Aerge Velocty g Defned Aerge Accelerton g Defned Knemtc Quntte Scler: Mgntude Tme Intnt,
ALGEBRA 2/TRIGONMETRY TOPIC REVIEW QUARTER 3 LOGS
ALGEBRA /TRIGONMETRY TOPIC REVIEW QUARTER LOGS Cnverting frm Epnentil frm t Lgrithmic frm: E B N Lg BN E Americn Ben t French Lg Ben-n Lg Prperties: Lg Prperties lg (y) lg + lg y lg y lg lg y lg () lg
UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II
Mcroeconomc Theory I UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS MSc n Economcs MICROECONOMIC THEORY I Techng: A Lptns (Note: The number of ndctes exercse s dffculty level) ()True or flse? If V( y )
This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.
Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus
Direct Current Circuits
Eler urren (hrges n Moon) Eler urren () The ne moun of hrge h psses hrough onduor per un me ny pon. urren s defned s: Dre urren rus = dq d Eler urren s mesured n oulom s per seond or mperes. ( = /s) n
Lesson 1: Quadratic Equations
Lesson 1: Qudrtic Equtions Qudrtic Eqution: The qudrtic eqution in form is. In this section, we will review 4 methods of qudrtic equtions, nd when it is most to use ech method. 1. 3.. 4. Method 1: Fctoring
Physics 2A HW #3 Solutions
Chper 3 Focus on Conceps: 3, 4, 6, 9 Problems: 9, 9, 3, 41, 66, 7, 75, 77 Phsics A HW #3 Soluions Focus On Conceps 3-3 (c) The ccelerion due o grvi is he sme for boh blls, despie he fc h he hve differen
x x
Mdeling the Dynamics f Life: Calculus and Prbability fr Life Scientists Frederick R. Adler cfrederick R. Adler, Department f Mathematics and Department f Bilgy, University f Utah, Salt Lake City, Utah
NAME: ANSWER KEY DATE: PERIOD. DIRECTIONS: MULTIPLE CHOICE. Choose the letter of the correct answer.
R A T T L E R S S L U G S NAME: ANSWER KEY DATE: PERIOD PREAP PHYSICS REIEW TWO KINEMATICS / GRAPHING FORM A DIRECTIONS: MULTIPLE CHOICE. Chs h r f h rr answr. Us h fgur bw answr qusns 1 and 2. 0 10 20
Brace-Gatarek-Musiela model
Chaper 34 Brace-Gaarek-Musiela mdel 34. Review f HJM under risk-neural IP where f ( T Frward rae a ime fr brrwing a ime T df ( T ( T ( T d + ( T dw ( ( T The ineres rae is r( f (. The bnd prices saisfy
Equations and Inequalities
Equtions nd Inequlities Equtions nd Inequlities Curriculum Redy ACMNA: 4, 5, 6, 7, 40 www.mthletics.com Equtions EQUATIONS & Inequlities & INEQUALITIES Sometimes just writing vribles or pronumerls in
1.B Appendix to Chapter 1
Secon.B.B Append o Chper.B. The Ordnr Clcl Here re led ome mporn concep rom he ordnr clcl. The Dervve Conder ncon o one ndependen vrble. The dervve o dened b d d lm lm.b. where he ncremen n de o n ncremen
Chapter 3: Vectors and Two-Dimensional Motion
Chape 3: Vecos and Two-Dmensonal Moon Vecos: magnude and decon Negae o a eco: eese s decon Mulplng o ddng a eco b a scala Vecos n he same decon (eaed lke numbes) Geneal Veco Addon: Tangle mehod o addon
² Ý ² ª ² Þ ² Þ Ң Þ ² Þ. ² à INTROIT. huc. per. xi, sti. su- sur. sum, cum. ia : ia, ia : am, num. VR Mi. est. lis. sci. ia, cta. ia.
str Dy Ps. 138 R 7 r r x, t huc t m m, l : p - í pr m m num m, l l : VR M rá s f ct st sc n -, l l -. Rpt nphn s fr s VR ftr ch vrs Ps. 1. D n, pr bá m, t c g ví m : c g ví ss s nm m m, t r r r c nm m
PH2200 Practice Exam I Summer 2003
PH00 Prctice Exm I Summer 003 INSTRUCTIONS. Write yur nme nd student identifictin number n the nswer sheet.. Plese cver yur nswer sheet t ll times. 3. This is clsed bk exm. Yu my use the PH00 frmul sheet
Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC
Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses
Minimum Squared Error
Minimum Squred Error LDF: Minimum Squred-Error Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > for ll smples y i solve sysem of liner inequliies MSE procedure y i = i for ll smples
Minimum Squared Error
Minimum Squred Error LDF: Minimum Squred-Error Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > 0 for ll smples y i solve sysem of liner inequliies MSE procedure y i i for ll smples
Chapter 2. Kinematics in One Dimension. Kinematics deals with the concepts that are needed to describe motion.
Chpe Kinemic in One Dimenin Kinemic del wih he cncep h e needed decibe min. Dynmic del wih he effec h fce he n min. Tgehe, kinemic nd dynmic fm he bnch f phyic knwn Mechnic.. Diplcemen. Diplcemen.0 m 5.0
_J _J J J J J J J J _. 7 particles in the blue state; 3 particles in the red state: 720 configurations _J J J _J J J J J J J J _
Dsrder and Suppse I have 10 partcles that can be n ne f tw states ether the blue state r the red state. Hw many dfferent ways can we arrange thse partcles amng the states? All partcles n the blue state:
Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =
Mi i fd l Phsic 3 Lecure 4 Min poins of od s lecure: Emple: ddiion of elociies Trjecories of objecs in dimensions: dimensions: g 9.8m/s downwrds ( ) g o g g Emple: A foobll pler runs he pern gien in he
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
Graduate Macroeconomics 2 Problem set 5. - Solutions
Graduae Macroeconomcs 2 Problem se. - Soluons Queson 1 To answer hs queson we need he frms frs order condons and he equaon ha deermnes he number of frms n equlbrum. The frms frs order condons are: F K
1/31/ :33 PM. Chapter 11. Kinematics of Particles. Mohammad Suliman Abuhaiba,Ph.D., P.E.
1/31/18 1:33 PM Chpter 11 Kinemtics of Prticles 1 1/31/18 1:33 PM First Em Sturdy 1//18 3 1/31/18 1:33 PM Introduction Mechnics Mechnics = science which describes nd predicts conditions of rest or motion
i-clicker Question How many beans are in the 900 ml beaker? A. Fewer than 1000 B C D E.
i-clicker Questin Hw many beans are in the 900 ml beaker? A. Fewer than 1000 B. 1000-1500 C. 1500-000 D. 000-500 E. Mre than 500 Reiew: Physics 13 Lecture 1 Dimensinal Mtin Displacement: Dx = x - x 1 (If
In the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal