1. 0 m/s m/s m/s m/s
|
|
- Wendy Powell
- 7 years ago
- Views:
Transcription
1 Version PREVIEW Kine Grphs PRACTICE burke (1111) 1 This print-out should he 30 questions. Multiple-choice questions m continue on the next column or pge find ll choices before nswering. Distnce Time Grph (prt 1 of 6) 10.0 points Consider the following grph of motion. 50 Distnce (m) Time (sec) How fr did the object trel between 2 s nd 4 s? m m m m m Explntion: The prticle moed from 40 m to 20 m, so d = 40 m 20 m = 20 m. 002 (prt 2 of 6) 10.0 points The grph indictes 1. constnt elocit. 2. incresing elocit. 3. no motion. 4. decresing elocit. 5. constnt position. Explntion: The slope of the grph is the sme eerwhere, so the grph indictes constnt positie elocit. 003 (prt 3 of 6) 10.0 points Wht is the speed from 2 s to 4 s? 1. 0 m/s m/s m/s 4. 5 m/s m/s Explntion: = d t = 40 m 20 m 2 s = 10 m/s. 004 (prt 4 of 6) 10.0 points Consider the following grph of motion. Distnce (m) Time (sec) How fr did the object trel between 3 s nd 9 s? m m m m m m m
2 Version PREVIEW Kine Grphs PRACTICE burke (1111) m m m Explntion: The prticle went from 50 m to 400 m, so the distnce d = 400 m 50 m = 350 m. 005 (prt 5 of 6) 10.0 points The grph indictes 1. decresing elocit. 2. constnt elocit. Explntion: = d t = 400 m 50 m 6 s = 58 m/s. Holt SF 02Re (prt 1 of 6) 10.0 points The figure shows the position of runner t different times during run. position ( 1000 m) no motion. 4. incresing elocit time (min) 5. constnt position. Explntion: The slopes re steeper s time goes on, so the elocities re incresing. 006 (prt 6 of 6) 10.0 points Wht is the erge speed from 3 s to 9 s? m/s Note: Figure is drwn to scle. For the time interl between 0 min nd 10 min, wht is the runner s displcement? Your nswer must be within ± m. Correct nswer: 2600 m. Explntion: m/s m/s m/s Let : x i = 0 m nd x f = 2600 m m/s m/s m/s m/s m/s x = x f x i = 2600 m 0 m = m. 008 (prt 2 of 6) 10.0 points For the sme time interl, find the runner s erge elocit. Your nswer must be within ± 0.4 m/s. Correct nswer: m/s.
3 Version PREVIEW Kine Grphs PRACTICE burke (1111) 3 Explntion: Let : t 1 = 10 min. g = x 1 = 2600 m min 1 t 1 10 min 60 s = m/s. 009 (prt 3 of 6) 10.0 points For the time interl between 10 min nd 20 min, wht is the runner s displcement? Correct nswer: 1000 m. Explntion: Let : x i = 2600 m nd x f = 3900 m. 012 (prt 6 of 6) 10.0 points Find the erge elocit for the entire run. Your nswer must be within ± 0.4 m/s. Correct nswer: m/s. Explntion: t 3 = 30 min 20 min = 10 min, t tot = 10 min + 10 min + 10 min = 30 min, nd g = x tot = 4200 m t tot 30 min 1 min 60 s = m/s. so x 2 = x f x i = 3600 m 2600 m = 1000 m. 010 (prt 4 of 6) 10.0 points For the sme time interl, find the runner s erge elocit. Your nswer must be within ± 0.5 m/s. Correct nswer: m/s. Explntion: t 2 = 20 min 10 min = 10 min, g = x 2 = 1000 m t 2 10 min 1 min 60 s = m/s. 011 (prt 5 of 6) 10.0 points Wht is the runner s totl displcement? Your nswer must be within ± m. Correct nswer: 4200 m. Explntion: x 3 = 4200 m 3600 m = +600 m, so x tot = x 1 + x 2 + x 3 = 2600 m m m = m. so Displcement s Time (prt 1 of 5) 10.0 points Consider the displcement cure OABC Displcement s Time x (m) O A t (s) Wht is the erge elocit from point O to A? 1. OA = 3 m/s 2. OA = + 3 m/s 3. OA = +2 m/s 4. OA = 2 m/s 5. OA = 0 m/s B C
4 Version PREVIEW Kine Grphs PRACTICE burke (1111) 4 Explntion: The displcement x is on the erticl xis nd the time t is on the horizontl xis. Velocit requires net displcement: OA = x A x O = 2 0 = +2 m/s. t A t O (prt 2 of 5) 10.0 points Wht is the erge elocit for the motion from point O to point B? 1. OB = + 3 m/s 2. OB = 3 m/s 3. OB = 0 m/s 4. OB = +2 m/s 5. OB = 2 m/s Explntion: OB = x B x O t B t O = = 0 m/s. 015 (prt 3 of 5) 10.0 points Wht is the erge speed for the motion from point O to point B? 1. s OB = 0 m/s 2. s OB = + 3 m/s 3. s OB = 3 m/s 4. s OB = 2 m/s 5. s OB = +2 m/s Explntion: s OB = x A x O + x B x A t B t O = = +2 m/s (prt 4 of 5) 10.0 points Wht is the instntneous elocit t point B? 1. B = 2 m/s 2. B = 0 m/s 3. B = + 3 m/s 4. B = +2 m/s 5. B = 3 m/s Explntion: The instntneous elocit t point B cn be obtined b first finding n expression for the position of the moing object nd tking its deritie eluted t time t B. Since the grph ner B is liner, it is simpler to clculte the slope of the line oer the interl from A to B. The result l describes the instntneous elocit t B becuse the deritie of stright line is constnt t ll points on the line nd cn be obtined for our cse b B = x B x A = 0 2 = 2 m/s. t B t A (prt 5 of 5) 10.0 points Wht is the instntneous speed t point B? 1. s B = 0 2. s B = 3 m/s 3. s B = + 3 m/s 4. s B = 2 m/s 5. s B = +2 m/s Explntion: Instntneous speed is simpl the mgnitude of the elocit: s B = B = 2 = +2 m/s. Velocit s Time 11
5 Version PREVIEW Kine Grphs PRACTICE burke (1111) (prt 1 of 3) 10.0 points The scle on the horizontl xis is 4 s per diision nd on the erticl xis 4 m/s per diision. The prticle hs n initil position t 3 m. elocit ( 4 m/s) time ( 4 s) Wht is the position of the prticle fter the first 8 s? Correct nswer: 131 m. Explntion: Chnge in position is the re under the elocit s time grph. p = t = 4 (4 m/s) t, so the position fter the first (8 s) seconds is p = p o + p = (3 m) + 4 (4 m/s) (8 s) = 131 m. 019 (prt 2 of 3) 10.0 points Wht is the elocit of the prticle fter the first 8 s? Correct nswer: 16 m/s. Explntion: Red the elocit corresponding to the fourth tic mrk on the erticl xis = 4 (4 m/s) = 16 m/s. 020 (prt 3 of 3) 10.0 points Wht is the ccelertion of the prticle fter the first 8 s? Correct nswer: 0 m/s 2. Explntion: The ccelertion is the slope of the elocit s time grph; i.e., the ccelertion is zero. Velocit s Time (prt 1 of 3) 10.0 points Consider the elocit cure of one dimensionl motion long the x-xis. The initil position is x = 10 m. The scle on the horizontl xis is 2 s per diision nd on the erticl xis 2 m/s per diision. elocit (2 m/s) per diision b time (2 s) per diision Wht is the position t t = 4 s? 1. x = 22 m 2. x = 16 m 3. x = 14 m 4. x = 30 m 5. x = 20 m 6. x = 18 m 7. x = 10 m 8. x = 28 m 9. x = 24 m c
6 Version PREVIEW Kine Grphs PRACTICE burke (1111) x = 12 m Explntion: the re of tringle is 1 bse height. 2 Chnge in position is the re under the elocit s time grph, so x = x + x o = 1 2 (10 m/s)(4 s) + (1 s)(10 m/s) = 30 m. 022 (prt 2 of 3) 10.0 points Wht is the erge elocit between 0 s nd 6 s? 1. 4 m/s < 5 m/s 2. 6 m/s < 7 m/s 3. 8 m/s < 9 m/s 4. 0 m/s < 1 m/s 5. 1 m/s < 2 m/s 6. 7 m/s < 8 m/s 7. 2 m/s < 3 m/s 8. 5 m/s < 6 m/s 9. 3 m/s < 4 m/s m/s < 10 m/s Explntion: During the time interl 0 to 6 s, x = 1 (10 m/s) (4 s) + (2 s) (10 m/s) 2 = 40 m, so the erge elocit between 0 to 6 s is = x t = 40 m m/s. 6 s Wht is the erge ccelertion between 14 s nd 16 s? 1. 1 m/s 2 < 2 m/s m/s 2 < 3 m/s m/s 2 < 4 m/s m/s 2 < 3 m/s m/s 2 < 4 m/s m/s 2 < 1 m/s m/s 2 < 5 m/s m/s 2 < 1 m/s m/s 2 < 0 m/s m/s 2 < 2 m/s 2 Explntion: The ccelertion is the slope of the cure in the elocit s time grph. The ccelertion is constnt from 12 s to 18 s, so the ccelertion is = t = 8 m/s 0 m/s 18 s 12 s m/s 2. Velocit s Time points An object ws suspended in fixed plce nd then llowed to drop in free fll. Tking down s the positie erticl direction, which grph l represents its motion s erticl elocit s time? 1. t 023 (prt 3 of 3) 10.0 points
7 Version PREVIEW Kine Grphs PRACTICE burke (1111) 7 ccelertion, so the grph is t Velocit s Time points An object is thrown erticll upwrd. Disregrding ir resistnce, which grph represents the elocit of the object s function of time t? 1. t 5. t 7. t 8. t Explntion: The object is undergoing constnt positie grittionl ccelertion g. The slope of elocit s time cure represents the Explntion: The object undergoes constnt downwrd grittionl ccelertion g. It hs decresing positie elocit on the w up, brief instnt of zero elocit, then negtie elocit on the w down (which continues to decrese in lue: 3 < 1).
8 Version PREVIEW Kine Grphs PRACTICE burke (1111) 8 = 0 g t This is stright line with negtie slope nd positie initil elocit. t 5. t Accelertion Time Grph (prt 1 of 5) 10.0 points Consider to cr which cn moe to the right (positie direction) or left on horizontl surfce long stright line. cr O + Wht is the ccelertion-time grph if the cr moes towrd the right (w from the origin), speeding up t sted rte? 1. None of these grphs is. 7. t 8. t Explntion: Since the cr speeds up t sted rte, the ccelertion is constnt. 027 (prt 2 of 5) 10.0 points Wht is the ccelertion-time grph if the cr moes towrd the right, slowing down t sted rte? 1. t
9 Version PREVIEW Kine Grphs PRACTICE burke (1111) 9 5. t 5. t 7. None of these grphs is. 8. t Explntion: Since the cr slows down, the ccelertion is in the opposite direction. 028 (prt 3 of 5) 10.0 points Wht is the ccelertion-time grph if the cr moes towrds the left (towrd the origin) t constnt elocit? 1. t 7. t 8. None of these grphs is. Explntion: Since the cr moes t constnt elocit, the ccelertion is zero. 029 (prt 4 of 5) 10.0 points Wht is the ccelertion-time grph if the cr moes towrd the left, speeding up t sted rte?
10 Version PREVIEW Kine Grphs PRACTICE burke (1111) t 030 (prt 5 of 5) 10.0 points Wht is the ccelertion-time grph if the cr moes towrd the right t constnt elocit? 1. None of these grphs is. 5. None of these grphs is. 7. t 8. t 5. t 7. t Explntion: The sme reson s Prt 1.
11 Version PREVIEW Kine Grphs PRACTICE burke (1111) t Explntion: The sme reson s Prt 3.
Version 001 Summer Review #03 tubman (IBII20142015) 1
Version 001 Summer Reiew #03 tubmn (IBII20142015) 1 This print-out should he 35 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Concept 20 P03
More informationv T R x m Version PREVIEW Practice 7 carroll (11108) 1
Version PEVIEW Prctice 7 crroll (08) his print-out should he 5 questions. Multiple-choice questions y continue on the next colun or pge find ll choices before nswering. Atwood Mchine 05 00 0.0 points A
More informationPROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.
More informationAAPT UNITED STATES PHYSICS TEAM AIP 2010
2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationSOLUTIONS TO CONCEPTS CHAPTER 5
1. m k S 10m Let, ccelertion, Initil velocity u 0. S ut + 1/ t 10 ½ ( ) 10 5 m/s orce: m 5 10N (ns) 40000. u 40 km/hr 11.11 m/s. 3600 m 000 k ; v 0 ; s 4m v u ccelertion s SOLUIONS O CONCEPS CHPE 5 0 11.11
More informationReview Problems for the Final of Math 121, Fall 2014
Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationAnswer, Key Homework 10 David McIntyre 1
Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationPHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationCypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:
Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A
More informationExponential and Logarithmic Functions
Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define
More informationApplications to Physics and Engineering
Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics
More informationGeometry 7-1 Geometric Mean and the Pythagorean Theorem
Geometry 7-1 Geometric Men nd the Pythgoren Theorem. Geometric Men 1. Def: The geometric men etween two positive numers nd is the positive numer x where: = x. x Ex 1: Find the geometric men etween the
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More information5. Unable to determine. 6. 4 m correct. 7. None of these. 8. 1 m. 9. 1 m. 10. 2 m. 1. 1 m/s. 2. None of these. 3. Unable to determine. 4.
Version PREVIEW B One D Kine REVIEW burke (1111) 1 This print-out should have 34 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Jogging
More informationtrademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007
trdemrk nd symbol guidelines trdemrk guidelines The trdemrk Cn be plced in either of the two usul configurtions but horizontl usge is preferble. Wherever possible the trdemrk should be plced on blck bckground.
More informationUnit 6: Exponents and Radicals
Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationAREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationt 3 t 4 Part A: Multiple Choice Canadian Association of Physicists 1999 Prize Exam
Cndin Assocition of Physicists 1999 Prize Exm This is three hour exm. Ntionl rnking nd prizes will be bsed on student s performnce on both sections A nd B of the exm. However, performnce on the multiple
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
More informationwww.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values)
www.mthsbo.org.uk CORE SUMMARY NOTES Functions A function is rule which genertes ectl ONE OUTPUT for EVERY INPUT. To be defined full the function hs RULE tells ou how to clculte the output from the input
More informationWeek 11 - Inductance
Week - Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n
More informationPure C4. Revision Notes
Pure C4 Revision Notes Mrch 0 Contents Core 4 Alger Prtil frctions Coordinte Geometry 5 Prmetric equtions 5 Conversion from prmetric to Crtesin form 6 Are under curve given prmetriclly 7 Sequences nd
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x
More information9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is so-clled becuse when the sclr product of two vectors
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More information1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?
Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationWarm-up for Differential Calculus
Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy
More informationPSW-4-Motion Worksheet Name:. Class #:
Speed, Velocity, nd Accelertion PSW-4-1 Vocbulry Distnce: Displcement: Speed: Velocity: Accelertion: How fr something trvels. How fr something trvels in given direction. How fst something is moving. How
More informationMATH PLACEMENT REVIEW GUIDE
MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your
More information6 Energy Methods And The Energy of Waves MATH 22C
6 Energy Methods And The Energy of Wves MATH 22C. Conservtion of Energy We discuss the principle of conservtion of energy for ODE s, derive the energy ssocited with the hrmonic oscilltor, nd then use this
More information4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
More information1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
More informationScalar and Vector Quantities. A scalar is a quantity having only magnitude (and possibly phase). LECTURE 2a: VECTOR ANALYSIS Vector Algebra
Sclr nd Vector Quntities : VECTO NLYSIS Vector lgebr sclr is quntit hving onl mgnitude (nd possibl phse). Emples: voltge, current, chrge, energ, temperture vector is quntit hving direction in ddition to
More informationTwo hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00
COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided
More informationRate and Activation Energy of the Iodination of Acetone
nd Activtion Energ of the Iodintion of Acetone rl N. eer Dte of Eperiment: //00 Florence F. Ls (prtner) Abstrct: The rte, rte lw nd ctivtion energ of the iodintion of cetone re detered b observing the
More informationSPH simulation of fluid-structure interaction problems
Diprtimento di ingegneri idrulic e mientle SPH simultion of fluid-structure interction prolems C. Antoci, M. Gllti, S. Siill Reserch project Prolem: deformtion of plte due to the ction of fluid (lrge displcement
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More information15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
More information3 The Utility Maximization Problem
3 The Utility Mxiiztion Proble We hve now discussed how to describe preferences in ters of utility functions nd how to forulte siple budget sets. The rtionl choice ssuption, tht consuers pick the best
More informationIntegration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
More informationDerivatives and Rates of Change
Section 2.1 Derivtives nd Rtes of Cnge 2010 Kiryl Tsiscnk Derivtives nd Rtes of Cnge Te Tngent Problem EXAMPLE: Grp te prbol y = x 2 nd te tngent line t te point P(1,1). Solution: We ve: DEFINITION: Te
More informationSection 7-4 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More informationP.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn
33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of
More informationPractice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn
Prtie Test 2 1. A highwy urve hs rdius of 0.14 km nd is unnked. A r weighing 12 kn goes round the urve t speed of 24 m/s without slipping. Wht is the mgnitude of the horizontl fore of the rod on the r?
More informationFirm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach
Pro. Jy Bhttchry Spring 200 The Theory o the Firm II st lecture we covered: production unctions Tody: Cost minimiztion Firm s supply under cost minimiztion Short vs. long run cost curves Firm Ojectives
More informationDesign Example 1 Special Moment Frame
Design Exmple 1 pecil Moment Frme OVERVIEW tructurl steel specil moment frmes (MF) re typiclly comprised of wide-flnge bems, columns, nd bem-column connections. Connections re proportioned nd detiled to
More informationThe Velocity Factor of an Insulated Two-Wire Transmission Line
The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
More informationMATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
More informationModule Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials
MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic
More informationIntroduction to Integration Part 2: The Definite Integral
Mthemtics Lerning Centre Introduction to Integrtion Prt : The Definite Integrl Mr Brnes c 999 Universit of Sdne Contents Introduction. Objectives...... Finding Ares 3 Ares Under Curves 4 3. Wht is the
More informationSection 5-4 Trigonometric Functions
5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More information10.6 Applications of Quadratic Equations
10.6 Applictions of Qudrtic Equtions In this section we wnt to look t the pplictions tht qudrtic equtions nd functions hve in the rel world. There re severl stndrd types: problems where the formul is given,
More informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint
More information4. DC MOTORS. Understand the basic principles of operation of a DC motor. Understand the operation and basic characteristics of simple DC motors.
4. DC MOTORS Almost every mechnicl movement tht we see round us is ccomplished by n electric motor. Electric mchines re mens o converting energy. Motors tke electricl energy nd produce mechnicl energy.
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More informationRIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS Known for over 500 yers is the fct tht the sum of the squres of the legs of right tringle equls the squre of the hypotenuse. Tht is +b c. A simple proof is
More informationThe Definite Integral
Chpter 4 The Definite Integrl 4. Determining distnce trveled from velocity Motivting Questions In this section, we strive to understnd the ides generted by the following importnt questions: If we know
More informationSINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 1470 - COLLEGE ALGEBRA (4 SEMESTER HOURS)
SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 470 - COLLEGE ALGEBRA (4 SEMESTER HOURS). COURSE DESCRIPTION: Polynomil, rdicl, rtionl, exponentil, nd logrithmic functions
More informationLinear Equations in Two Variables
Liner Equtions in Two Vribles In this chpter, we ll use the geometry of lines to help us solve equtions. Liner equtions in two vribles If, b, ndr re rel numbers (nd if nd b re not both equl to 0) then
More informationaddition, there are double entries for the symbols used to signify different parameters. These parameters are explained in this appendix.
APPENDIX A: The ellipse August 15, 1997 Becuse of its importnce in both pproximting the erth s shpe nd describing stellite orbits, n informl discussion of the ellipse is presented in this ppendix. The
More informationWeek 7 - Perfect Competition and Monopoly
Week 7 - Perfect Competition nd Monopoly Our im here is to compre the industry-wide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between
More informationA.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
More informationUNIVERSITY OF OSLO FACULTY OF MATHEMATICS AND NATURAL SCIENCES
UNIVERSITY OF OSLO FACULTY OF MATHEMATICS AND NATURAL SCIENCES Solution to exm in: FYS30, Quntum mechnics Dy of exm: Nov. 30. 05 Permitted mteril: Approved clcultor, D.J. Griffiths: Introduction to Quntum
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of
More informationOrbits and Kepler s Laws
Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how
More informationNetwork Configuration Independence Mechanism
3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting
More informationDS/EN 1991-1-4 DK NA:2010-03
DS/EN 1991-1-4 DK NA:010-03 Ntionl Annex to Eurocode 1: Actions on structures - Prt 1-4: Generl ctions Wind ctions Foreword This Ntionl Annex (NA) is reision of preious edition of EN 1991-1-4 DK NA:007
More informationI calculate the unemployment rate as (In Labor Force Employed)/In Labor Force
Introduction to the Prctice of Sttistics Fifth Edition Moore, McCbe Section 4.5 Homework Answers to 98, 99, 100,102, 103,105, 107, 109,110, 111, 112, 113 Working. In the lnguge of government sttistics,
More informationGive a formula for the velocity as a function of the displacement given that when s = 1 metre, v = 2 m s 1. (7)
. The acceleration of a bod is gien in terms of the displacement s metres as s a =. s (a) Gie a formula for the elocit as a function of the displacement gien that when s = metre, = m s. (7) (b) Hence find
More informationDrawing Diagrams From Labelled Graphs
Drwing Digrms From Lbelled Grphs Jérôme Thièvre 1 INA, 4, venue de l Europe, 94366 BRY SUR MARNE FRANCE Anne Verroust-Blondet 2 INRIA Rocquencourt, B.P. 105, 78153 LE CHESNAY Cedex FRANCE Mrie-Luce Viud
More informationMr. Kepple. Motion at Constant Acceleration 1D Kinematics HW#5. Name: Date: Period: (b) Distance traveled. (a) Acceleration.
Moion Consn Accelerion 1D Kinemics HW#5 Mr. Kepple Nme: De: Period: 1. A cr cceleres from 1 m/s o 1 m/s in 6.0 s. () Wh ws is ccelerion? (b) How fr did i rel in his ime? Assume consn ccelerion. () Accelerion
More informationRadius of the Earth - Radii Used in Geodesy James R. Clynch February 2006
dius of the Erth - dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.
More information10 AREA AND VOLUME 1. Before you start. Objectives
10 AREA AND VOLUME 1 The Tower of Pis is circulr bell tower. Construction begn in the 1170s, nd the tower strted lening lmost immeditely becuse of poor foundtion nd loose soil. It is 56.7 metres tll, with
More informationVendor Rating for Service Desk Selection
Vendor Presented By DATE Using the scores of 0, 1, 2, or 3, plese rte the vendor's presenttion on how well they demonstrted the functionl requirements in the res below. Also consider how efficient nd functionl
More informationTITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING
TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING Sung Joon Kim*, Dong-Chul Che Kore Aerospce Reserch Institute, 45 Eoeun-Dong, Youseong-Gu, Dejeon, 35-333, Kore Phone : 82-42-86-231 FAX
More informationLesson 4.1 Triangle Sum Conjecture
Lesson 4.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q 2., y 3., b 31 82 p 98 q 28 53 y 17 79 23 50 b 4. r, s, 5., y 6. y t t s r 100 85 100 y 30 4 7 y 31 7. s 8.
More informationReview guide for the final exam in Math 233
Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered
More informationChapter 2 Solutions. 4. We find the average velocity from
Chapter 2 Solutions 4. We find the aerage elocity from = (x 2 x 1 )/(t 2 t 1 ) = ( 4.2 cm 3.4 cm)/(6.1 s 3.0 s) = 2.5 cm/s (toward x). 6. (a) We find the elapsed time before the speed change from speed
More informationBayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
More information2001 Attachment Sequence No. 118
Form Deprtment of the Tresury Internl Revenue Service Importnt: Return of U.S. Persons With Respect to Certin Foreign Prtnerships Attch to your tx return. See seprte instructions. Informtion furnished
More informationAP STATISTICS SUMMER MATH PACKET
AP STATISTICS SUMMER MATH PACKET This pcket is review of Algebr I, Algebr II, nd bsic probbility/counting. The problems re designed to help you review topics tht re importnt to your success in the clss.
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only
More informationRotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
More information2m + V ( ˆX) (1) 2. Consider a particle in one dimensions whose Hamiltonian is given by
Teoretisk Fysik KTH Advnced QM SI2380), Exercise 8 12 1. 3 Consider prticle in one dimensions whose Hmiltonin is given by Ĥ = ˆP 2 2m + V ˆX) 1) with [ ˆP, ˆX] = i. By clculting [ ˆX, [ ˆX, Ĥ]] prove tht
More informationB Conic Sections. B.1 Conic Sections. Introduction to Conic Sections. Appendix B.1 Conic Sections B1
Appendi B. Conic Sections B B Conic Sections B. Conic Sections Recognize the four bsic conics: circles, prbols, ellipses, nd hperbols. Recognize, grph, nd write equtions of prbols (verte t origin). Recognize,
More informationWhy is the NSW prison population falling?
NSW Bureu of Crime Sttistics nd Reserch Bureu Brief Issue pper no. 80 September 2012 Why is the NSW prison popultion flling? Jcqueline Fitzgerld & Simon Corben 1 Aim: After stedily incresing for more thn
More information