Chapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr


 Katrina Conley
 2 years ago
 Views:
Transcription
1 Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i migh seem. I is emping o simply average he wo velociies ha are given. The problem is ha he car does no spend he same amoun of ime a each velociy, so his approach will give he wrong answer. We need o use he definiion of average speed o ge he correc answer. s oaldis oalime For his problem, we ll consider he disance from he boom o he op of he hill o be d and calculae he ime up and he ime down he hill o find he oal ime. d up 40km / hr d down 60km / h d oal up + down 40km / hr + d 60km / hr 60km / hr + 40km / hr 40km / hr 60km / hr d s 2 d 2d 2 40km / hr 60km / hr oal 60km / hr + 40km / hr 40km / hr 60km / hr d 60km / hr + 40km / hr 48km / hr 2.3 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s 90km 1000m h 1km 1h 3600s 25m / s d s 25m / s 0.5s 12.5m / s 2.5 The posiion of an objec moving in a sraigh line is given by x , where x is in meers and in seconds (a). Wha is he posiion of he objec a 1,2,3, and 4s? (b) Wha is he objec s displacemen beween 0 and 4s. (c) Wha is he average velociy for he ime inerval from 2 s o 4s? (d) Graph x vs for 0 4s and indicae how he answer for c can be found from he graph. (ad) We plug in o calculae posiions.
2 x(1) 0m x(2) 2.0m x(3) 0m x(4) 12m (e) We can calculae he displacemen from he posiions. Δx x(4) x(0) 12m 0m 12m (f) We calculae he average velociy using he displacemens and ime inerval. v x(4) x(2) 12m ( 2m) 7m/ s 4s 2s 2s (g) A graph of x vs.. The average velociy can be compued by connecing x(4) and x(2) wih a sraigh line and compuing he slope. Noe: Graph done wih Mahemaica Traffic Shock wave. An abrup slowdown in concenraed raffic can ravel as a pulse, ermed a shock wave, along ahe line of cars, eiher downsreame (in he raffic direcion) or upsream, or i can be saionary. Figure 223 shows a uniformly spaced line of cars moving a speed v 25m / s oward a uniformly spaced line of slow cars, moving a speed 5m / s. Assume ha each faser car adds lengh L 12m (car lengh plus buffer zone) o he line of cars when i joins he line, and assume i slows abruply a he las insan. (a) For wha separaion disance d beween he faser cars does he shock wave remain saionary? If he separaion is wice ha amoun, wha are he (b) speed and (c) direcion (upsream or downsream) of he shock wave. To do his problem, is useful o consider he las slow car and he firs fas car. We ll coun he rear of he car as he place whre we measure is posiion. If he pulse is o remain saionary, he picure looks like
3 v vs fas slow L d fas slow L In a ime, he slow car goes a disance L and he fas car goes a disance d + L. We can wrie consan acceleraion equaions for boh cars. We hen solve he equaion for he slow car for and hen use ha ime in he equaion L 0 + Fas Car x if L d 0 v 25m / s x if + v 0 L d + v Slow Car x is 0 x fs L 5m / s x fs x is + v f L 0 + L 0 L d + v 0 L d + v L d L( v 1) L( v 25m / s 5m / s ) 12m ( ) 5m / s d 48m We can find he movemen of he wave by finding he posiion of he car when i reaches he wave. We do his by wriing he posiion of each car, recognizing ha he slow car is a disance L in fron of he fas car when he fas car joins he line. We use his condiion o find he ime when he cars mee. Using he final posiion of he fas car and he ime, we can find he velociy of he pulse.
4 v vs fas slow L d fas slow xff xfsxff+l Fas Car x if L d? v 25m / s x if + v L d + v Slow Car x is 0 x fs + L 5m / s x fs x is + v f + L 0 + L d + v + L L L d + v + L (1 v ) L( v 1) d ( v ) L( v ) d ( )d L v 5m / s ( ) 96m 12m 25m / s 5m / s 12m + L 12m +12m 4.8s 5m / s v pulse 12m / s m / s
5 2.14 The posiion funcion x() of a paricle moving along an x axis is x() where x() is in m and in seconds. (a) A wha ime and (b) where does he paricle (momanarily) sop? A wha (c) negaive ime and (d) posiive ime does he paricle pass hrough he origin? (e) Graph x() vs. for he range 5s o +5s. (f) To shif he curve righward on he graph should we include he erm +20 or he erm 20 in he x()? (g) Does ha incluseion increase or decrease he value of x a which he paricle momenarily sops. Le s begin by ploing he posiion as a funcion of ime beween 5 and 5 Here is a close upploed 1 o +1. We can see from he graph ha he paricle sops a x 4, 0. We can ge his from our equaion by seing he velociy o zero and solving for he ime.
6 x() v d x d x(0) 4.0 We can find when he paricle passes hrough zero... x() ± 2 3 s ±0.8165s To shif he curve o he righ, we need o include +20. If we plo wih his erm included we can see he shif we wan. Where and when does he sop occur? We can calculae his
7 x() v d x d s 4 3 s x( 4 3 ) 20m The graph is misleading (i mislead me!) in ha he curve looks he same and Mahemaica has rescaled he verical axisso i looks as if he x posiion is he same as before. If you look carefully a he new scale, you can see ha he sopping poin is a 20m An elecron moving along he x axis has a posiion given by x 16 e m where is in seconds. How far is he elecron from he origin when i momenarily sops. We need o find ou when he elecron sops. If we know when i sops, we can find ou where i is. To find ou when i sops, we find he insananeous v dx d d d (16 e ) 16 e 16(1 )e 0 16(1 )e 1s 16 e x(1) 16 1 e 1 m 5.886m posiion ime
8 2.18 (a) If he posiion of a paricle is given by x() where x() is in m and is in seconds, when if ever is he paricle s velociy zero? (b) When is is acceleraion a zero? (c) For wha ime range (posiive or negaive) is a negaive? (c) Posiive (e) Graph x(), v() and a( ) Firs we wrie expressions for x(), v() and a( ). (a) We can solv for when he velociy is zero: (b) The acceleraion is zero a 0s (c) Acceleraion is posiive when < 0s (d) Acceleraion is negaive when > 0s x() v() dx d a( ) dv d 30 v() ± s ±1.155s
9
10 2.23 An elecron has a consan acceleraion of +3.2m / s 2. A a cerain insan is velociy is +9.6m/s. Wha is is velociy 2.5 s earlier and (b) 2.5s laer? Take he ime o be zero when he velociy is 9.6 m/s. a. A 2.5s, v 1.6m/ s b. A +2.5s, v 17.6m/ s. a 3.2m / s 2 v 0 9.6m / s v v 0 + a 2.26 On a dry road, a car wih good ires may be able o brake wih a consan deceleraion of 4.92 m / s 2 (a) How long does such a car, iniially raveling a 24.6 m/s ake o sop? (b) How far does i ravel in his ime? Graph x verses and v versus for he deceleraion. 24.6m/s This is a classic consan acceleraion problem. We begin by wriing ou wha we know and hen solving for ime. x i 0 x f? v i 24.6m / s v f 0 a 4.92m / s 2? b. Now we can find he sopping poin v f v i + a 0 v i + a v i a 24.6 m / s 4.92m / s 2 5s x f x i + v i a 2 x f 0 + (24.6m / s) 5s+ 1 2 ( 4.92m / s2 ) (5s) m
11
12 2.30 A world s land speed record was se by Colonel John P. Sapp when in March 1954 he rode a rockepropelled sled ha moved along a rack a 1020 km/h. He and he sled were brough o a sop in 1.4 s. In erms of g, wha acceleraion did he experience while sopping? v i 1020km hr v f 0 1.4s 1000m 1km 1hr 3600s 283.3m / s v f v i + a a v f v i # g's m / s 1.4s m / s2 9.8m / s m / s When a highspeed passenger rain raveling a 161 km/h rounds a bend, he engineer is shocked o see ha a locomoive has improperly enered ono he rack from he siding is a disance D676 m ahead (Fig 224). The locomoive is moving a 29 km/h. he engineer of he high speed rain immediaely applies he brakes (a) Wha mus be he magniude of he resuling consan deceleraion if a collision is o be jus avoided? (b) Assume he engineer is a x0 when, a 0, he firs spos he locomoive. Skech curves for he e locomoive and he high speed rain for he case in which a collision is jus avoided and is no quie avoided. We begin by wriing wha we know abou each rain High Speed Train x i h 0 x f h? v i h 161km h v f h? a h? 1000m 1km 1h 3600s 44.72m / s Low Speed Train x i l 676m x f l? v i l 29km h v f v i a l m 1km 1h 3600s 8.06m / s The correc condiion is ha he velociy of he fas rain maches he velociy of he slow rain. If he rains have no collided by he ime his happens, hey never will. Afer his occurs, he fas rain will fall furher and furher behind. We need o se he wo posiions equal o each oher o find ou when he collision will occur.
13 x i h + v i h a h 2 x i l + v i l a l v i h a h 2 x i l + v i l + 0 v i l v i h + a h v i l v i h a h v v i h i l v i h a v i l v i h h a h a h 2 v x i l + v i l i l v i h v i h (v i l v i h ) + 1 (v i l v i h ) 2 x i l + v (v i l i l v i h ) a h 2 a h a h v i h (v i l v i h ) (v v i l i h )2 a h x i l + v i l (v i l v i h ) v i h (v i l v i h ) v i l (v i l v i h ) (v v i l i h )2 a h x i l a h (v i h v i l )(v i l v i h ) (v i l v i h )2 a h x i l (v i h v i l )(v i l v i h ) + 1 a h 2 (v v i l i h )2 a h x i l
14 a 0 m / s 2 a 0.5m / s 2
15 a 0.9 m / s 2 a m / s 2 Noice ha in he las picure, he slopes of he curves mach jus where hey mee.
16 2.47 (a) Wih wha speed mus a ball be hrown verically from ground level o rise o a maximum heigh of 50m. (b) How long will i be in he air. Skech y, v, a, vs. (a). We compue he iniial velociy firs. y i 0m y f 50m v i? v f 0m / s? a g v f 2 v i 2 + 2a (y f y i ) 0 v i 2 2g (y f 0) v i 2g (50m) 31.3m / s (b) Now ha we know iniial velociy, we can find he ime o reach he highes poin. v f v i + a 0 v i g v i g 31.3m / s 9.8m / s 3.19s 2 The pah is symmeric, so he enire ime of fligh is 6.38s.
17
Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More information1. The graph shows the variation with time t of the velocity v of an object.
1. he graph shows he variaion wih ime of he velociy v of an objec. v Which one of he following graphs bes represens he variaion wih ime of he acceleraion a of he objec? A. a B. a C. a D. a 2. A ball, iniially
More informationMOTION ALONG A STRAIGHT LINE
Chaper 2: MOTION ALONG A STRAIGHT LINE 1 A paricle moes along he ais from i o f Of he following alues of he iniial and final coordinaes, which resuls in he displacemen wih he larges magniude? A i =4m,
More information( ) in the following way. ( ) < 2
Sraigh Line Moion  Classwork Consider an obbec moving along a sraigh line eiher horizonally or verically. There are many such obbecs naural and manmade. Wrie down several of hem. Horizonal cars waer
More informationChapter 2 Kinematics in One Dimension
Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how
More informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More informationWeek #9  The Integral Section 5.1
Week #9  The Inegral Secion 5.1 From Calculus, Single Variable by HughesHalle, Gleason, McCallum e. al. Copyrigh 005 by John Wiley & Sons, Inc. This maerial is used by permission of John Wiley & Sons,
More informationSection A: Forces and Motion
I is very useful o be able o make predicions abou he way moving objecs behave. In his chaper you will learn abou some equaions of moion ha can be used o calculae he speed and acceleraion of objecs, and
More informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prinou should hae 1 quesions. Muliplechoice quesions may coninue on he ne column or page find all choices before making your selecion. The
More informationRelative velocity in one dimension
Connexions module: m13618 1 Relaive velociy in one dimension Sunil Kumar Singh This work is produced by The Connexions Projec and licensed under he Creaive Commons Aribuion License Absrac All quaniies
More informationRotational Inertia of a Point Mass
Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha
More informationA Curriculum Module for AP Calculus BC Curriculum Module
Vecors: A Curriculum Module for AP Calculus BC 00 Curriculum Module The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy.
More informationNewton's second law in action
Newon's second law in acion In many cases, he naure of he force acing on a body is known I migh depend on ime, posiion, velociy, or some combinaion of hese, bu is dependence is known from experimen In
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a missiondriven noforprofi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More informationMotion Along a Straight Line
Moion Along a Sraigh Line On Sepember 6, 993, Dave Munday, a diesel mechanic by rade, wen over he Canadian edge of Niagara Falls for he second ime, freely falling 48 m o he waer (and rocks) below. On his
More informationApplication of kinematic equation:
HELP: See me (office hours). There will be a HW help session on Monda nigh from 78 in Nicholson 109. Tuoring a #10 of Nicholson Hall. Applicaion of kinemaic equaion: a = cons. v= v0 + a = + v + 0 0 a
More informationChapter 6. First Order PDEs. 6.1 Characteristics The Simplest Case. u(x,t) t=1 t=2. t=0. Suppose u(x, t) satisfies the PDE.
Chaper 6 Firs Order PDEs 6.1 Characerisics 6.1.1 The Simples Case Suppose u(, ) saisfies he PDE where b, c are consan. au + bu = 0 If a = 0, he PDE is rivial (i says ha u = 0 and so u = f(). If a = 0,
More informationAP1 Kinematics (A) (C) (B) (D) Answer: C
1. A ball is hrown verically upward from he ground. Which pair of graphs bes describes he moion of he ball as a funcion of ime while i is in he air? Neglec air resisance. y a v a (A) (C) y a v a (B) (D)
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area workedou s o OddNumbered Eercises Do no read hese workedou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More information4kq 2. D) south A) F B) 2F C) 4F D) 8F E) 16F
efore you begin: Use black pencil. Wrie and bubble your SU ID Number a boom lef. Fill bubbles fully and erase cleanly if you wish o change! 20 Quesions, each quesion is 10 poins. Each quesion has a mos
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationSection 7.1 Angles and Their Measure
Secion 7.1 Angles and Their Measure Greek Leers Commonly Used in Trigonomery Quadran II Quadran III Quadran I Quadran IV α = alpha β = bea θ = hea δ = dela ω = omega γ = gamma DEGREES The angle formed
More informationName: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINAL EXAMINATION. June 2009.
Name: Teacher: DO NOT OPEN THE EXMINTION PPER UNTIL YOU RE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINL EXMINTION June 2009 Value: 100% General Insrucions This examinaion consiss of wo pars. Boh pars
More informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationImagine a Source (S) of sound waves that emits waves having frequency f and therefore
heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationAP Physics Velocity and Linear Acceleration Unit 1 Problems:
Uni 1 Problems: Linear Velociy and Acceleraion This enire se of problems is due he day of he es. I will no accep hese for a lae grade. * = Problems we do ogeher; all oher problems are homework (bu we will
More informationCHAPTER FIVE. Solutions for Section 5.1
CHAPTER FIVE 5. SOLUTIONS 87 Soluions for Secion 5.. (a) The velociy is 3 miles/hour for he firs hours, 4 miles/hour for he ne / hour, and miles/hour for he las 4 hours. The enire rip lass + / + 4 = 6.5
More informationPhysics 107 HOMEWORK ASSIGNMENT #2
Phsics 7 HOMEWORK ASSIGNMENT # Cunell & Johnson, 7 h ediion Chaper : Problem 5 Chaper : Problems 44, 54, 56 Chaper 3: Problem 38 *5 MulipleConcep Example 9 deals wih he conceps ha are imporan in his problem.
More information2.6 Limits at Infinity, Horizontal Asymptotes Math 1271, TA: Amy DeCelles. 1. Overview. 2. Examples. Outline: 1. Definition of limits at infinity
.6 Limis a Infiniy, Horizonal Asympoes Mah 7, TA: Amy DeCelles. Overview Ouline:. Definiion of is a infiniy. Definiion of horizonal asympoe 3. Theorem abou raional powers of. Infinie is a infiniy This
More informationRepresenting Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1
Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals
More informationEXERCISES AND PROBLEMS
Exercises and Problems 71 EXERCISES AND PROBLEMS The icon in fron of a problem indicaes ha he problem can be done on a Dnamics Workshee. Dnamics Workshees are found a he back of he Suden Workbook. If ou
More informationDiscussion Examples Chapter 10: Rotational Kinematics and Energy
Discussion Examples Chaper : Roaional Kinemaics and Energy 9. The Crab Nebula One o he mos sudied objecs in he nigh sky is he Crab nebula, he remains o a supernova explosion observed by he Chinese in 54.
More informationChapter 2 Motion in One Dimension
Chaper Moion in One Dimension Concepual Problems 5 Sand in he cener of a large room. Call he direcion o your righ posiie, and he direcion o your lef negaie. Walk across he room along a sraigh line, using
More informationNewton s Laws of Motion
Newon s Laws of Moion MS4414 Theoreical Mechanics Firs Law velociy. In he absence of exernal forces, a body moves in a sraigh line wih consan F = 0 = v = cons. Khan Academy Newon I. Second Law body. The
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationGraphing the Von Bertalanffy Growth Equation
file: d:\b1732013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and
More informationSection 2.3 Linear and Angular Velocities
Secion 2.3 Linear and Angular Velociies The mos inuiive measure of he rae a which he rider is raveling around he wheel is wha we call linear velociy. Anoher way o specify how fas he rider is raveling around
More informationChapter 15: Superposition and Interference of Waves
Chaper 5: Superposiion and Inerference of Waves Real waves are rarely purely sinusoidal (harmonic, bu hey can be represened by superposiions of harmonic waves In his chaper we explore wha happens when
More informationPermutations and Combinations
Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes  ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he kvalue for he middle erm, divide
More informationLAB 6: SIMPLE HARMONIC MOTION
1 Name Dae Day/Time of Lab Parner(s) Lab TA Objecives LAB 6: SIMPLE HARMONIC MOTION To undersand oscillaion in relaion o equilibrium of conservaive forces To manipulae he independen variables of oscillaion:
More information2. Waves in Elastic Media, Mechanical Waves
2. Waves in Elasic Media, Mechanical Waves Wave moion appears in almos ever branch of phsics. We confine our aenion o waves in deformable or elasic media. These waves, for eample ordinar sound waves in
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO
Profi Tes Modelling in Life Assurance Using Spreadshees, par wo PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO Erik Alm Peer Millingon Profi Tes Modelling in Life Assurance Using Spreadshees,
More information1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t,
Homework6 Soluions.7 In Problem hrough 4 use he mehod of variaion of parameers o find a paricular soluion of he given differenial equaion. Then check your answer by using he mehod of undeermined coeffiens..
More informationHANDOUT 14. A.) Introduction: Many actions in life are reversible. * Examples: Simple One: a closed door can be opened and an open door can be closed.
Inverse Funcions Reference Angles Inverse Trig Problems Trig Indeniies HANDOUT 4 INVERSE FUNCTIONS KEY POINTS A.) Inroducion: Many acions in life are reversible. * Examples: Simple One: a closed door can
More informationName: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling
Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: Solving Exponenial Equaions (The Mehod of Common Bases) Solving Exponenial Equaions (Using Logarihms)
More informationKinematics in 1D From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard.
Chaper 2 Kinemaics in 1D From Problems and Soluions in Inroducory Mechanics (Draf ersion, Augus 2014) Daid Morin, morin@physics.harard.edu As menioned in he preface, his book should no be hough of as
More informationAP Calculus AB 2007 Scoring Guidelines
AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and
More informationChapter 8 Copyright Henning Umland All Rights Reserved
Chaper 8 Copyrigh 19972004 Henning Umland All Righs Reserved Rise, Se, Twiligh General Visibiliy For he planning of observaions, i is useful o know he imes during which a cerain body is above he horizon
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More information9. Capacitor and Resistor Circuits
ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren
More informationChapter 2 Motion in One Dimension
Chaper Moion in One Dimension Concepual Problems Wha is he aerage elociy oer he round rip of an objec ha is launched sraigh up from he ground and falls sraigh back down o he ground? Deermine he Concep
More informationRC (ResistorCapacitor) Circuits. AP Physics C
(ResisorCapacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationThe Torsion of Thin, Open Sections
EM 424: Torsion of hin secions 26 The Torsion of Thin, Open Secions The resuls we obained for he orsion of a hin recangle can also be used be used, wih some qualificaions, for oher hin open secions such
More informationYTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.
. Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure
More informationChapter 11A Angular Motion. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chaper 11A Angular Moion A PowerPoin Presenaion by Paul E. Tippens, Proessor o Physics Souhern Polyechnic Sae Universiy 007 WIND TUBINES such as hese can generae signiican energy in a way ha is environmenally
More informationFullwave rectification, bulk capacitor calculations Chris Basso January 2009
ullwave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
More informationEconomics 140A Hypothesis Testing in Regression Models
Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1
More informationAP Calculus AB 2010 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College
More information4.2 Trigonometric Functions; The Unit Circle
4. Trigonomeric Funcions; The Uni Circle Secion 4. Noes Page A uni circle is a circle cenered a he origin wih a radius of. Is equaion is as shown in he drawing below. Here he leer represens an angle measure.
More information4. The Poisson Distribution
Virual Laboraories > 13. The Poisson Process > 1 2 3 4 5 6 7 4. The Poisson Disribuion The Probabiliy Densiy Funcion We have shown ha he k h arrival ime in he Poisson process has he gamma probabiliy densiy
More informationWhen one talks about a 'projectile', the implicabion is itrai we give an object
LAB, PROJECTLE MOruO.^\ 45 Lab Projecile Moion 1 nroducion n his lab we will look a he moion of a projecile in wo dimensions. When one alks abou a 'projecile', he implicabion is irai we give an objec an
More informationChapter 3. Motion in Two or Three Dimensions
Chaper 3 Moion in Two or Three Dimensions 1 Ouline 1. Posiion, eloci, acceleraion. Moion in a plane (Se of equaions) 3. Projecile Moion (Range, Heigh, Veloci, Trajecor) 4. Circular Moion (Polar coordinaes,
More informationChapter 4: Exponential and Logarithmic Functions
Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion
More information4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay
324 CHAPTER 4 Exponenial and Logarihmic Funcions 4.8 Exponenial Growh and Decay; Newon s Law; Logisic Growh and Decay OBJECTIVES 1 Find Equaions of Populaions Tha Obey he Law of Uninhibied Growh 2 Find
More informationMA261A Calculus III 2006 Fall Homework 4 Solutions Due 9/29/2006 8:00AM
MA6A Calculus III 006 Fall Homework 4 Soluions Due 9/9/006 00AM 97 #4 Describe in words he surface 3 A halflane in he osiive x and y erriory (See Figure in Page 67) 97 # Idenify he surface cos We see
More informationLenz's Law. Definition from the book:
Lenz's Law Definiion from he book: The induced emf resuling from a changing magneic flux has a polariy ha leads o an induced curren whose direcion is such ha he induced magneic field opposes he original
More informationInterference, Diffraction and Polarization
L.1  Simple nerference Chaper L nerference, Diffracion and Polarizaion A sinusoidal wave raveling in one dimension has he form: Blinn College  Physics 2426  Terry Honan A coshk x w L where in he case
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationConvexity. Concepts and Buzzwords. Dollar Convexity Convexity. Curvature, Taylor series, Barbell, Bullet. Convexity 1
Deb Insrumens and Markes Professor Carpener Convexiy Conceps and Buzzwords Dollar Convexiy Convexiy Curvaure, Taylor series, Barbell, Bulle Convexiy Deb Insrumens and Markes Professor Carpener Readings
More informationUnderstanding Sequential Circuit Timing
ENGIN112: Inroducion o Elecrical and Compuer Engineering Fall 2003 Prof. Russell Tessier Undersanding Sequenial Circui Timing Perhaps he wo mos disinguishing characerisics of a compuer are is processor
More informationMath 201 Lecture 12: CauchyEuler Equations
Mah 20 Lecure 2: CauchyEuler Equaions Feb., 202 Many examples here are aken from he exbook. The firs number in () refers o he problem number in he UA Cusom ediion, he second number in () refers o he problem
More informationRevisions to Nonfarm Payroll Employment: 1964 to 2011
Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm
More informationBasic Assumption: population dynamics of a group controlled by two functions of time
opulaion Models Basic Assumpion: populaion dynamics of a group conrolled by wo funcions of ime Birh Rae β(, ) = average number of birhs per group member, per uni ime Deah Rae δ(, ) = average number of
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More information1 The basic circulation problem
2WO08: Graphs and Algorihms Lecure 4 Dae: 26/2/2012 Insrucor: Nikhil Bansal The Circulaion Problem Scribe: Tom Slenders 1 The basic circulaion problem We will consider he maxflow problem again, bu his
More information23.3. Even and Odd Functions. Introduction. Prerequisites. Learning Outcomes
Even and Odd Funcions 23.3 Inroducion In his Secion we examine how o obain Fourier series of periodic funcions which are eiher even or odd. We show ha he Fourier series for such funcions is considerabl
More informationchapter Describing Motion chapter outline chapter overview unit one
Describing Moion chaper 2 chaper oeriew The main purpose of his chaper is o proide clear definiions and illusraions of he erms used in physics o describe moion, such as he moion of he car described in
More informationTHE PRESSURE DERIVATIVE
Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics THE PRESSURE DERIVATIVE The ressure derivaive has imoran diagnosic roeries. I is also imoran for making ye curve analysis more reliable.
More informationTwo Compartment Body Model and V d Terms by Jeff Stark
Two Comparmen Body Model and V d Terms by Jeff Sark In a onecomparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics  By his, we mean ha eliminaion is firs order and ha pharmacokineic
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationPart 1: White Noise and Moving Average Models
Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical
More informationM3. Experiment 3 NEWTON S LAWS OF MOTION M3. Purpose: Investigation of Newton s Laws of Motion using air track rail.
Experien 3 NEWTON S LAWS O OTION Purpose: Invesigaion of Newon s Laws of oion using air rack rail. Equipens: Air rack, blower (air source), ier, phoogaes, s wih differen asses, asses (0g), rope, pencil,
More informationChapter 2: Principles of steadystate converter analysis
Chaper 2 Principles of SeadySae Converer Analysis 2.1. Inroducion 2.2. Inducor volsecond balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationDIFFERENTIAL EQUATIONS with TI89 ABDUL HASSEN and JAY SCHIFFMAN. A. Direction Fields and Graphs of Differential Equations
DIFFERENTIAL EQUATIONS wih TI89 ABDUL HASSEN and JAY SCHIFFMAN We will assume ha he reader is familiar wih he calculaor s keyboard and he basic operaions. In paricular we have assumed ha he reader knows
More informationINVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS
INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,
More informationGraduate Macro Theory II: Notes on Neoclassical Growth Model
Graduae Macro Theory II: Noes on Neoclassical Growh Model Eric Sims Universiy of Nore Dame Spring 2011 1 Basic Neoclassical Growh Model The economy is populaed by a large number of infiniely lived agens.
More informationand Decay Functions f (t) = C(1± r) t / K, for t 0, where
MATH 116 Exponenial Growh and Decay Funcions Dr. Neal, Fall 2008 A funcion ha grows or decays exponenially has he form f () = C(1± r) / K, for 0, where C is he iniial amoun a ime 0: f (0) = C r is he rae
More informationFourier Series Solution of the Heat Equation
Fourier Series Soluion of he Hea Equaion Physical Applicaion; he Hea Equaion In he early nineeenh cenury Joseph Fourier, a French scienis and mahemaician who had accompanied Napoleon on his Egypian campaign,
More informationm m m m m correct
Version 055 Miderm 1 OConnor (05141) 1 This prinou should have 36 quesions. Muliplechoice quesions ma coninue on he ne column or pae find all choices before answerin. V1:1, V:1, V3:3, V4:, V5:1. 001
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67  FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1  TRANSIENTS
EDEXEL NAIONAL ERIFIAE/DIPLOMA UNI 67  FURHER ELERIAL PRINIPLE NQF LEEL 3 OUOME 2 UORIAL 1  RANIEN Uni conen 2 Undersand he ransien behaviour of resisorcapacior (R) and resisorinducor (RL) D circuis
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More informationMTH6121 Introduction to Mathematical Finance Lesson 5
26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random
More informationLecture III: Finish Discounted Value Formulation
Lecure III: Finish Discouned Value Formulaion I. Inernal Rae of Reurn A. Formally defined: Inernal Rae of Reurn is ha ineres rae which reduces he ne presen value of an invesmen o zero.. Finding he inernal
More informationCircuit Types. () i( t) ( )
Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All
More information