Rectilinear Kinematics

Size: px
Start display at page:

Download "Rectilinear Kinematics"

Transcription

1 Recilinear Kinemaic Coninuou Moion Sir Iaac Newon Leonard Euler

2 Oeriew Kinemaic Coninuou Moion Erraic Moion Michael Schumacher. 7-ime Formula 1 World Champion

3 Kinemaic The objecie of kinemaic i o characerize he following properie of an objec a an inan during i in moion: Poiion Velociy acceleraion Sir Iaac Newon

4 Kinemaic Aumpion in kinemaic : he objec i negligible ize and hape (paricle) The ma i no conidered in he calculaion Roaion of he objec i negleced We hall look a he kinemaic of an objec moing in a raigh line. We call hi Recilinear Kinemaic

5 Recilinear Kinemaic: Coninuou Moion Conider a paricle in recilinear moion from a fixed origin O in he S direcion. O S Poiion For a gien inan, i he poiion coordinae of he paricle The magniude of i he diance from he origin (in fee, meer or he relean uni of meaure)

6 Recilinear Kinemaic: Coninuou Moion Noe ha he poiion coordinae would be negaie if he paricle raeled in he oppoie direcion according o our frame of reference Poiion i ha a magniude (diance from origin) and i baed on a pecific direcion. I i herefore a ecor quaniy

7 Coninuou Moion - Diplacemen Diplacemen i defined a he change in poiion O S Diplacemen

8 Coninuou Moion - Diplacemen Diplacemen i alo a ecor quaniy characerized by a magniude and a direcion Noe ha diance on he oher hand i a calar quaniy repreening he lengh from an origin. France Wale. Six Naion Cup. Lineou

9 Coninuou Moion Aerage Velociy If he paricle undergoe diplacemen oer a ime ineral hen he aerage elociy oer hi ime ineral ag O S Velociy

10 Coninuou Moion Inan. Velociy If we were o ake maller and maller alue of hen would alo ge maller and maller. A ome poin would no longer be an ineral bu a poin in he ime dimenion (inan). The aociaed elociy i called he inananeou elociy

11 Coninuou Moion Inan. Velociy By definiion, inananeou elociy lim 0 Alernaely repreened a d d (1) Ye Roy. Rockeman

12 Coninuou Moion Velociy Velociy i a ecor quaniy If we had moed o he lef, he elociy would be a negaie alue The magniude of he elociy i called peed The uni of elociy (and peed) include f/, mph (mile per hour), m/, kph (kilomeer per hour)

13 Coninuou Moion Aerage Speed Aerage peed i a poiie calar alue defined a he oal diance diided by he ime elaped p ag T Pi Sop. McClaren Mercede Team, Formula 1

14 Coninuou Moion Aerage Speed Conider he following moion ha occur oer a ime ineral P P S O Aerage elociy eru aerage peed T T bu p ag ag

15 Coninuou Moion - Acceleraion If he elociy a wo inance i known hen can obain he aerage acceleraion of he objec during he ime ineral a a ag a O Acceleraion S

16 Coninuou Moion - Acceleraion If we reduce o an infinieimally mall ineral (aka inan), we ge he inananeou acceleraion a d lim or a () 0 d We can ee ha acceleraion i a ecor quaniy

17 Coninuou Moion - Acceleraion Commonly ued uni: f/, m/, ec Subiuing Eqn () in Eqn (1); a d d d d d d From Eqn (1) and Eqn () if elociy i conan, hen a = 0 If <, hen we will hae a negaie alue of acceleraion. Thi i called deceleraion

18 Coninuou Moion - Acceleraion From Eqn (1) we can wrie d d From Eqn () d d a Equaing he aboe a d d (3) Galileo Galilei

19 Equaion of Moion: Under Conan Conider he following: Acceleraion our acceleraion o be conan, i.e. a = a c a = 0, = 0, and = 0 From Eqn () a c d d Rearranging and inegraing 0 d 0 a c d

20 Moion Under Conan Acceleraion Soling he definie inegral, we obain elociy a a funcion of ime: 0 ac (4) Subiuing Eqn (4) ino Eqn (1) 0 d 0 d d 0 0 a a c c d

21 Moion Under Conan Acceleraion we obain poiion a a funcion of ime: ac We can rearrange Eqn (4) a and ubiue in Eqn (5) 0 a c (5)

22 Moion Under Conan Acceleraion We obain elociy a a funcion of poiion 0 ac (6) 0 Apollo 11 Launch

23 Example How Did Tha Go?

24 Joeph Loui Lagrange Recilinear Kinemaic Erraic Moion

25 Oeriew Erraic Moion Graphical approach Sample problem Rober H. Goddard (196) Rocke pioneer

26 Erraic Moion When he moion of an objec i erraic, we canno ue he ingle coninuou funcion o decribe i kinemaic In oher word he acceleraion i no conan Serie of funcion hae o be ued o pecify he moion oer differen ime ineral In general graph are ued o faciliae he calculaion Pierre-Simon Laplace

27 Velociy = Slope of graph a ime d d 1 d d 1 d d 3 d d 3 Beijing, PRC 0 0 d d O 1 3 O 1 3 3

28 Acceleraion = Slope of graph a ime d d a a 1 d d 1 a d d a 3 d d 3 3 a Cro Counry Race, MN a 0 d d 0 O a 0 = 0 a 1 a a 3 1 3

29 Change in elociy from a graph a d a d d a d a d a 0 O 1 a d O 1

30 Diplacemen from graph d d d d d 0 O 1 d O 1

31 Graph of & a (Velociy) a d d a d d a d a a d O a 0 1 O 1 1 0

32 Graph of & a (Acceleraion) a d d a d d a d d 0 a 0 d a d O O

33 Example How Did Tha Go?

Phys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole

Phys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole Phys 221 Fall 2014 Chaper 2 Moion in One Dimension 2014, 2005 A. Dzyubenko 2004 Brooks/Cole 1 Kinemaics Kinemaics, a par of classical mechanics: Describes moion in erms of space and ime Ignores he agen

More information

Motion In One Dimension. Graphing Constant Speed

Motion In One Dimension. Graphing Constant Speed Moion In One Dimenion PLATO AND ARISTOTLE GALILEO GALILEI LEANING TOWER OF PISA Graphing Conan Speed Diance v. Time for Toy Car (0-5 ec.) be-fi line (from TI calculaor) d = 207.7 12.6 Diance (cm) 1000

More information

PHYSICS 151 Notes for Online Lecture #4

PHYSICS 151 Notes for Online Lecture #4 PHYSICS 5 Noe for Online Lecure #4 Acceleraion The ga pedal in a car i alo called an acceleraor becaue preing i allow you o change your elociy. Acceleraion i how fa he elociy change. So if you ar fro re

More information

Equations of motion for constant acceleration

Equations of motion for constant acceleration Lecure 3 Chaper 2 Physics I 01.29.2014 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1spring.hml

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

TP B.2 Rolling resistance, spin resistance, and "ball turn"

TP B.2 Rolling resistance, spin resistance, and ball turn echnical proof TP B. olling reiance, pin reiance, and "ball urn" upporing: The Illuraed Principle of Pool and Billiard hp://billiard.coloae.edu by Daid G. Alciaore, PhD, PE ("Dr. Dae") echnical proof originally

More information

Discussion Session 2 Constant Acceleration/Relative Motion Week 03

Discussion Session 2 Constant Acceleration/Relative Motion Week 03 PHYS 100 Dicuion Seion Conan Acceleraion/Relaive Moion Week 03 The Plan Today you will work wih your group explore he idea of reference frame (i.e. relaive moion) and moion wih conan acceleraion. You ll

More information

One-Dimensional Kinematics

One-Dimensional Kinematics One-Dimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3-dimension world, moion can ofen be absraced o a single dimension. We can also describe moion

More information

Physics 101: Lecture 03 Kinematics Today s lecture will cover Textbook Sections (and some Ch. 4)

Physics 101: Lecture 03 Kinematics Today s lecture will cover Textbook Sections (and some Ch. 4) Physics 101: Lecure 03 Kinemaics Today s lecure will coer Texbook Secions 3.1-3.3 (and some Ch. 4) Physics 101: Lecure 3, Pg 1 A Refresher: Deermine he force exered by he hand o suspend he 45 kg mass as

More information

Linear Motion, Speed & Velocity

Linear Motion, Speed & Velocity Add Iporan Linear Moion, Speed & Velociy Page: 136 Linear Moion, Speed & Velociy NGSS Sandard: N/A MA Curriculu Fraework (2006): 1.1, 1.2 AP Phyic 1 Learning Objecive: 3.A.1.1, 3.A.1.3 Knowledge/Underanding

More information

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3 A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 1-3 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew:

More information

INSTANTANEOUS VELOCITY

INSTANTANEOUS VELOCITY INSTANTANEOUS VELOCITY I claim ha ha if acceleraion is consan, hen he elociy is a linear funcion of ime and he posiion a quadraic funcion of ime. We wan o inesigae hose claims, and a he same ime, work

More information

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance Ch: Moion along a sraigh line Moion Posiion and Displacemen Average Velociy and Average Speed Insananeous Velociy and Speed Acceleraion Consan Acceleraion: A Special Case Anoher Look a Consan Acceleraion

More information

Physics for Scientists and Engineers. Chapter 2 Kinematics in One Dimension

Physics for Scientists and Engineers. Chapter 2 Kinematics in One Dimension Physics for Scieniss and Engineers Chaper Kinemaics in One Dimension Spring, 8 Ho Jung Paik Kinemaics Describes moion while ignoring he agens (forces) ha caused he moion For now, will consider moion in

More information

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still. Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in

More information

Chapter 12: Velocity, acceleration, and forces

Chapter 12: Velocity, acceleration, and forces To Feel a Force Chaper Spring, Chaper : A. Saes of moion For moion on or near he surface of he earh, i is naural o measure moion wih respec o objecs fixed o he earh. The 4 hr. roaion of he earh has a measurable

More information

Kinematics in two dimensions

Kinematics in two dimensions Lecure 5 Phsics I 9.18.13 Kinemaics in wo dimensions Course websie: hp://facul.uml.edu/andri_danlo/teaching/phsicsi Lecure Capure: hp://echo36.uml.edu/danlo13/phsics1fall.hml 95.141, Fall 13, Lecure 5

More information

Math 2214 Solution Test 1 B Spring 2016

Math 2214 Solution Test 1 B Spring 2016 Mah 14 Soluion Te 1 B Spring 016 Problem 1: Ue eparaion of ariable o ole he Iniial alue DE Soluion (14p) e =, (0) = 0 d = e e d e d = o = ln e d uing u-du b leing u = e 1 e = + where C = for he iniial

More information

Course II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle

Course II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle Course II Lesson 7 Applicaions o Physics 7A Velociy and Acceleraion of a Paricle Moion in a Sraigh Line : Velociy O Aerage elociy Moion in he -ais + Δ + Δ 0 0 Δ Δ Insananeous elociy d d Δ Δ Δ 0 lim [ m/s

More information

Ground Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan

Ground Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure

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

Brock University Physics 1P21/1P91 Fall 2013 Dr. D Agostino. Solutions for Tutorial 3: Chapter 2, Motion in One Dimension

Brock University Physics 1P21/1P91 Fall 2013 Dr. D Agostino. Solutions for Tutorial 3: Chapter 2, Motion in One Dimension Brock Uniersiy Physics 1P21/1P91 Fall 2013 Dr. D Agosino Soluions for Tuorial 3: Chaper 2, Moion in One Dimension The goals of his uorial are: undersand posiion-ime graphs, elociy-ime graphs, and heir

More information

Topic 1: Linear motion and forces

Topic 1: Linear motion and forces TOPIC 1 Topic 1: Linear moion and forces 1.1 Moion under consan acceleraion Science undersanding 1. Linear moion wih consan elociy is described in erms of relaionships beween measureable scalar and ecor

More information

2. VECTORS. R Vectors are denoted by bold-face characters such as R, V, etc. The magnitude of a vector, such as R, is denoted as R, R, V

2. VECTORS. R Vectors are denoted by bold-face characters such as R, V, etc. The magnitude of a vector, such as R, is denoted as R, R, V ME 352 VETS 2. VETS Vecor algebra form he mahemaical foundaion for kinemaic and dnamic. Geomer of moion i a he hear of boh he kinemaic and dnamic of mechanical em. Vecor anali i he imehonored ool for decribing

More information

Curvature. Institute of Lifelong Learning, University of Delhi pg. 1

Curvature. Institute of Lifelong Learning, University of Delhi pg. 1 Dicipline Coure-I Semeer-I Paper: Calculu-I Leon: Leon Developer: Chaianya Kumar College/Deparmen: Deparmen of Mahemaic, Delhi College of r and Commerce, Univeriy of Delhi Iniue of Lifelong Learning, Univeriy

More information

EF 151 Exam #2 - Spring, 2014 Page 1 of 6

EF 151 Exam #2 - Spring, 2014 Page 1 of 6 EF 5 Exam # - Spring, 04 Page of 6 Name: Secion: Inrucion: Pu your name and ecion on he exam. Do no open he e unil you are old o do o. Wrie your final anwer in he box proided If you finih wih le han 5

More information

1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a

1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a Kinemaics Paper 1 1. The graph below shows he ariaion wih ime of he acceleraion a of an objec from = o = T. a T The shaded area under he graph represens change in A. displacemen. B. elociy. C. momenum.

More information

NEWTON S SECOND LAW OF MOTION

NEWTON S SECOND LAW OF MOTION Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during

More information

MODEL PAPER 2 PHYSICS. I PUC Time: 3 hours Max Marks: 70

MODEL PAPER 2 PHYSICS. I PUC Time: 3 hours Max Marks: 70 MODEL PAPE PHYSICS I PUC Time: hour Ma Mark: 7 General Inrucion: i) All par are compulory. ii) Anwer wihou relean diagram / figure/ circui whereer neceary will no carry any mark. iii) Direc anwer o he

More information

KINEMATICS IN ONE DIMENSION

KINEMATICS IN ONE DIMENSION KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec

More information

Welcome Back to Physics 215!

Welcome Back to Physics 215! Welcome Back o Physics 215! (General Physics I) Thurs. Jan 19 h, 2017 Lecure01-2 1 Las ime: Syllabus Unis and dimensional analysis Today: Displacemen, velociy, acceleraion graphs Nex ime: More acceleraion

More information

Q2.4 Average velocity equals instantaneous velocity when the speed is constant and motion is in a straight line.

Q2.4 Average velocity equals instantaneous velocity when the speed is constant and motion is in a straight line. CHAPTER MOTION ALONG A STRAIGHT LINE Discussion Quesions Q. The speedomeer measures he magniude of he insananeous eloci, he speed. I does no measure eloci because i does no measure direcion. Q. Graph (d).

More information

LAB # 2 - Equilibrium (static)

LAB # 2 - Equilibrium (static) AB # - Equilibrium (saic) Inroducion Isaac Newon's conribuion o physics was o recognize ha despie he seeming compleiy of he Unierse, he moion of is pars is guided by surprisingly simple aws. Newon's inspiraion

More information

Angular Motion, Speed and Velocity

Angular Motion, Speed and Velocity Add Imporan Angular Moion, Speed and Velociy Page: 163 Noe/Cue Here Angular Moion, Speed and Velociy NGSS Sandard: N/A MA Curriculum Framework (006): 1.1, 1. AP Phyic 1 Learning Objecive: 3.A.1.1, 3.A.1.3

More information

13.1 Accelerating Objects

13.1 Accelerating Objects 13.1 Acceleraing Objec A you learned in Chaper 12, when you are ravelling a a conan peed in a raigh line, you have uniform moion. However, mo objec do no ravel a conan peed in a raigh line o hey do no

More information

4.5 Constant Acceleration

4.5 Constant Acceleration 4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x -componen of he velociy is a linear funcion (Figure 4.8(a)),

More information

Displacement ( x) x x x

Displacement ( x) x x x Kinemaics Kinemaics is he branch of mechanics ha describes he moion of objecs wihou necessarily discussing wha causes he moion. 1-Dimensional Kinemaics (or 1- Dimensional moion) refers o moion in a sraigh

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

Kinematics. introduction to kinematics 15A

Kinematics. introduction to kinematics 15A 15 15A Inroducion o kinemaics 15B Velociy ime graphs and acceleraion ime graphs 15C Consan acceleraion formulas 15D Insananeous raes of change Kinemaics AreAS of STuDy Diagrammaic and graphical represenaion

More information

AP Calculus BC Chapter 10 Part 1 AP Exam Problems

AP Calculus BC Chapter 10 Part 1 AP Exam Problems AP Calculus BC Chaper Par AP Eam Problems All problems are NO CALCULATOR unless oherwise indicaed Parameric Curves and Derivaives In he y plane, he graph of he parameric equaions = 5 + and y= for, is a

More information

Buckling of a structure means failure due to excessive displacements (loss of structural stiffness), and/or

Buckling of a structure means failure due to excessive displacements (loss of structural stiffness), and/or Buckling Buckling of a rucure mean failure due o exceive diplacemen (lo of rucural iffne), and/or lo of abiliy of an equilibrium configuraion of he rucure The rule of humb i ha buckling i conidered a mode

More information

Physics 240: Worksheet 16 Name

Physics 240: Worksheet 16 Name Phyic 4: Workhee 16 Nae Non-unifor circular oion Each of hee proble involve non-unifor circular oion wih a conan α. (1) Obain each of he equaion of oion for non-unifor circular oion under a conan acceleraion,

More information

Lecture 4 Kinetics of a particle Part 3: Impulse and Momentum

Lecture 4 Kinetics of a particle Part 3: Impulse and Momentum MEE Engineering Mechanics II Lecure 4 Lecure 4 Kineics of a paricle Par 3: Impulse and Momenum Linear impulse and momenum Saring from he equaion of moion for a paricle of mass m which is subjeced o an

More information

1. VELOCITY AND ACCELERATION

1. VELOCITY AND ACCELERATION 1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under

More information

!!"#"$%&#'()!"#&'(*%)+,&',-)./0)1-*23)

!!#$%&#'()!#&'(*%)+,&',-)./0)1-*23) "#"$%&#'()"#&'(*%)+,&',-)./)1-*) #$%&'()*+,&',-.%,/)*+,-&1*#$)()5*6$+$%*,7&*-'-&1*(,-&*6&,7.$%$+*&%'(*8$&',-,%'-&1*(,-&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',-9*(&,%)?%*,('&5

More information

Kinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.

Kinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8. Kinemaics Vocabulary Kinemaics and One Dimensional Moion 8.1 WD1 Kinema means movemen Mahemaical descripion of moion Posiion Time Inerval Displacemen Velociy; absolue value: speed Acceleraion Averages

More information

u(t) Figure 1. Open loop control system

u(t) Figure 1. Open loop control system Open loop conrol v cloed loop feedbac conrol The nex wo figure preen he rucure of open loop and feedbac conrol yem Figure how an open loop conrol yem whoe funcion i o caue he oupu y o follow he reference

More information

Mechanics Acceleration The Kinematics Equations

Mechanics Acceleration The Kinematics Equations Mechanics Acceleraion The Kinemaics Equaions Lana Sheridan De Anza College Sep 27, 2018 Las ime kinemaic quaniies graphs of kinemaic quaniies Overview acceleraion he kinemaics equaions (consan acceleraion)

More information

IB Physics Kinematics Worksheet

IB Physics Kinematics Worksheet IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?

More information

Algorithms and Data Structures 2011/12 Week 9 Solutions (Tues 15th - Fri 18th Nov)

Algorithms and Data Structures 2011/12 Week 9 Solutions (Tues 15th - Fri 18th Nov) Algorihm and Daa Srucure 2011/ Week Soluion (Tue 15h - Fri 18h No) 1. Queion: e are gien 11/16 / 15/20 8/13 0/ 1/ / 11/1 / / To queion: (a) Find a pair of ube X, Y V uch ha f(x, Y) = f(v X, Y). (b) Find

More information

Energy Problems 9/3/2009. W F d mgh m s 196J 200J. Understanding. Understanding. Understanding. W F d. sin 30

Energy Problems 9/3/2009. W F d mgh m s 196J 200J. Understanding. Understanding. Understanding. W F d. sin 30 9/3/009 nderanding Energy Proble Copare he work done on an objec o a.0 kg a) In liing an objec 0.0 b) Puhing i up a rap inclined a 30 0 o he ae inal heigh 30 0 puhing 0.0 liing nderanding Copare he work

More information

Two Dimensional Dynamics

Two Dimensional Dynamics Physics 11: Lecure 6 Two Dimensional Dynamics Today s lecure will coer Chaper 4 Saring Wed Sep 15, W-F oice hours will be in 3 Loomis. Exam I M oice hours will coninue in 36 Loomis Physics 11: Lecure 6,

More information

Chapter 2. Motion along a straight line

Chapter 2. Motion along a straight line Chaper Moion along a sraigh line Kinemaics & Dynamics Kinemaics: Descripion of Moion wihou regard o is cause. Dynamics: Sudy of principles ha relae moion o is cause. Basic physical ariables in kinemaics

More information

Network Flow. Data Structures and Algorithms Andrei Bulatov

Network Flow. Data Structures and Algorithms Andrei Bulatov Nework Flow Daa Srucure and Algorihm Andrei Bulao Algorihm Nework Flow 24-2 Flow Nework Think of a graph a yem of pipe We ue hi yem o pump waer from he ource o ink Eery pipe/edge ha limied capaciy Flow

More information

Differential Geometry: Revisiting Curvatures

Differential Geometry: Revisiting Curvatures Differenial Geomery: Reisiing Curaures Curaure and Graphs Recall: hus, up o a roaion in he x-y plane, we hae: f 1 ( x, y) x y he alues 1 and are he principal curaures a p and he corresponding direcions

More information

PROBLEMS ON RECTILINEAR MOTION

PROBLEMS ON RECTILINEAR MOTION PROBLEMS ON RECTILINEAR MOTION PROBLEM 1. The elociy of a paricle which oe along he -ai i gien by 5 (/). Ealuae he diplaceen elociy and acceleraion a when = 4. The paricle i a he origin = when =. (/) /

More information

Introduction. If there are no physical guides, the motion is said to be unconstrained. Example 2. - Airplane, rocket

Introduction. If there are no physical guides, the motion is said to be unconstrained. Example 2. - Airplane, rocket Kinemaic f Paricle Chaper Inrducin Kinemaic: i he branch f dynamic which decribe he min f bdie wihu reference he frce ha eiher caue he min r are generaed a a reul f he min. Kinemaic i fen referred a he

More information

total distance cov ered time int erval v = average speed (m/s)

total distance cov ered time int erval v = average speed (m/s) Physics Suy Noes Lesson 4 Linear Moion 1 Change an Moion a. A propery common o eeryhing in he unierse is change. b. Change is so imporan ha he funamenal concep of ime woul be meaningless wihou i. c. Since

More information

Physics Unit Workbook Two Dimensional Kinematics

Physics Unit Workbook Two Dimensional Kinematics Name: Per: L o s A l o s H i g h S c h o o l Phsics Uni Workbook Two Dimensional Kinemaics Mr. Randall 1968 - Presen adam.randall@mla.ne www.laphsics.com a o 1 a o o ) ( o o a o o ) ( 1 1 a o g o 1 g o

More information

Physics for Scientists and Engineers I

Physics for Scientists and Engineers I Physics for Scieniss and Engineers I PHY 48, Secion 4 Dr. Beariz Roldán Cuenya Universiy of Cenral Florida, Physics Deparmen, Orlando, FL Chaper - Inroducion I. General II. Inernaional Sysem of Unis III.

More information

Kinematics in two Dimensions

Kinematics in two Dimensions Lecure 5 Chaper 4 Phsics I Kinemaics in wo Dimensions Course websie: hp://facul.uml.edu/andri_danlo/teachin/phsicsi PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics Toda we are oin o discuss:

More information

Kinematics Motion in 1 Dimension and Graphs

Kinematics Motion in 1 Dimension and Graphs Kinemaics Moion in 1 Dimension and Graphs Lana Sheridan De Anza College Sep 27, 2017 Las ime moion in 1-dimension some kinemaic quaniies graphs Overview velociy and speed acceleraion more graphs Kinemaics

More information

Chapter 2: One-Dimensional Kinematics

Chapter 2: One-Dimensional Kinematics Chaper : One-Dimensional Kinemaics Answers o Een-Numbered Concepual Quesions. An odomeer measures he disance raeled by a car. You can ell his by he fac ha an odomeer has a nonzero reading afer a round

More information

x(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp-03 Page 1 of 4

x(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp-03 Page 1 of 4 Homework #2. Ph 231 Inroducory Physics, Sp-03 Page 1 of 4 2-1A. A person walks 2 miles Eas (E) in 40 minues and hen back 1 mile Wes (W) in 20 minues. Wha are her average speed and average velociy (in ha

More information

Two Dimensional Dynamics

Two Dimensional Dynamics Physics 11: Lecure 6 Two Dimensional Dynamics Today s lecure will coer Chaper 4 Exam I Physics 11: Lecure 6, Pg 1 Brie Reiew Thus Far Newon s Laws o moion: SF=ma Kinemaics: x = x + + ½ a Dynamics Today

More information

Integration of the equation of motion with respect to time rather than displacement leads to the equations of impulse and momentum.

Integration of the equation of motion with respect to time rather than displacement leads to the equations of impulse and momentum. Inegraion of he equaion of moion wih respec o ime raher han displacemen leads o he equaions of impulse and momenum. These equaions greal faciliae he soluion of man problems in which he applied forces ac

More information

Laplace Transform. Inverse Laplace Transform. e st f(t)dt. (2)

Laplace Transform. Inverse Laplace Transform. e st f(t)dt. (2) Laplace Tranform Maoud Malek The Laplace ranform i an inegral ranform named in honor of mahemaician and aronomer Pierre-Simon Laplace, who ued he ranform in hi work on probabiliy heory. I i a powerful

More information

Parametrics and Vectors (BC Only)

Parametrics and Vectors (BC Only) Paramerics and Vecors (BC Only) The following relaionships should be learned and memorized. The paricle s posiion vecor is r() x(), y(). The velociy vecor is v(),. The speed is he magniude of he velociy

More information

Homework 2: Kinematics and Dynamics of Particles Due Friday Feb 8, 2019

Homework 2: Kinematics and Dynamics of Particles Due Friday Feb 8, 2019 EN4: Dynamics and Vibraions Homework : Kinemaics and Dynamics of Paricles Due Friday Feb 8, 19 School of Engineering Brown Universiy 1. Sraigh Line Moion wih consan acceleraion. Virgin Hyperloop One is

More information

Chapter 8 Torque and Angular Momentum

Chapter 8 Torque and Angular Momentum Chaper 8 Torque and Angular Moenu Reiew of Chaper 5 We had a able coparing paraeer fro linear and roaional oion. Today we fill in he able. Here i i Decripion Linear Roaional poiion diplaceen Rae of change

More information

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx

More information

EE Control Systems LECTURE 2

EE Control Systems LECTURE 2 Copyrigh F.L. Lewi 999 All righ reerved EE 434 - Conrol Syem LECTURE REVIEW OF LAPLACE TRANSFORM LAPLACE TRANSFORM The Laplace ranform i very ueful in analyi and deign for yem ha are linear and ime-invarian

More information

ū(e )(1 γ 5 )γ α v( ν e ) v( ν e )γ β (1 + γ 5 )u(e ) tr (1 γ 5 )γ α ( p ν m ν )γ β (1 + γ 5 )( p e + m e ).

ū(e )(1 γ 5 )γ α v( ν e ) v( ν e )γ β (1 + γ 5 )u(e ) tr (1 γ 5 )γ α ( p ν m ν )γ β (1 + γ 5 )( p e + m e ). PHY 396 K. Soluion for problem e #. Problem (a: A poin of noaion: In he oluion o problem, he indice µ, e, ν ν µ, and ν ν e denoe he paricle. For he Lorenz indice, I hall ue α, β, γ, δ, σ, and ρ, bu never

More information

Suggested Practice Problems (set #2) for the Physics Placement Test

Suggested Practice Problems (set #2) for the Physics Placement Test Deparmen of Physics College of Ars and Sciences American Universiy of Sharjah (AUS) Fall 014 Suggesed Pracice Problems (se #) for he Physics Placemen Tes This documen conains 5 suggesed problems ha are

More information

RECTILINEAR MOTION. Contents. Theory Exercise Exercise Exercise Exercise Answer Key

RECTILINEAR MOTION. Contents. Theory Exercise Exercise Exercise Exercise Answer Key RECTILINEAR MOTION Conens Topic Page No. Theory 01-01 Exercise - 1 0-09 Exercise - 09-14 Exercise - 3 15-17 Exercise - 4 17-0 Answer Key 1 - Syllabus Kinemaics in one dimension. Name : Conac No. ARRIDE

More information

EF 151 Exam #1, Spring, 2009 Page 1 of 6

EF 151 Exam #1, Spring, 2009 Page 1 of 6 EF 5 Exam #, Spring, 009 Page of 6 Name: Guideline: Aume 3 ignifican figure for all given number unle oherwie aed Show all of your work no work, no credi Wrie your final anwer in he box provided Include

More information

MEI Mechanics 1 General motion. Section 1: Using calculus

MEI Mechanics 1 General motion. Section 1: Using calculus Soluions o Exercise MEI Mechanics General moion Secion : Using calculus. s 4 v a 6 4 4 When =, v 4 a 6 4 6. (i) When = 0, s = -, so he iniial displacemen = - m. s v 4 When = 0, v = so he iniial velociy

More information

New View of Relativity Theory

New View of Relativity Theory Journal of Phyic: Conference Serie OPEN ACCESS New View of Relaiiy Theory To cie hi aricle: Luiz Cear Marini 4 J Phy: Conf Ser 495 View he aricle online for updae enhancemen Relaed conen - The Space-Time

More information

Physics 20 Lesson 5 Graphical Analysis Acceleration

Physics 20 Lesson 5 Graphical Analysis Acceleration Physics 2 Lesson 5 Graphical Analysis Acceleraion I. Insananeous Velociy From our previous work wih consan speed and consan velociy, we know ha he slope of a posiion-ime graph is equal o he velociy of

More information

Ch.1. Group Work Units. Continuum Mechanics Course (MMC) - ETSECCPB - UPC

Ch.1. Group Work Units. Continuum Mechanics Course (MMC) - ETSECCPB - UPC Ch.. Group Work Unis Coninuum Mechanics Course (MMC) - ETSECCPB - UPC Uni 2 Jusify wheher he following saemens are rue or false: a) Two sreamlines, corresponding o a same insan of ime, can never inersec

More information

Roller-Coaster Coordinate System

Roller-Coaster Coordinate System Winer 200 MECH 220: Mechanics 2 Roller-Coaser Coordinae Sysem Imagine you are riding on a roller-coaer in which he rack goes up and down, wiss and urns. Your velociy and acceleraion will change (quie abruply),

More information

Velocity is a relative quantity

Velocity is a relative quantity Veloci is a relaie quani Disenangling Coordinaes PHY2053, Fall 2013, Lecure 6 Newon s Laws 2 PHY2053, Fall 2013, Lecure 6 Newon s Laws 3 R. Field 9/6/2012 Uniersi of Florida PHY 2053 Page 8 Reference Frames

More information

where the coordinate X (t) describes the system motion. X has its origin at the system static equilibrium position (SEP).

where the coordinate X (t) describes the system motion. X has its origin at the system static equilibrium position (SEP). Appendix A: Conservaion of Mechanical Energy = Conservaion of Linear Momenum Consider he moion of a nd order mechanical sysem comprised of he fundamenal mechanical elemens: ineria or mass (M), siffness

More information

CHAPTER THREE MOTION IN A STRAIGHT LINE

CHAPTER THREE MOTION IN A STRAIGHT LINE PHYSICS Moion In ne Dimenion j k CHPTER THREE MTIN IN STRIGHT LINE. INTRDUCTIN Moion n objec i aid o be in moion, if i poiion chane wih repec o ime. Thi i relaed o he oberer. If i poiion i no chanin, he

More information

Review Equations. Announcements 9/8/09. Table Tennis

Review Equations. Announcements 9/8/09. Table Tennis Announcemens 9/8/09 1. Course homepage ia: phsics.bu.edu Class web pages Phsics 105 (Colon J). (Class-wide email sen) Iclicker problem from las ime scores didn ge recorded. Clicker quizzes from lecures

More information

Answers to 1 Homework

Answers to 1 Homework Answers o Homework. x + and y x 5 y To eliminae he parameer, solve for x. Subsiue ino y s equaion o ge y x.. x and y, x y x To eliminae he parameer, solve for. Subsiue ino y s equaion o ge x y, x. (Noe:

More information

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,

More information

Position, Velocity, and Acceleration

Position, Velocity, and Acceleration rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME-9493 1 Car ME-9454 1 Fan Accessory ME-9491 1 Moion Sensor II CI-6742A 1 Track Barrier Purpose The purpose

More information

Solution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration

Solution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration PHYS 54 Tes Pracice Soluions Spring 8 Q: [4] Knowing ha in he ne epression a is acceleraion, v is speed, is posiion and is ime, from a dimensional v poin of view, he equaion a is a) incorrec b) correc

More information

Kinematics in One Dimension

Kinematics in One Dimension Kinemaics in One Dimension PHY 7 - d-kinemaics - J. Hedberg - 7. Inroducion. Differen Types of Moion We'll look a:. Dimensionaliy in physics 3. One dimensional kinemaics 4. Paricle model. Displacemen Vecor.

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

PHYS 100: Lecture 2. Motion at Constant Acceleration. Relative Motion: Reference Frames. x Tortoise. Tortoise. d Achilles. Reference frame = Earth

PHYS 100: Lecture 2. Motion at Constant Acceleration. Relative Motion: Reference Frames. x Tortoise. Tortoise. d Achilles. Reference frame = Earth a PHYS 1: Lecure 2 Moion a Consan Acceleraion a Area = a a v = ad v v = a v x = vd A=(1/2)( v) Area = v v = v-v v x x = v + a 1 2 2 Relaive Moion: Reference Frames x d Achilles Toroise x Toroise Reference

More information

Chapter 15 Oscillatory Motion I

Chapter 15 Oscillatory Motion I Chaper 15 Oscillaory Moion I Level : AP Physics Insrucor : Kim Inroducion A very special kind of moion occurs when he force acing on a body is proporional o he displacemen of he body from some equilibrium

More information

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile

More information

3, so θ = arccos

3, so θ = arccos Mahemaics 210 Professor Alan H Sein Monday, Ocober 1, 2007 SOLUTIONS This problem se is worh 50 poins 1 Find he angle beween he vecors (2, 7, 3) and (5, 2, 4) Soluion: Le θ be he angle (2, 7, 3) (5, 2,

More information

A B C D September 25 Exam I Physics 105. Circle the letter of the single best answer. Each question is worth 1 point

A B C D September 25 Exam I Physics 105. Circle the letter of the single best answer. Each question is worth 1 point 2012 Sepember 25 Eam I Physics 105 Circle he leer of he single bes answer. Each uesion is worh 1 poin Physical Consans: Earh s free-fall acceleraion = g = 9.80 m/s 2 3. (Mark wo leers!) The below graph

More information

Single Phase Line Frequency Uncontrolled Rectifiers

Single Phase Line Frequency Uncontrolled Rectifiers Single Phae Line Frequency Unconrolle Recifier Kevin Gaughan 24-Nov-03 Single Phae Unconrolle Recifier 1 Topic Baic operaion an Waveform (nucive Loa) Power Facor Calculaion Supply curren Harmonic an Th

More information

AQA Maths M2. Topic Questions from Papers. Differential Equations. Answers

AQA Maths M2. Topic Questions from Papers. Differential Equations. Answers AQA Mahs M Topic Quesions from Papers Differenial Equaions Answers PhysicsAndMahsTuor.com Q Soluion Marks Toal Commens M 600 0 = A Applying Newonís second law wih 0 and. Correc equaion = 0 dm Separaing

More information

To become more mathematically correct, Circuit equations are Algebraic Differential equations. from KVL, KCL from the constitutive relationship

To become more mathematically correct, Circuit equations are Algebraic Differential equations. from KVL, KCL from the constitutive relationship Laplace Tranform (Lin & DeCarlo: Ch 3) ENSC30 Elecric Circui II The Laplace ranform i an inegral ranformaion. I ranform: f ( ) F( ) ime variable complex variable From Euler > Lagrange > Laplace. Hence,

More information