Physics 201 Lecture 3. dx v x. l What was the average velocity? l Two legs with constant velocity but. l Average velocity:

Size: px
Start display at page:

Download "Physics 201 Lecture 3. dx v x. l What was the average velocity? l Two legs with constant velocity but. l Average velocity:"

Transcription

1 Phscs Lecure 3 Lecure 3 l Moon n one-dmenson (k Knemcs Emne ssems wh non-zero cceleron (oen consn Sole D problems wh zero nd consn cceleron (ncludn ree-ll nd moon on n nclne Phscs : Lecure 3, P Poson, nsnneous eloc & cceleron ( uncon( ( d d d d ( d d Phscs : Lecure 3, P Oen so Emple problem l Veloc uncon cn be used o obn poson uncon ( l A cr moes o he rh rs or. sec. m/s nd hen 4. seconds. m/s. d d ( ( d ( l Are under he ( cure elds he dsplcemen l Specl cse: Veloc s consn ( l Wh ws he ere eloc? l Two les wh consn eloc bu. l Aere eloc:,, chnen poson chne n me Phscs : Lecure 3, P 3 Phscs : Lecure 3, P 4 Emple problem l A prcle moes o he rh rs or. seconds. m/s nd hen 4. seconds. m/s. l Wh ws he ere eloc? l Two les wh consn eloc l Fnd he ol dsplcemen ( l Consn eloc ( ( - ( - l - ( - ( ( - ( - l m/s ( s m/s (4 s m n 6. s or.7 m/s Phscs : Lecure 3, P 5 Anoher specl cse, consn cceleron l Prcle moon wh consn cceleron The eloc ecor chnes d consn d d d re under cure Phscs : Lecure 3, P 6 Pe

2 Phscs Lecure 3 Consn cceleron n D l Prcle moon wh consn cceleron l A cr, srn res, wh smoohl ncresn eloc (o he rh: ( I consn cceleron we cn nere wce cons ( Phscs : Lecure 3, P 7 Phscs : Lecure 3, P 8 I consn cceleron hen we lso e: (, ( (,, ( Phscs : Lecure 3, P 9 Phscs : Lecure 3, P Dsplcemen wh consn cceleron A prcle srn res & mon lon lne wh consn cceleron hs dsplcemen whose mnude s proporonl o (. Ths cn be esed. Ths s poenll useul resul Phscs : Lecure 3, P Free Fll l When n objec s le o lls owrd he round!! The orce h cuses he objecs o ll s clled r. l Ths cceleron on he Erh s surce, cused b r, s pcll wren s lle l An objec, be bsebll or n elephn, eperences he sme cceleron ( when s dropped, hrown, sp, or hurled,.e. s consn. - ( Phscs : Lecure 3, P Pe

3 Phscs Lecure 3 Gr cs: l does no depend on he nure o he merl! Glleo ( ured hs ou whou nc clocks & rulers! Eercse Moon n One Dmenson When hrown bll srh up, whch o he ollown s rue bou s eloc nd s cceleron he hhes pon n s ph? l Feher & penn behe jus he sme n cuum l Nomnll, 9.8 m/s A he equor 9.78 m/s A. Boh nd B., bu C., bu D. None o he boe A he Norh pole 9.83 m/s Phscs : Lecure 3, P 3 Phscs 7: Lecure 3, P 4 Thrown bll up l You hrow bll up 9.8 m/s, how hh does oes nd how lon does ke? l nl eloc 9.8 m/s nl eloc m/s ( m/s 9.8 m/s 9.8 m/s. s ( 4.9 m 9.8 m/s (s 4.9 m/s (s Phscs 7: Lecure 3, P 5 Thrown bll up l You hrow bll up 9.8 m/s, l Inorn r ressnce, how s s relln when lls ps ou? ( m 9.8 m/s ( 4.9 m/s (. s,. s ( 9.8 m/s 9.8 m/s 9.8 m/s (. s Phscs 7: Lecure 3, P 6 Home Eercse More comple Poson s. Tme Grphs In drn rom Mdson o Chco, nll m speed s consn 65 mph. Aer some me, I see n ccden hed o me on I-9 nd mus sop quckl so I decelere ncresnl s unl I sop. The mnude o m cceleron s me s en b, Queson: M eloc s me rph looks mos lke whch o he ollown? A. B. C. Phscs 7: Lecure 3, P 7 Eercse D Freell l Alce nd Bll re sndn he op o cl o heh H.. Boh hrow bll wh nl speed, Alce srh down nd Bll srh up.. The speed o he blls when he h he round re A nd B respecel. A. A < B B. A B C. A > B Alce Bll H A B Phscs 7: Lecure 3, P 8 Pe 3

4 Phscs Lecure 3 Eercse D Freell : Grphcl soluon l Alce nd Bll re sndn he op o cl o heh H.. Boh hrow bll wh nl speed, Alce srh down nd Bll srh up. cl bck urnround - pon cl - dencl dsplcemens (one nd one - round round round Phscs 7: Lecure 3, P 9 The rph rh shows he eloc ersus me rph or bll. Gr s cn downwrd n he - drecon nd he -s s lon he horzonl. Whch eplnon bes s he moon o he bll s shown b he eloc-me me rph below? Eercse,D Freell A. The bll s lln srh down, s cuh, nd s hen hrown srh down wh reer eloc. B. The bll s rolln horzonll, sops, nd hen connues rolln. C. The bll s rsn srh up, hs he celn, bounces, nd hen lls srh down. D. The bll s lln srh down, hs he loor, nd hen bounces srh up. E. The bll s rsn srh up, s cuh nd held or whle, nd hen s hrown srh down. Phscs 7: Lecure 3, P Fe Seps: Problem Soluon Mehod: Focus he Problem - drw pcure wh re we skn or? Descrbe he phscs - wh phscs des re pplcble - wh re he relen rbles known nd unknown 3 Pln he soluon - wh re he relen phscs equons 4 Eecue he pln - sole n erms o rbles - sole n erms o numbers 5 Elue he nswer - re he dmensons nd uns correc? - do he numbers mke sense? A scence projec l You drop bus o he Wlls Tower (44 m boe he sde wlk. I so hppens h Supermn les b he sme nsn ou relese he bus. Supermn s ln down 35 m/s. l How s s he bus on when cches up o Supermn? Phscs 7: Lecure 3, P Phscs 7: Lecure 3, P A scence projec A scence projec l You drop bus o he Wlls Tower (44 m boe he sde wlk. I so hppens h Supermn les b he sme nsn ou relese he cr. Supermn s ln down 35 m/s. l How s s he bus on when cches up o Supermn? l Drw pcure Phscs 7: Lecure 3, P 3 l Drw pcure l Cures nersec wo pons Supermn Supermn bus Supermn Supermn Supermn Phscs 7: Lecure 3, P 4 Pe 4

5 Phscs Lecure 3 Home eercse o D moon problem l A cr s nll reln Es consn speed o m/s. When s hlw (n dsnce! o s desnon s speed suddenl ncreses nd hereer remns consn. All old he cr spends ol o s n rns wh n ere speed o 5 m/s. l Wh s he speed o he cr durn he nd hl o he rp? l Ths s ron on he n clss emple bu much more dcul. Home eercse o D moon problem l A cr s nll reln Es consn speed o m/s. When s hlw (n dsnce! o s desnon s speed suddenl ncreses nd hereer remns consn. All old he cr spends ol o s n rns wh n ere speed o 5 m/s. l Wh s he speed o he cr durn he nd hl o he rp? l Dnmcl relonshps (onl consn cceleron: cons ( ( ( Phscs 7: Lecure 3, P 5 And (dsplceme n ( ere eloc (ol me Phscs 7: Lecure 3, P 6 Drwn he pcure Usn ( > ( > m/s m/s m/s m/s l Plus he ere eloc l Knowns: m s m/s s 5 m/s relonshp beween nd l Four unknowns & nd mus nd n erms o knowns Phscs 7: Lecure 3, P 7 ( ( l Four unknowns l Four relonshps l Focus on ( Phscs 7: Lecure 3, P 8 Usn ( > Usn ( > m/s m/s m/s m/s ( / s 5 m 5 / s 5/4 s m 5 s 5 m s 5 m 5 m 5 m ( 5 / 4 s (5 / 4 s Phscs 7: Lecure 3, P 9 l Elmne unknowns rs ne ( hen 3 & ( ( 4 ( 4 Mul. b / Phscs 7: Lecure 3, P 3 ( Pe 5

6 Phscs Lecure 3 m/s l Plus he ere eloc l Gen: m/s s 5 m/s Fn ( > m/s ( 5m/s m/s 5m/s m/s m/s 5m/s Phscs 7: Lecure 3, P 3 Tps: l Red! Beore ou sr work on problem, red he problem semen horouhl. Mke sure ou undersnd wh normon s en, wh s sked or, nd he menn o ll he erms used n sn he problem. l Wch our uns (dmensonl nlss! Alws check he uns o our nswer, nd crr he uns lon wh our numbers durn he clculon. l Ask quesons! Phscs 7: Lecure 3, P 3 Cone Rch Problem: For dscusson Problem: l On brh sunn d ou re wlkn round he cmpus wchn one o he mn consrucon ses. To l bunch o brcks rom cenrl re, he he brouh n helcoper. As he plo s hoern he/she ccdenll releses he brcks when he re m boe he round. A worker, drecl below, snds sll or seconds beore wlkn w. (Le m/s There s no wnd or oher eecs.. We need o nd he me kes or he brck o h he round.. I > sec. hen he worker s ssured surl. m Does he worker le? (Crer or ln..he worker moes beore he brcks srke he round Phscs 7: Lecure 3, P 33 Phscs 7: Lecure 3, P 34 Problem # (Group or home l You re wrn shor denure sor or our Enlsh clss. In our sor, wo submrnes on secre msson need o rre plce n he mddle o he Alnc ocen he sme me. The sr ou he sme me rom posons equll dsn rom he rendezous pon. The rel deren eloces bu boh o n srh lne. The rs submrne rels n ere eloc o km/hr or he rs 5 km, 4 km/hr or he ne 5 km, 3 km/hr or he ne 5 km nd 5 km/hr or he nl 5 km. In he plo, he second submrne s requred o rel consn eloc, whch ou wsh o eplcl menon n he sor. Wh s h eloc?. Drw drm h shows he ph o boh submrnes, nclude ll o he semens o he rp or boh bos. b. Wh ecl do ou need o clcule o be ble o wre he sor? c. Whch knemcs equons wll be useul? d. Sole he problem n erms o smbols. e. Does ou nswer he he correc dmensons (wh re he?. Sole he problem wh numbers. Problem # (A home l As ou re drn o school one d, ou pss consrucon se or new buldn nd sop o wch or ew mnues. A crne s ln bch o brcks on plle o n upper loor o he buldn. Suddenl brck lls o he rsn plle. You clock he me kes or he brck o h he round.5 seconds. The crne, orunel, hs heh mrkns nd ou see he brck ell o he plle heh o meers boe he round. A lln brck cn be dnerous, nd ou wonder how s he brck ws on when h he round. Snce ou re kn phscs, ou quckl clcule he nswer.. Drw pcure llusrn he ll o he brck, he lenh lls, nd he drecon o s cceleron. b. Wh s he problem skn ou o nd? c. Wh knemcs equons wll be useul? d. Sole he problem n erms o smbols. e. Does ou nswer he he correc dmensons?. Sole he problem wh numbers. Phscs 7: Lecure 3, P 35 Phscs 7: Lecure 3, P 36 Pe 6

Physics 201 Lecture 2

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

More information

Physics 207, Lecture 3

Physics 207, Lecture 3 Physcs 7 Lecue 3 Physcs 7, Lecue 3 l Tody (Fnsh Ch. & s Ch. 3) Emne sysems wh non-zeo cceleon (ofen consn) Sole D poblems wh zeo nd consn cceleon (ncludng fee-fll nd moon on n nclne) Use Cesn nd pol coodne

More information

Average & instantaneous velocity and acceleration Motion with constant acceleration

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

More information

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration

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

More information

PHYS 1443 Section 001 Lecture #4

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

More information

Chapters 2 Kinematics. Position, Distance, Displacement

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

More information

Chapter 4: Motion in Two Dimensions Part-1

Chapter 4: Motion in Two Dimensions Part-1 Lecue 4: Moon n Two Dmensons Chpe 4: Moon n Two Dmensons P- In hs lesson we wll dscuss moon n wo dmensons. In wo dmensons, s necess o use eco noon o descbe phscl qunes wh boh mnude nd decon. In hs chpe,

More information

Chapter 2 Linear Mo on

Chapter 2 Linear Mo on Chper Lner M n .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

More information

3 Motion with constant acceleration: Linear and projectile motion

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

More information

PHY2053 Summer C 2013 Exam 1 Solutions

PHY2053 Summer C 2013 Exam 1 Solutions PHY053 Sue C 03 E Soluon. The foce G on o G G The onl cobnon h e '/ = doubln.. The peed of lh le 8fulon c 86,8 le 60 n 60n h 4h d 4d fonh.80 fulon/ fonh 3. The dnce eled fo he ene p,, 36 (75n h 45 The

More information

Motion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.

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

More information

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.

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

More information

Physics 101 Lecture 4 Motion in 2D and 3D

Physics 101 Lecture 4 Motion in 2D and 3D Phsics 11 Lecure 4 Moion in D nd 3D Dr. Ali ÖVGÜN EMU Phsics Deprmen www.ogun.com Vecor nd is componens The componens re he legs of he righ ringle whose hpoenuse is A A A A A n ( θ ) A Acos( θ) A A A nd

More information

Displacement, Velocity, and Acceleration. (WHERE and WHEN?)

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

More information

PHYSICS 1210 Exam 1 University of Wyoming 14 February points

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

More information

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218

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

More information

2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.

2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information. Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl

More information

Use 10 m/s 2 for the acceleration due to gravity.

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

More information

Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =

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

More information

Physics 2A HW #3 Solutions

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

More information

A 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m

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

More information

(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.

(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)

More information

WebAssign HW Due 11:59PM Tuesday Clicker Information

WebAssign HW Due 11:59PM Tuesday Clicker Information WebAssgn HW Due 11:59PM Tuesday Clcker Inormaon Remnder: 90% aemp, 10% correc answer Clcker answers wll be a end o class sldes (onlne). Some days we wll do a lo o quesons, and ew ohers Each day o clcker

More information

Direct Current Circuits

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

More information

Motion in a Straight Line

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

More information

Physics 120 Spring 2007 Exam #1 April 20, Name

Physics 120 Spring 2007 Exam #1 April 20, Name Phc 0 Spng 007 E # pl 0, 007 Ne P Mulple Choce / 0 Poble # / 0 Poble # / 0 Poble # / 0 ol / 00 In eepng wh he Unon College polc on cdec hone, ued h ou wll nehe ccep no pode unuhozed nce n he copleon o

More information

Chapter 3: Vectors and Two-Dimensional Motion

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

More information

Rotations.

Rotations. oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse

More information

Motion in Two Dimensions

Motion in Two Dimensions Phys 1 Chaper 4 Moon n Two Dmensons adzyubenko@csub.edu hp://www.csub.edu/~adzyubenko 005, 014 A. Dzyubenko 004 Brooks/Cole 1 Dsplacemen as a Vecor The poson of an objec s descrbed by s poson ecor, r The

More information

Introduction. Voice Coil Motors. Introduction - Voice Coil Velocimeter Electromechanical Systems. F = Bli

Introduction. Voice Coil Motors. Introduction - Voice Coil Velocimeter Electromechanical Systems. F = Bli UNIVERSITY O TECHNOLOGY, SYDNEY ACULTY O ENGINEERING 4853 Elecroechncl Syses Voce Col Moors Topcs o cover:.. Mnec Crcus 3. EM n Voce Col 4. orce n Torque 5. Mhecl Moel 6. Perornce Voce cols re wely use

More information

Notes on the stability of dynamic systems and the use of Eigen Values.

Notes on the stability of dynamic systems and the use of Eigen Values. Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon

More information

An object moving with speed v around a point at distance r, has an angular velocity. m/s m

An object moving with speed v around a point at distance r, has an angular velocity. m/s m Roion The mosphere roes wih he erh n moions wihin he mosphere clerly follow cure phs (cyclones, nicyclones, hurricnes, ornoes ec.) We nee o epress roion quniiely. For soli objec or ny mss h oes no isor

More information

Physics Notes - Ch. 2 Motion in One Dimension

Physics Notes - Ch. 2 Motion in One Dimension Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,

More information

Page 1 o 13 1. The brighes sar in he nigh sky is α Canis Majoris, also known as Sirius. I lies 8.8 ligh-years away. Express his disance in meers. ( ligh-year is he disance coered by ligh in one year. Ligh

More information

Chapter 6 Plane Motion of Rigid Bodies

Chapter 6 Plane Motion of Rigid Bodies Chpe 6 Pne oon of Rd ode 6. Equon of oon fo Rd bod. 6., 6., 6.3 Conde d bod ced upon b ee een foce,, 3,. We cn ume h he bod mde of e numbe n of pce of m Δm (,,, n). Conden f he moon of he m cene of he

More information

MODEL SOLUTIONS TO IIT JEE ADVANCED 2014

MODEL SOLUTIONS TO IIT JEE ADVANCED 2014 MODEL SOLUTIONS TO IIT JEE ADVANCED Pper II Code PART I 6 7 8 9 B A A C D B D C C B 6 C B D D C A 7 8 9 C A B D. Rhc(Z ). Cu M. ZM Secon I K Z 8 Cu hc W mu hc 8 W + KE hc W + KE W + KE W + KE W + KE (KE

More information

Chapter Direct Method of Interpolation

Chapter Direct Method of Interpolation Chper 5. Direc Mehod of Inerpolion Afer reding his chper, you should be ble o:. pply he direc mehod of inerpolion,. sole problems using he direc mehod of inerpolion, nd. use he direc mehod inerpolns o

More information

A Kalman filtering simulation

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

More information

Physics Worksheet Lesson 4: Linear Motion Section: Name:

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.

More information

(3.2.3) r x x x y y y. 2. Average Velocity and Instantaneous Velocity 2 1, (3.2.2)

(3.2.3) r x x x y y y. 2. Average Velocity and Instantaneous Velocity 2 1, (3.2.2) Lecture 3- Kinemtics in Two Dimensions Durin our preious discussions we he been tlkin bout objects moin lon the striht line. In relity, howeer, it rrely hppens when somethin moes lon the striht pth. For

More information

( ) () we define the interaction representation by the unitary transformation () = ()

( ) () we define the interaction representation by the unitary transformation () = () Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger

More information

f t f a f x dx By Lin McMullin f x dx= f b f a. 2

f t f a f x dx By Lin McMullin f x dx= f b f a. 2 Accumulion: Thoughs On () By Lin McMullin f f f d = + The gols of he AP* Clculus progrm include he semen, Sudens should undersnd he definie inegrl s he ne ccumulion of chnge. 1 The Topicl Ouline includes

More information

( ) ( ) ( ) 0. Conservation of Energy & Poynting Theorem. From Maxwell s equations we have. M t. From above it can be shown (HW)

( ) ( ) ( ) 0. Conservation of Energy & Poynting Theorem. From Maxwell s equations we have. M t. From above it can be shown (HW) 8 Conson o n & Ponn To Fo wll s quons w D B σ σ Fo bo n b sown (W) o s W w bo on o s l us n su su ul ow ns [W/ ] [W] su P su B W W 4 444 s W A A s V A A : W W R o n o so n n: [/s W] W W 4 44 9 W : W F

More information

a) mass inversely proportional b) force directly proportional

a) mass inversely proportional b) force directly proportional 1. Wht produces ccelertion? A orce 2. Wht is the reltionship between ccelertion nd ) mss inersely proportionl b) orce directly proportionl 3. I you he orce o riction, 30N, on n object, how much orce is

More information

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function

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

More information

UNIT 1 ONE-DIMENSIONAL MOTION GRAPHING AND MATHEMATICAL MODELING. Objectives

UNIT 1 ONE-DIMENSIONAL MOTION GRAPHING AND MATHEMATICAL MODELING. Objectives UNIT 1 ONE-DIMENSIONAL MOTION GRAPHING AND MATHEMATICAL MODELING Objeces To learn abou hree ways ha a physcs can descrbe moon along a sragh lne words, graphs, and mahemacal modelng. To acqure an nue undersandng

More information

PHYSICS 211 MIDTERM I 21 April 2004

PHYSICS 211 MIDTERM I 21 April 2004 PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of

More information

Introduction to Mechanics Practice using the Kinematics Equations

Introduction to Mechanics Practice using the Kinematics Equations Introduction to Mechnics Prctice using the Kinemtics Equtions Ln Sheridn De Anz College Jn 24, 2018 Lst time finished deriing the kinemtics equtions some problem soling prctice Oeriew using kinemtics equtions

More information

Physics 15 Second Hour Exam

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.

More information

First-order piecewise-linear dynamic circuits

First-order piecewise-linear dynamic circuits Frs-order pecewse-lnear dynamc crcus. Fndng he soluon We wll sudy rs-order dynamc crcus composed o a nonlnear resse one-por, ermnaed eher by a lnear capacor or a lnear nducor (see Fg.. Nonlnear resse one-por

More information

Properties of Logarithms. Solving Exponential and Logarithmic Equations. Properties of Logarithms. Properties of Logarithms. ( x)

Properties of Logarithms. Solving Exponential and Logarithmic Equations. Properties of Logarithms. Properties of Logarithms. ( x) Properies of Logrihms Solving Eponenil nd Logrihmic Equions Properies of Logrihms Produc Rule ( ) log mn = log m + log n ( ) log = log + log Properies of Logrihms Quoien Rule log m = logm logn n log7 =

More information

Introduction to LoggerPro

Introduction to LoggerPro Inroducion o LoggerPro Sr/Sop collecion Define zero Se d collecion prmeers Auoscle D Browser Open file Sensor seup window To sr d collecion, click he green Collec buon on he ool br. There is dely of second

More information

4.8 Improper Integrals

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

More information

4. Runge-Kutta Formula For Differential Equations. A. Euler Formula B. Runge-Kutta Formula C. An Example for Fourth-Order Runge-Kutta Formula

4. Runge-Kutta Formula For Differential Equations. A. Euler Formula B. Runge-Kutta Formula C. An Example for Fourth-Order Runge-Kutta Formula NCTU Deprme o Elecrcl d Compuer Egeerg Seor Course By Pro. Yo-Pg Ce. Ruge-Ku Formul For Derel Equos A. Euler Formul B. Ruge-Ku Formul C. A Emple or Four-Order Ruge-Ku Formul

More information

Chapter Lagrangian Interpolation

Chapter Lagrangian Interpolation Chaper 5.4 agrangan Inerpolaon Afer readng hs chaper you should be able o:. dere agrangan mehod of nerpolaon. sole problems usng agrangan mehod of nerpolaon and. use agrangan nerpolans o fnd deraes and

More information

4. Runge-Kutta Formula For Differential Equations

4. Runge-Kutta Formula For Differential Equations NCTU Deprme o Elecrcl d Compuer Egeerg 5 Sprg Course by Pro. Yo-Pg Ce. Ruge-Ku Formul For Derel Equos To solve e derel equos umerclly e mos useul ormul s clled Ruge-Ku ormul

More information

J i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes.

J i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes. umercal negraon of he dffuson equaon (I) Fne dfference mehod. Spaal screaon. Inernal nodes. R L V For hermal conducon le s dscree he spaal doman no small fne spans, =,,: Balance of parcles for an nernal

More information

Review: Transformations. Transformations - Viewing. Transformations - Modeling. world CAMERA OBJECT WORLD CSE 681 CSE 681 CSE 681 CSE 681

Review: Transformations. Transformations - Viewing. Transformations - Modeling. world CAMERA OBJECT WORLD CSE 681 CSE 681 CSE 681 CSE 681 Revew: Trnsforons Trnsforons Modelng rnsforons buld cople odels b posonng (rnsforng sple coponens relve o ech oher ewng rnsforons plcng vrul cer n he world rnsforon fro world coordnes o cer coordnes Perspecve

More information

Uniform Circular Motion

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

More information

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 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

More information

Modeling and Predicting Sequences: HMM and (may be) CRF. Amr Ahmed Feb 25

Modeling and Predicting Sequences: HMM and (may be) CRF. Amr Ahmed Feb 25 Modelg d redcg Sequeces: HMM d m be CRF Amr Ahmed 070 Feb 25 Bg cure redcg Sgle Lbel Ipu : A se of feures: - Bg of words docume - Oupu : Clss lbel - Topc of he docume - redcg Sequece of Lbels Noo Noe:

More information

e t dt e t dt = lim e t dt T (1 e T ) = 1

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

More information

Motion. Acceleration. Part 2: Constant Acceleration. October Lab Phyiscs. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.

Motion. Acceleration. Part 2: Constant Acceleration. October Lab Phyiscs. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration. Motion ccelertion Prt : Constnt ccelertion ccelertion ccelertion ccelertion is the rte of chnge of elocity. = - o t = Δ Δt ccelertion = = - o t chnge of elocity elpsed time ccelertion is ector, lthough

More information

CHAPTER 2 Quick Quizzes

CHAPTER 2 Quick Quizzes CHAPTER Quck Quzzes (a) 00 yd (b) 0 (c) 0 (a) False The car may be slowng down, so ha he drecon o s acceleraon s oppose he drecon o s elocy (b) True I he elocy s n he drecon chosen as negae, a pose acceleraon

More information

Version 001 test-1 swinney (57010) 1. is constant at m/s.

Version 001 test-1 swinney (57010) 1. is constant at m/s. Version 001 es-1 swinne (57010) 1 This prin-ou should hve 20 quesions. Muliple-choice quesions m coninue on he nex column or pge find ll choices before nswering. CubeUniVec1x76 001 10.0 poins Acubeis1.4fee

More information

PHUN. Phy 521 2/10/2011. What is physics. Kinematics. Physics is. Section 2 1: Picturing Motion

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

More information

t s (half of the total time in the air) d?

t s (half of the total time in the air) d? .. In Cl or Homework Eercie. An Olmpic long jumper i cpble of jumping 8.0 m. Auming hi horizonl peed i 9.0 m/ he lee he ground, how long w he in he ir nd how high did he go? horizonl? 8.0m 9.0 m / 8.0

More information

Physics 100: Lecture 1

Physics 100: Lecture 1 Physics : Lecure Agen for Toy Aice Scope of his course Mesuremen n Unis Funmenl unis Sysems of unis Conering beween sysems of unis Dimensionl Anlysis -D Kinemics (reiew) Aerge & insnneous elociy n ccelerion

More information

Chapter Simpson s 1/3 Rule of Integration. ( x)

Chapter Simpson s 1/3 Rule of Integration. ( x) Cper 7. Smpso s / Rule o Iegro Aer redg s per, you sould e le o. derve e ormul or Smpso s / rule o egro,. use Smpso s / rule o solve egrls,. develop e ormul or mulple-segme Smpso s / rule o egro,. use

More information

Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis 2/3/2007 Physics 253

Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis   2/3/2007 Physics 253 Science Adeisemen Inegoenmenl Pnel on Clime Chnge: The Phsicl Science Bsis hp://www.ipcc.ch/spmfeb7.pdf /3/7 Phsics 53 hp://www.fonews.com/pojecs/pdf/spmfeb7.pdf /3/7 Phsics 53 3 Sus: Uni, Chpe 3 Vecos

More information

T h e C S E T I P r o j e c t

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

More information

a = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114

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

More information

Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!

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

More information

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 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

More information

1. Six acceleration vectors are shown for the car whose velocity vector is directed forward. For each acceleration vector describe in words the

1. Six acceleration vectors are shown for the car whose velocity vector is directed forward. For each acceleration vector describe in words the Si ccelerio ecors re show for he cr whose eloci ecor is direced forwrd For ech ccelerio ecor describe i words he iseous moio of he cr A ri eers cured horizol secio of rck speed of 00 km/h d slows dow wih

More information

Including the ordinary differential of distance with time as velocity makes a system of ordinary differential equations.

Including the ordinary differential of distance with time as velocity makes a system of ordinary differential equations. Soluons o Ordnary Derenal Equaons An ordnary derenal equaon has only one ndependen varable. A sysem o ordnary derenal equaons consss o several derenal equaons each wh he same ndependen varable. An eample

More information

Physics 201 Lecture 4

Physics 201 Lecture 4 Phscs 1 Lectue 4 ltoda: hapte 3 Lectue 4 v Intoduce scalas and vectos v Peom basc vecto aleba (addton and subtacton) v Inteconvet between atesan & Pola coodnates Stat n nteestn 1D moton poblem: ace 9.8

More information

Believethatyoucandoitandyouar. Mathematics. ngascannotdoonlynotyetbelieve thatyoucandoitandyouarehalfw. Algebra

Believethatyoucandoitandyouar. Mathematics. ngascannotdoonlynotyetbelieve thatyoucandoitandyouarehalfw. Algebra Believethtoucndoitndour ehlfwtherethereisnosuchthi Mthemtics ngscnnotdoonlnotetbelieve thtoucndoitndourehlfw Alger therethereisnosuchthingsc nnotdoonlnotetbelievethto Stge 6 ucndoitndourehlfwther S Cooper

More information

s in boxe wers ans Put

s in boxe wers ans Put Pu answers in boxes Main Ideas in Class Toda Inroducion o Falling Appl Old Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs

More information

Wave Phenomena Physics 15c

Wave Phenomena Physics 15c Wv hnon hyscs 5c cur 4 Coupl Oscllors! H& con 4. Wh W D s T " u forc oscllon " olv h quon of oon wh frcon n foun h sy-s soluon " Oscllon bcos lr nr h rsonnc frquncy " hs chns fro 0 π/ π s h frquncy ncrss

More information

Logarithms. Logarithm is another word for an index or power. POWER. 2 is the power to which the base 10 must be raised to give 100.

Logarithms. Logarithm is another word for an index or power. POWER. 2 is the power to which the base 10 must be raised to give 100. Logrithms. Logrithm is nother word for n inde or power. THIS IS A POWER STATEMENT BASE POWER FOR EXAMPLE : We lred know tht; = NUMBER 10² = 100 This is the POWER Sttement OR 2 is the power to which the

More information

Mechanics Physics 151

Mechanics Physics 151 Mechancs Physcs 5 Lecure 0 Canoncal Transformaons (Chaper 9) Wha We Dd Las Tme Hamlon s Prncple n he Hamlonan formalsm Dervaon was smple δi δ Addonal end-pon consrans pq H( q, p, ) d 0 δ q ( ) δq ( ) δ

More information

Physics 201, Lecture 5

Physics 201, Lecture 5 Phsics 1 Lecue 5 Tod s Topics n Moion in D (Chp 4.1-4.3): n D Kinemicl Quniies (sec. 4.1) n D Kinemics wih Consn Acceleion (sec. 4.) n D Pojecile (Sec 4.3) n Epeced fom Peiew: n Displcemen eloci cceleion

More information

Released Assessment Questions, 2017 QUESTIONS

Released Assessment Questions, 2017 QUESTIONS Relese Assessmen Quesions, 17 QUESTIONS Gre 9 Assessmen of Mhemis Aemi Re he insruions elow. Along wih his ookle, mke sure ou hve he Answer Bookle n he Formul Shee. You m use n spe in his ook for rough

More information

Lecture 18: The Laplace Transform (See Sections and 14.7 in Boas)

Lecture 18: The Laplace Transform (See Sections and 14.7 in Boas) Lecure 8: The Lalace Transform (See Secons 88- and 47 n Boas) Recall ha our bg-cure goal s he analyss of he dfferenal equaon, ax bx cx F, where we emloy varous exansons for he drvng funcon F deendng on

More information

The ray paths and travel times for multiple layers can be computed using ray-tracing, as demonstrated in Lab 3.

The ray paths and travel times for multiple layers can be computed using ray-tracing, as demonstrated in Lab 3. C. Trael me cures for mulple reflecors The ray pahs ad rael mes for mulple layers ca be compued usg ray-racg, as demosraed Lab. MATLAB scrp reflec_layers_.m performs smple ray racg. (m) ref(ms) ref(ms)

More information

P-Convexity Property in Musielak-Orlicz Function Space of Bohner Type

P-Convexity Property in Musielak-Orlicz Function Space of Bohner Type J N Sce & Mh Res Vol 3 No (7) -7 Alble ole h://orlwlsogocd/deh/sr P-Coey Proery Msel-Orlcz Fco Sce o Boher ye Yl Rodsr Mhecs Edco Deree Fcly o Ss d echology Uerss sl Neger Wlsogo Cerl Jdoes Absrcs Corresodg

More information

DEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL

DEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL DEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL Sco Wsdom, John Hershey 2, Jonahan Le Roux 2, and Shnj Waanabe 2 Deparmen o Elecrcal Engneerng, Unversy o Washngon, Seale, WA, USA

More information

Chapter 3 Kinematics in Two Dimensions

Chapter 3 Kinematics in Two Dimensions Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Two-dimensional moion includes objecs which are moing in wo direcions a he same ime, such as a projecile, which has boh horizonal and erical moion. These wo

More information

CS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4

CS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4 CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped

More information

THE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS

THE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS THE PREICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS INTROUCTION The wo dmensonal paral dfferenal equaons of second order can be used for he smulaon of compeve envronmen n busness The arcle presens he

More information

OP = OO' + Ut + Vn + Wb. Material We Will Cover Today. Computer Vision Lecture 3. Multi-view Geometry I. Amnon Shashua

OP = OO' + Ut + Vn + Wb. Material We Will Cover Today. Computer Vision Lecture 3. Multi-view Geometry I. Amnon Shashua Comuer Vson 27 Lecure 3 Mul-vew Geomer I Amnon Shashua Maeral We Wll Cover oa he srucure of 3D->2D rojecon mar omograh Marces A rmer on rojecve geomer of he lane Eolar Geomer an Funamenal Mar ebrew Unvers

More information

[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5

[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5 TPG460 Reservor Smulaon 08 page of 5 DISCRETIZATIO OF THE FOW EQUATIOS As we already have seen, fne dfference appromaons of he paral dervaves appearng n he flow equaons may be obaned from Taylor seres

More information

Scattering at an Interface: Oblique Incidence

Scattering at an Interface: Oblique Incidence Course Insrucor Dr. Raymond C. Rumpf Offce: A 337 Phone: (915) 747 6958 E Mal: rcrumpf@uep.edu EE 4347 Appled Elecromagnecs Topc 3g Scaerng a an Inerface: Oblque Incdence Scaerng These Oblque noes may

More information

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY [Mjuh, : Jury, 0] ISSN: -96 Scefc Jourl Impc Fcr: 9 ISRA, Impc Fcr: IJESRT INTERNATIONAL JOURNAL OF ENINEERIN SCIENCES & RESEARCH TECHNOLOY HAMILTONIAN LACEABILITY IN MIDDLE RAPHS Mjuh*, MurlR, B Shmukh

More information

Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( )

Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( ) Clculu 4, econ Lm/Connuy & Devve/Inel noe y Tm Plchow, wh domn o el Wh we hve o : veco-vlued uncon, ( ) ( ) ( ) j ( ) nume nd ne o veco The uncon, nd A w done wh eul uncon ( x) nd connuy e he componen

More information

Forms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics:

Forms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics: SPH4U: Inroducion o ork ork & Energy ork & Energy Discussion Definiion Do Produc ork of consn force ork/kineic energy heore ork of uliple consn forces Coens One of he os iporn conceps in physics Alernive

More information

Supporting information How to concatenate the local attractors of subnetworks in the HPFP

Supporting information How to concatenate the local attractors of subnetworks in the HPFP n Effcen lgorh for Idenfyng Prry Phenoype rcors of Lrge-Scle Boolen Newor Sng-Mo Choo nd Kwng-Hyun Cho Depren of Mhecs Unversy of Ulsn Ulsn 446 Republc of Kore Depren of Bo nd Brn Engneerng Kore dvnced

More information

Advanced time-series analysis (University of Lund, Economic History Department)

Advanced time-series analysis (University of Lund, Economic History Department) Advanced me-seres analss (Unvers of Lund, Economc Hsor Dearmen) 3 Jan-3 Februar and 6-3 March Lecure 4 Economerc echnues for saonar seres : Unvarae sochasc models wh Box- Jenns mehodolog, smle forecasng

More information

Variants of Pegasos. December 11, 2009

Variants of Pegasos. December 11, 2009 Inroducon Varans of Pegasos SooWoong Ryu bshboy@sanford.edu December, 009 Youngsoo Cho yc344@sanford.edu Developng a new SVM algorhm s ongong research opc. Among many exng SVM algorhms, we wll focus on

More information