1. The graph shows the variation with time t of the velocity v of an object.

Size: px
Start display at page:

Download "1. The graph shows the variation with time t of the velocity v of an object."

Transcription

1 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 a res, akes ime o fall hrough a verical disance h. If air resisance is ignored, he ime aken for he ball o fall from res hrough a verical disance 9h is A. 3. B. 5. C. 9. D. 1. 1

2 3. An ahlee runs round a circular rack a consan speed. Which one of he following graphs bes represens he variaion wih ime of he magniude d of he displacemen of he ahlee from he saring posiion during one lap of he rack? A. d B. d C. d D. d 4. A ball is released from res near he surface of he Moon. Which one of he following quaniies increases a a consan rae? A. Only disance fallen B. Only speed C. Only speed and disance fallen D. Only speed and acceleraion 2

3 5. A ball is dropped from res a ime = on o a horizonal surface from which i rebounds. he graph shows he variaion of ime wih speed v of he ball. v A C B D Which one of he following bes represens he poin a which he ball jus loses conac wih he surface afer he firs bounce? A. A B. B C. C D. D 6. he diagram below shows he variaion wih ime of he velociy v of an objec. v 3

4 he area beween he line of he graph and he ime-axis represens A. he average velociy of he objec. B. he displacemen of he objec. C. he impulse acing on he objec. D. he work done on he objec. 7. he graph below shows he variaion wih ime of he disance moved by a car along a sraigh road. During which ime inerval does he car have is greaes acceleraion? disance moved A B C D ime 4

5 8. he minue hand of a clock hung on a verical wall has lengh L. P L he minue hand is observed a he ime shown above and hen again, 3 minues laer. Wha is he displacemen of, and he disance moved by, he end P of he minue hand during his ime inerval? displacemen disance moved A. 2L verically downwards πl B. 2L verically upwards πl C. 2L verically downwards 2L D. 2L verically upwards 2L 9. Which one of he following is a correc definiion of displacemen? A. Disance from a fixed poin B. Disance moved from a fixed poin C. Disance from a fixed poin in a given direcion D. Disance moved in a given direcion 5

6 1. he variaion wih ime of he speed v of a car moving along a sraigh road is shown below. v S S S Which area, S 1, S 2 or S 3, or combinaion of areas, represens he oal disance moved by he car during he ime ha is speed is reducing? A. S 1 B. S 3 C. S 1 + S 3 D. S 1 + S 2 + S 3 6

7 11. A ball is held a res in air. he ball is hen released. Which one of he following graphs bes shows he variaion wih ime of he disance d fallen by he ball? A. d B. d C. d D. d 7

8 12. A car acceleraes uniformly from res. I hen coninues a consan speed before he brakes are applied, bringing he car o res. Which of he following graphs bes shows he variaion wih ime of he acceleraion a of he car? A. a B. a C. a D. a 8

9 13. he graph below shows he variaion wih ime of he acceleraion a of a spaceship. a he spaceship is a res a =. he shaded area represens A. he disance ravelled by he spaceship beween = and =. B. he speed of he spaceship a =. C. he rae a which he speed of he spaceship changes beween = and =. D. he rae a which he acceleraion changes beween = and =. 14. A paricle moves from a poin P o a poin Q in a ime. Which one of he following correcly defines boh he average velociy and average acceleraion of he paricle? A. B. C. D. Average velociy displacemen of Q and P displacemen of Q and P disance beween Q and P disance beween Q and P Average acceleraion change in speed from Q o P change in velociy from Q o P change in speed from Q o P change in velociy from Q o P 9

10 15. wo sones, X and Y, of differen mass are dropped from he op of a cliff. Sone Y is dropped a shor ime afer sone X. Air resisance is negligible. Whils he sones are falling, he disance beween hem will A. decrease if he mass of Y is greaer han he mass of X. B. increase if he mass of X is greaer han he mass of Y. C. decrease wheher he mass of X is greaer or less han he mass of Y. D. increase wheher he mass of X is greaer or less han he mass of Y. 16. An archer shoos an arrow a an angle o he horizonal. Air resisance is negligible. Which of he following graphs bes represens he variaion wih ime of he horizonal componen of he arrow s velociy from he ime i is launched o he ime jus before i his he ground? A. velociy B. velociy ime ime C. velociy D. velociy ime ime 1

11 17. A ball is hrown verically upwards from he ground. he graph shows he variaion wih ime of he verical displacemen d of he ball. d D Which one of he following gives he final displacemen afer ime and he average speed beween ime = and ime =? Displacemen Average speed A. B. 2D C. 2D 2D D. 2D 11

12 18. he graph below shows how a quaniy y varies wih ime for a falling objec. y Which one of he following quaniies could be represened by y? A. Speed when air resisance is negligible B. Speed when air resisance is no negligible C. Disance moved from res when air resisance is negligible D. Disance moved from res when air resisance is no negligible 12

13 19. A ball is hrown verically upwards a ime =. Air resisance is no negligible and he acceleraion of free fall is g. he ball reaches a maximum heigh a ime = and hen descends, reaching a erminal speed. Which graph bes shows he variaion wih ime of he acceleraion a of he ball? A. a +g B. a +g g g C. a +g D. a +g g g 13

14 2. A body saring from res moves along a sraigh-line under he acion of a consan force. Afer ravelling a disance d he speed of he body is v. iniial posiion v d he speed of he body when i has ravelled a disance d 2 from is iniial posiion is v A.. 4 v B.. 2 v C.. 2 v D

15 21. he graph shows he variaion wih ime of he acceleraion a of an objec a / ms / s he objec is a res a ime =. Which of he following is he velociy of he objec a ime = 6. s? A..5 m s 1. B. 2. m s 1. C. 36 m s 1. D. 72 m s 1. 15

16 22. An objec is dropped from res from a poin several hundred meres above he surface of he Earh a ime =. he objec srikes he ground a = and air resisance is no negligible. Which of he following skech graphs bes shows he variaion wih ime, of he speed v of he objec? A. B. v v C. D. v v 16

17 23. Which of he following is a correc definiion of average acceleraion? A. B. C. D. changein velociy ime aken velociy ime aken change in speed ime aken speed ime aken 24. An objec has iniial speed u and acceleraion a. Afer ravelling a disance s, is final speed is v. he quaniies u, v, a and s are relaed by he expression v 2 = u 2 + 2as. Which of he following includes he wo condiions necessary for he equaion o apply? A. a has consan direcion u and v are in he same direcion B. a has consan direcion a, u and v are in he same direcion C. a has consan magniude a has consan direcion D. a has consan magniude u and v are in he same direcion 17

18 25. he graph below shows he variaion wih ime of he displacemen s of an objec moving along a sraigh-line. s / m / s he bes esimae of he insananeous speed of he objec a = 2. s is A.. ms 1. B..2 ms 1. C. 5. ms 1. D. 1. ms A small seel ball falls from res hrough a disance of 3 m. When calculaing he ime of fall, air resisance can be ignored because A. air is less dense han seel. B. air resisance increases wih he speed of he ball. C. he air is no moving. D. air resisance is much less han he weigh of he ball. 18

19 27. wo idenical meal spheres are held above he ground as shown. spheres (no o scale) ground he separaion beween hem is small compared o heir disance above he ground. When he spheres are released, he separaion of he spheres will A. remain consan. B. decrease coninuously. C. increase coninuously. D. increase iniially and hen remain consan. 28. An objec is falling, in air, owards he Earh s surface. Wha changes occur in he acceleraion and in he velociy of he objec as i approaches erminal velociy? acceleraion velociy A. decreases o zero increases coninuously B. decreases o zero increases o a consan value C. consan increases o a consan value D. consan increases coninuously 19

20 29. he graph below shows he variaion wih ime of he acceleraion a of an objec from = o =. a he shaded area under he graph represens change in A. displacemen. B. velociy. C. momenum. D. kineic energy. 3. his quesion is abou linear moion. A police car P is saionary by he side of a road. A car S, exceeding he speed limi, passes he police car P a a consan speed of 18 m s 1. he police car P ses off o cach car S jus as car S passes he police car P. Car P acceleraes a 4.5 m s 2 for a ime of 6. s and hen coninues a consan speed. Car P akes a ime seconds o draw level wih car S. (a) (i) Sae an expression, in erms of, for he disance car S ravels in seconds... (ii) Calculae he disance ravelled by he police car P during he firs 6. seconds of is moion

21 (iii) Calculae he speed of he police car P afer i has compleed is acceleraion..... (iv) Sae an expression, in erms of, for he disance ravelled by he police car P during he ime ha i is ravelling a consan speed... (b) Using your answers o (a), deermine he oal ime aken for he police car P o draw level wih car S (2) (oal 6 marks) 31. Linear moion (a) Define he erm acceleraion (2) 21

22 (b) An objec has an iniial speed u and an acceleraion a. Afer ime, is speed is v and i has moved hrough a disance s. he moion of he objec may be summarized by he equaions v = u + a, 1 s = ( v + u). (i) Sae he assumpion made in hese equaions abou he acceleraion a. 2 (ii) Derive, using hese equaions, an expression for v in erms of u, s and a. (2) 22

23 (c) he shuer speed of a camera is he ime ha he film is exposed o ligh. In order o deermine he shuer speed of a camera, a meal ball is held a res a he zero mark of a verical scale, as shown below. he ball is released. he shuer of a camera is opened as he ball falls. cm scale 196 cm camera 28 cm he phoograph of he ball shows ha he shuer opened as he ball reached he 196 cm mark on he scale and closed as i reached he 28 cm mark. Air resisance is negligible and he acceleraion of free fall is 9.81 m s 2. (i) Calculae he ime for he ball o fall from res o he 196 cm mark. (2) (ii) Deermine he ime for which he shuer was open. ha is, he ime for he ball o fall from he 196 cm mark o he 28 cm mark. (2) (oal 9 marks) 23

24 32. Moion of a ball A ball of mass.25 kg is projeced verically upwards from he ground wih an iniial velociy of 3 m s 1. he acceleraion of free fall is 1 m s 2, bu air resisance canno be negleced. he graph below shows he variaion wih ime of he velociy v of his ball for he upward par of he moion. v / ms /s (a) Sae wha he area under he graph represens

25 (b) Esimae he maximum heigh reached by he ball (c) Deermine, for he ball a = 1. s, (i) he acceleraion; (3) (ii) he magniude of he force of air resisance. (2) (d) Use he graph o explain, wihou any furher calculaions, ha he force of air resisance is decreasing in magniude as he ball moves upward (2) 25

26 (e) he diagram below is a skech graph of he upward moion of he ball. Draw a line o indicae he downward moion of he ball. he line should indicae he moion from he maximum heigh of he ball unil jus before i his he ground. v / ms / s (2) (f) Sae and explain, by reference o energy ransformaions, wheher he speed wih which he ball his he ground is equal o 3 m s (2) (g) Use your answer in (f) o sae and explain wheher he ball akes 2. s o move from is maximum heigh o he ground (2) (oal 15 marks) 26

MOTION ALONG A STRAIGHT LINE

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,

More information

Chapter 2 Kinematics in One Dimension

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

More information

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

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 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

More information

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

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 information

Rotational Inertia of a Point Mass

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

More information

Relative velocity in one dimension

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

More information

( ) in the following way. ( ) < 2

( ) 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

More information

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

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

More information

Newton's second law in action

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

More information

Acceleration Lab Teacher s Guide

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

More information

Physics 107 HOMEWORK ASSIGNMENT #2

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.

More information

AP1 Kinematics (A) (C) (B) (D) Answer: C

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)

More information

Section A: Forces and Motion

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

More information

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 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 information

Newton s Laws of Motion

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

More information

Name: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling

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)

More information

Application of kinematic equation:

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

More information

AP Calculus BC 2010 Scoring Guidelines

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

More information

Section 7.1 Angles and Their Measure

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

More information

4kq 2. D) south A) F B) 2F C) 4F D) 8F E) 16F

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

More information

Week #9 - The Integral Section 5.1

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,

More information

Chapter 11A Angular Motion. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

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

More information

A Curriculum Module for AP Calculus BC Curriculum Module

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.

More information

Discussion Examples Chapter 10: Rotational Kinematics and Energy

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.

More information

AP Physics Velocity and Linear Acceleration Unit 1 Problems:

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

More information

AP Calculus AB 2013 Scoring Guidelines

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

More information

m m m m m correct

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

More information

Motion Along a Straight Line

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

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

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

More information

Chapter 2 Motion in One Dimension

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

More information

Chapter 2 Motion in One Dimension

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

More information

RC, RL and RLC circuits

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.

More information

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

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

More information

Section 2.3 Linear and Angular Velocities

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

More information

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

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

More information

4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay

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

More information

LAB 6: SIMPLE HARMONIC MOTION

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:

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

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

More information

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 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

More information

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

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

More information

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

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

More information

Chapter 2: Principles of steady-state converter analysis

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

More information

RC (Resistor-Capacitor) Circuits. AP Physics C

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

More information

Chapter 3. Motion in Two or Three Dimensions

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,

More information

Lenz's Law. Definition from the book:

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

More information

M-3. Experiment 3 NEWTON S LAWS OF MOTION M-3. Purpose: Investigation of Newton s Laws of Motion using air track rail.

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,

More information

Velocity & Acceleration Analysis

Velocity & Acceleration Analysis Velociy & Acceleraion Analysis Secion 4 Velociy analysis deermines how fas pars of a machine are moving. Linear Velociy (v) Sraigh line, insananeous speed of a poin. ds s v = d Linear velociy is a vecor.

More information

CHARGE AND DISCHARGE OF A CAPACITOR

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:

More information

Chapter 8 Copyright Henning Umland All Rights Reserved

Chapter 8 Copyright Henning Umland All Rights Reserved 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

More information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO

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,

More information

Renewal processes and Poisson process

Renewal processes and Poisson process CHAPTER 3 Renewal processes and Poisson process 31 Definiion of renewal processes and limi heorems Le ξ 1, ξ 2, be independen and idenically disribued random variables wih P[ξ k > 0] = 1 Define heir parial

More information

A Mathematical Description of MOSFET Behavior

A Mathematical Description of MOSFET Behavior 10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical

More information

Imagine a Source (S) of sound waves that emits waves having frequency f and therefore

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

More information

Two Compartment Body Model and V d Terms by Jeff Stark

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

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1 - TRANSIENTS

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

More information

9. Capacitor and Resistor Circuits

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

More information

Chabot College Physics Lab RC Circuits Scott Hildreth

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

More information

When one talks about a 'projectile', the implicabion is itrai we give an object

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

More information

AP Calculus AB 2010 Scoring Guidelines

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

More information

Contents. TOPIC 1 Working as a Physicist 8 1 Units 8 2 Estimation 10

Contents. TOPIC 1 Working as a Physicist 8 1 Units 8 2 Estimation 10 7 Behaviour can Conens be learned1 Conens How o use his book 6 TOPIC 1 Working as a Physicis 1 Unis Esimaion 1 TOPIC Mechanics.1 Moion 1 1 Velociy and acceleraion 1 Moion graphs 14 3 Adding forces 17 4

More information

Circuit Types. () i( t) ( )

Circuit 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

Physic 231 Lecture 6. Main points of today s lecture: Trajectories of objects in 2 dimensions:

Physic 231 Lecture 6. Main points of today s lecture: Trajectories of objects in 2 dimensions: Main poins of oda s lecure: Trajecories of objecs in dimensions: Relaie Veloci Phsic 31 Lecure 6 Main poins of las lecure: Two dimension coordinae ssems Vecors and componens Trajecories of objecs in dimensions:

More information

2. Waves in Elastic Media, Mechanical Waves

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

More information

and Decay Functions f (t) = C(1± r) t / K, for t 0, where

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

More information

AP Calculus AB 2007 Scoring Guidelines

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

More information

Capacitors and inductors

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

More information

EXERCISES AND PROBLEMS

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

More information

chapter Describing Motion chapter outline chapter overview unit one

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

More information

Graphing the Von Bertalanffy Growth Equation

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

More information

Physics 111 Fall 2007 Electric Currents and DC Circuits

Physics 111 Fall 2007 Electric Currents and DC Circuits Physics 111 Fall 007 Elecric Currens and DC Circuis 1 Wha is he average curren when all he sodium channels on a 100 µm pach of muscle membrane open ogeher for 1 ms? Assume a densiy of 0 sodium channels

More information

6.5. Modelling Exercises. Introduction. Prerequisites. Learning Outcomes

6.5. Modelling Exercises. Introduction. Prerequisites. Learning Outcomes Modelling Exercises 6.5 Inroducion This Secion provides examples and asks employing exponenial funcions and logarihmic funcions, such as growh and decay models which are imporan hroughou science and engineering.

More information

State Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University

State Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University Inroducion ae Machines: Brief Inroducion o equencers Prof. Andrew J. Mason, Michigan ae Universiy A sae machine models behavior defined by a finie number of saes (unique configuraions), ransiions beween

More information

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.

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,

More information

The Transport Equation

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

More information

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.

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

More information

Period 4 Activity Solutions: Transfer of Thermal Energy

Period 4 Activity Solutions: Transfer of Thermal Energy Period 4 Aciviy Soluions: Transfer of Thermal nergy 4.1 How Does Temperaure Differ from Thermal nergy? a) Temperaure Your insrucor will demonsrae molecular moion a differen emperaures. 1) Wha happens o

More information

Representing Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1

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

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

The Torsion of Thin, Open Sections

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

More information

Understanding Sequential Circuit Timing

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

More information

Fourier Series Solution of the Heat Equation

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,

More information

Chapter 12 PURE TORSION

Chapter 12 PURE TORSION Chaper 1 PURE TORSION 1.1 GENERALS A member is subjeced o pure orsion if in any cross secion of his member he single sress differen from zero is he momen of orsion or wising (shorer TORQUE). Pure orsion

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

Inductance and Transient Circuits

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

More information

Chapter 6: Business Valuation (Income Approach)

Chapter 6: Business Valuation (Income Approach) Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he

More information

YTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.

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

More information

Revisions to Nonfarm Payroll Employment: 1964 to 2011

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

More information

5.5 Modeling Harmonic Motion

5.5 Modeling Harmonic Motion 44 CHAPTER 5 Trigonomeric Funcions of Real Numbers 77(b)Skech a graph of he funcion d for. (c) Wha happens o he disance d as approaches? (c) From he graph deermine he values of a which he lengh of he shadow

More information

Chapter 4: Exponential and Logarithmic Functions

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

More information

2.6 Limits at Infinity, Horizontal Asymptotes Math 1271, TA: Amy DeCelles. 1. Overview. 2. Examples. Outline: 1. Definition of limits at infinity

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

More information

Using RCtime to Measure Resistance

Using RCtime to Measure Resistance Basic Express Applicaion Noe Using RCime o Measure Resisance Inroducion One common use for I/O pins is o measure he analog value of a variable resisance. Alhough a buil-in ADC (Analog o Digial Converer)

More information

Damped Harmonic Motion Closing Doors and Bumpy Rides

Damped Harmonic Motion Closing Doors and Bumpy Rides Prerequisies and Goal Damped Harmonic Moion Closing Doors and Bumpy Rides Andrew Forreser May 4, 21 Assuming you are familiar wih simple harmonic moion, is equaion of moion, and is soluions, we will now

More information

CHAPTER FIVE. Solutions for Section 5.1

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

More information

Capital budgeting techniques

Capital budgeting techniques Capial budgeing echniques A reading prepared by Pamela Peerson Drake O U T L I N E 1. Inroducion 2. Evaluaion echniques 3. Comparing echniques 4. Capial budgeing in pracice 5. Summary 1. Inroducion The

More information

TEACHER NOTES HIGH SCHOOL SCIENCE NSPIRED

TEACHER NOTES HIGH SCHOOL SCIENCE NSPIRED Radioacive Daing Science Objecives Sudens will discover ha radioacive isoopes decay exponenially. Sudens will discover ha each radioacive isoope has a specific half-life. Sudens will develop mahemaical

More information

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z o ffix uden abel ere uden ame chool ame isric ame/ ender emale ale onh ay ear ae of irh an eb ar pr ay un ul ug ep c ov ec as ame irs ame lace he uden abel ere ae uden denifier chool se nly rined in he

More information

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are

More information

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

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

More information