# 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

Save this PDF as:

Size: px
Start display at page:

Download "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"

## 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. (a-d) 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 2-23 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 up--ploed -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 axis--so 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 rocke-propelled 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 high-speed 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 2-24). 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

### 1. 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

### MOTION 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,

### ( ) 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 man-made. Wrie down several of hem. Horizonal cars waer

### Chapter 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

### Acceleration 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

### Week #9 - The Integral Section 5.1

Week #9 - The Inegral Secion 5.1 From Calculus, Single Variable by Hughes-Halle, Gleason, McCallum e. al. Copyrigh 005 by John Wiley & Sons, Inc. This maerial is used by permission of John Wiley & Sons,

### Section 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

### Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prin-ou should hae 1 quesions. Muliple-choice quesions may coninue on he ne column or page find all choices before making your selecion. The

### Relative 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

### Rotational 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

### A 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 no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy.

### Newton'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

### Chapter 7. Response of First-Order RL and RC Circuits

Chaper 7. esponse of Firs-Order 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

### AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

### Motion 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

### Application of kinematic equation:

HELP: See me (office hours). There will be a HW help session on Monda nigh from 7-8 in Nicholson 109. Tuoring a #10 of Nicholson Hall. Applicaion of kinemaic equaion: a = cons. v= v0 + a = + v + 0 0 a

### Chapter 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,

### AP1 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)

### Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa

### cooking 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

### 4kq 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

### AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

### Section 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

### Name: 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

### Random Walk in 1-D. 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

### 11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

Inroducion Chaper 14: Dynamic D-S 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 cuing-edge

### Imagine 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

### CHARGE 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:

### Mathematics 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

### AP 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

### CHAPTER 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

### Physics 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 Muliple-Concep Example 9 deals wih he conceps ha are imporan in his problem.

### 2.6 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

### Representing 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

### EXERCISES 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

### Discussion 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.

### Chapter 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

### Newton 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

### RC, 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.

### Graphing the Von Bertalanffy Growth Equation

file: d:\b173-2013\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

### Section 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

### Chapter 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

### Permutations 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 k-value for he middle erm, divide

### LAB 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:

### 2. 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

### PROFIT 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,

### 1. 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..

### HANDOUT 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

### Name: 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)

### Kinematics in 1-D From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard.

Chaper 2 Kinemaics in 1-D 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

### AP Calculus AB 2007 Scoring Guidelines

AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and

Chaper 8 Copyrigh 1997-2004 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

### The 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

### 9. 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

### Chapter 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

### RC (Resistor-Capacitor) Circuits. AP Physics C

(Resisor-Capacior 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

### Chabot 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

### The 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

### YTM 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

### Chapter 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

### Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

ull-wave 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

### Economics 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

### AP Calculus AB 2010 Scoring Guidelines

AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College

### 4.2 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.

### 4. 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

### When 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

### Chapter 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,

### Chapter 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

### 4.8 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

### MA261-A Calculus III 2006 Fall Homework 4 Solutions Due 9/29/2006 8:00AM

MA6-A Calculus III 006 Fall Homework 4 Soluions Due 9/9/006 00AM 97 #4 Describe in words he surface 3 A half-lane in he osiive x and y erriory (See Figure in Page 67) 97 # Idenify he surface cos We see

### Lenz'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

### Interference, 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

### Inductance 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

### Convexity. 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

### Understanding 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

### Math 201 Lecture 12: Cauchy-Euler Equations

Mah 20 Lecure 2: Cauchy-Euler 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

### Revisions 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

### Basic 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

### PROFIT 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

### 1 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 max-flow problem again, bu his

### 23.3. 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

### chapter 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

### THE 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.

### Two Compartment Body Model and V d Terms by Jeff Stark

Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

### Economics 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

### Part 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

### M-3. Experiment 3 NEWTON S LAWS OF MOTION M-3. 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,

### Chapter 2: Principles of steady-state converter analysis

Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer

### DIFFERENTIAL EQUATIONS with TI-89 ABDUL HASSEN and JAY SCHIFFMAN. A. Direction Fields and Graphs of Differential Equations

DIFFERENTIAL EQUATIONS wih TI-89 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

### INVESTIGATION 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,

### Graduate 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.

### and 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

### Fourier 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,

### m m m m m correct

Version 055 Miderm 1 OConnor (05141) 1 This prin-ou should have 36 quesions. Muliple-choice quesions ma coninue on he ne column or pae find all choices before answerin. V1:1, V:1, V3:3, V4:, V5:1. 001

### EDEXCEL 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 resisor-capacior (R) and resisor-inducor (RL) D circuis

### Capacitors 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

### MTH6121 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