1. Analytically determine the equation of the line tangent to f at x = 2.


 Nathaniel Wilcox
 1 years ago
 Views:
Transcription
1 Warm Up!! Given: 1. Analytically determine the equation of the line tangent to f at x = Using transformations to help you, sketch the graph of. 3. On the same grid, sketch the graph of. y x
2 Given: 4. Is f increasing or decreasing at x = 2? Justify analytically. 5. Write the equation of. 2
3 Big Ideas: * Displacement versus Position versus Distance Traveled * Velocity versus Speed * Speeding up and slowing down Goals * Given an equation for the displacement or position of a moving particle, write an equation for > the velocity of the object at any time, t > the acceleration of the object at any time, t * Analytically analyze the motion of the particle using the equations for the velocity and acceleration. 3
4 Displacement vs. Distance Traveled Displacement is the directed distance between a particle's terminal position and its initial position. May be positive or negative or zero The distance traveled is the total distance traveled from first point to second point. Always non negative Displacement: you only care where you end up. Distance: you care how you got there 4
5 The velocity is the instantaneous rate of change in the displacement with respect to time. That is, the velocity function is the derivative of the displacement function. Let be the displacement of a particle. The unit for f is a unit of length (ft, in, m, etc) Then is the velocity. The unit for is. 5
6 A velocity has two parts: the sign and the rate The sign of the velocity tells you the direction you are moving: * positive means displacement is increasing (so usually particle is moving up or to the right). * negative means the displacement is decreasing (so usually the particle is moving down or to the left). The rate tells you have fast the displacement is changing in the given direction. A velocity of zero means the particle is at rest. 6
7 Example: The height in meters of a falcon above the ground at x minutes is given by a. What is the displacement of the falcon at 1.5 minutes? b. What is the velocity of the falcon at min? Justify your answer using correct notation and include units. c. At t = 2 min, is the falcon flying up or down? How do you know? 7
8 Velocity vs. Speed Velocity describes the direction and rate that a particle is moving. Velocity is the derivative of displacement. Speed describes the rate that a particle is moving. Speed has no direction. Speed is the absolute value of velocity. 8
9 Acceleration is the instantaneous rate of change of velocity. Acceleration is the derivative of the velocity. The unit of acceleration is the unit of velocity divided by time. displacement velocity acceleration The sign of the acceleration describes whether the velocity function is increasing or decreasing since acceleration is the "slope" of velocity. (Note: This does not tell you whether a particle is speeding up! Remember "speed" and "velocity" are different.) 9
10 Remember our falcon? (minutes, meters) Is the falcon moving up or down at t = 1.8 min? Justify analytically. What is the falcon's speed at t = 1.8? Justify analytically. What is the falcon's acceleration at t = 1.8. Justify analytically. 10
11 Speeding up Slowing down Speed is increasing Speed is decreasing Velocity and acceleration have the same sign. Velocity and acceleration have the different signs. If the velocity is positive and the slope of the velocity is positive, then the velocity is getting further from zero. The speed, therefore, is getting further from zero. Similarly, if the velocity is negative and the slope of the velocity is positive, then the velocity is getting further from zero. Therefore, the speed is getting further from zero so is increasing. If the velocity is positive but the slope of the velocity is negative, then the velocity is getting closer to zero. The speed, therefore, is getting closer to zero. Similarly, if the velocity is negative but the slope of the velocity is positive, then the velocity is getting closer to zero. Therefore, the speed is getting closer to zero. 11
12 1. What is the difference between displacement of an object and the distance it travels while it is in motion? 2. What is the difference between the velocity of a moving object and the speed at which it is traveling? 12
13 3. True or False: "If the acceleration of a moving object is negative, then the object is slowing down." 13
14 4. A particle moves along the x axis with a displacement x feet from the origin given as a function of t seconds by. a. Write the equation of the velocity. b. At t = 2, what are the velocity and acceleration of the particle? c. Is the particle speeding up or slowing down at t = 2? At what rate? 14
15 15
16 16
17 Attachments TI SmartView_TI 84.exe
In order to describe motion you need to describe the following properties.
Chapter 2 One Dimensional Kinematics How would you describe the following motion? Ex: random 1D path speeding up and slowing down In order to describe motion you need to describe the following properties.
More informationWorksheet 1. What You Need to Know About Motion Along the xaxis (Part 1)
Worksheet 1. What You Need to Know About Motion Along the xaxis (Part 1) In discussing motion, there are three closely related concepts that you need to keep straight. These are: If x(t) represents the
More information1.3.1 Position, Distance and Displacement
In the previous section, you have come across many examples of motion. You have learnt that to describe the motion of an object we must know its position at different points of time. The position of an
More information1 One Dimensional Horizontal Motion Position vs. time Velocity vs. time
PHY132 Experiment 1 One Dimensional Horizontal Motion Position vs. time Velocity vs. time One of the most effective methods of describing motion is to plot graphs of distance, velocity, and acceleration
More information= f x 1 + h. 3. Geometrically, the average rate of change is the slope of the secant line connecting the pts (x 1 )).
Math 1205 Calculus/Sec. 3.3 The Derivative as a Rates of Change I. Review A. Average Rate of Change 1. The average rate of change of y=f(x) wrt x over the interval [x 1, x 2 ]is!y!x ( )  f( x 1 ) = y
More informationTo define concepts such as distance, displacement, speed, velocity, and acceleration.
Chapter 7 Kinematics of a particle Overview In kinematics we are concerned with describing a particle s motion without analysing what causes or changes that motion (forces). In this chapter we look at
More informationAverage rate of change of y = f(x) with respect to x as x changes from a to a + h:
L151 Lecture 15: Section 3.4 Definition of the Derivative Recall the following from Lecture 14: For function y = f(x), the average rate of change of y with respect to x as x changes from a to b (on [a,
More informationScalar versus Vector Quantities. Speed. Speed: Example Two. Scalar Quantities. Average Speed = distance (in meters) time (in seconds) v =
Scalar versus Vector Quantities Scalar Quantities Magnitude (size) 55 mph Speed Average Speed = distance (in meters) time (in seconds) Vector Quantities Magnitude (size) Direction 55 mph, North v = Dx
More informationMotion. Complete Table 1. Record all data to three decimal places (e.g., 4.000 or 6.325 or 0.000). Do not include units in your answer.
Labs for College Physics: Mechanics Worksheet Experiment 21 Motion As you work through the steps in the lab procedure, record your experimental values and the results on this worksheet. Use the exact
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. Dr Tay Seng Chuan
Ground Rules PC11 Fundamentals of Physics I Lectures 3 and 4 Motion in One Dimension Dr Tay Seng Chuan 1 Switch off your handphone and pager Switch off your laptop computer and keep it No talking while
More information18.01 Single Variable Calculus Fall 2006
MIT OpenCourseWare http://ocw.mit.edu 8.0 Single Variable Calculus Fall 2006 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Unit : Derivatives A. What
More informationMotion Graphs. It is said that a picture is worth a thousand words. The same can be said for a graph.
Motion Graphs It is said that a picture is worth a thousand words. The same can be said for a graph. Once you learn to read the graphs of the motion of objects, you can tell at a glance if the object in
More informationChapter 2: Describing Motion
Chapter 2: Describing Motion 1. An auto, starting from rest, undergoes constant acceleration and covers a distance of 1000 meters. The final speed of the auto is 80 meters/sec. How long does it take the
More information1 of 7 9/5/2009 6:12 PM
1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]
More informationGraph Matching. walk back and forth in front of Motion Detector
Experiment 1 One of the most effective methods of describing motion is to plot graphs of distance, velocity, and acceleration vs. time. From such a graphical representation, it is possible to determine
More informationGRAPH MATCHING EQUIPMENT/MATERIALS
GRAPH MATCHING LAB MECH 6.COMP. From Physics with Computers, Vernier Software & Technology, 2000. Mathematics Teacher, September, 1994. INTRODUCTION One of the most effective methods of describing motion
More informationSection 1: Instantaneous Rate of Change and Tangent Lines Instantaneous Velocity
Chapter 2 The Derivative Business Calculus 74 Section 1: Instantaneous Rate of Change and Tangent Lines Instantaneous Velocity Suppose we drop a tomato from the top of a 100 foot building and time its
More informationEXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives
EXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives to verify how the distance of a freelyfalling body varies with time to investigate whether the velocity
More informationPhysics Kinematics Model
Physics Kinematics Model I. Overview Active Physics introduces the concept of average velocity and average acceleration. This unit supplements Active Physics by addressing the concept of instantaneous
More informationGraphing Motion. Every Picture Tells A Story
Graphing Motion Every Picture Tells A Story Read and interpret motion graphs Construct and draw motion graphs Determine speed, velocity and accleration from motion graphs If you make a graph by hand it
More informationCalculus Card Matching
Card Matching Card Matching A Game of Matching Functions Description Give each group of students a packet of cards. Students work as a group to match the cards, by thinking about their card and what information
More information2.4 Motion and Integrals
2 KINEMATICS 2.4 Motion and Integrals Name: 2.4 Motion and Integrals In the previous activity, you have seen that you can find instantaneous velocity by taking the time derivative of the position, and
More informationStudent Activity: To investigate an ESB bill
Student Activity: To investigate an ESB bill Use in connection with the interactive file, ESB Bill, on the Student s CD. 1. What are the 2 main costs that contribute to your ESB bill? 2. a. Complete the
More informationPLOTTING DATA AND INTERPRETING GRAPHS
PLOTTING DATA AND INTERPRETING GRAPHS Fundamentals of Graphing One of the most important sets of skills in science and mathematics is the ability to construct graphs and to interpret the information they
More informationThe slope m of the line passes through the points (x 1,y 1 ) and (x 2,y 2 ) e) (1, 3) and (4, 6) = 1 2. f) (3, 6) and (1, 6) m= 6 6
Lines and Linear Equations Slopes Consider walking on a line from left to right. The slope of a line is a measure of its steepness. A positive slope rises and a negative slope falls. A slope of zero means
More informationCalculus 1st Semester Final Review
Calculus st Semester Final Review Use the graph to find lim f ( ) (if it eists) 0 9 Determine the value of c so that f() is continuous on the entire real line if f ( ) R S T, c /, > 0 Find the limit: lim
More informationPhysics 1010: The Physics of Everyday Life. TODAY Velocity, Acceleration 1D motion under constant acceleration Newton s Laws
Physics 11: The Physics of Everyday Life TODAY, Acceleration 1D motion under constant acceleration Newton s Laws 1 VOLUNTEERS WANTED! PHET, The PHysics Educational Technology project, is looking for students
More informationMotion Graphs. Plotting distance against time can tell you a lot about motion. Let's look at the axes:
Motion Graphs 1 Name Motion Graphs Describing the motion of an object is occasionally hard to do with words. Sometimes graphs help make motion easier to picture, and therefore understand. Remember: Motion
More informationf(x) f(a) x a Our intuition tells us that the slope of the tangent line to the curve at the point P is m P Q =
Lecture 6 : Derivatives and Rates of Cange In tis section we return to te problem of finding te equation of a tangent line to a curve, y f(x) If P (a, f(a)) is a point on te curve y f(x) and Q(x, f(x))
More informationLINEAR INEQUALITIES. less than, < 2x + 5 x 3 less than or equal to, greater than, > 3x 2 x 6 greater than or equal to,
LINEAR INEQUALITIES When we use the equal sign in an equation we are stating that both sides of the equation are equal to each other. In an inequality, we are stating that both sides of the equation are
More informationSlope and Rate of Change
Chapter 1 Slope and Rate of Change Chapter Summary and Goal This chapter will start with a discussion of slopes and the tangent line. This will rapidly lead to heuristic developments of limits and the
More informationChapter 4 One Dimensional Kinematics
Chapter 4 One Dimensional Kinematics 41 Introduction 1 4 Position, Time Interval, Displacement 41 Position 4 Time Interval 43 Displacement 43 Velocity 3 431 Average Velocity 3 433 Instantaneous Velocity
More informationLearning Objectives for Math 165
Learning Objectives for Math 165 Chapter 2 Limits Section 2.1: Average Rate of Change. State the definition of average rate of change Describe what the rate of change does and does not tell us in a given
More informationPhysics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE
1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object
More informationSpeed, velocity and acceleration
Chapter Speed, velocity and acceleration Figure.1 What determines the maximum height that a polevaulter can reach? 1 In this chapter we look at moving bodies, how their speeds can be measured and how
More information1 of 10 11/23/2009 6:37 PM
hapter 14 Homework Due: 9:00am on Thursday November 19 2009 Note: To understand how points are awarded read your instructor's Grading Policy. [Return to Standard Assignment View] Good Vibes: Introduction
More information21 Position, Displacement, and Distance
21 Position, Displacement, and Distance In describing an object s motion, we should first talk about position where is the object? A position is a vector because it has both a magnitude and a direction:
More informationcorrectchoice plot f(x) and draw an approximate tangent line at x = a and use geometry to estimate its slope comment The choices were:
Topic 1 2.1 mode MultipleSelection text How can we approximate the slope of the tangent line to f(x) at a point x = a? This is a Multiple selection question, so you need to check all of the answers that
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension
Physics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension Conceptual Questions 1) Suppose that an object travels from one point in space to another. Make
More informationAverage rate of change
Average rate of change 1 1 Average rate of change A fundamental philosophical truth is that everything changes. 1 Average rate of change A fundamental philosophical truth is that everything changes. In
More informationProblem 12.33. s s o v o t 1 2 a t2. Ball B: s o 0, v o 19 m s, a 9.81 m s 2. Apply eqn. 125: When the balls pass each other: s A s B. t 2.
ENPH 131 Assignment # Solutions Tutorial Problem (Rocket Height) A rocket, initially at rest on the ground, accelerates straight upward with a constant acceleration of 3. m s. The rocket accelerates for
More informationWorksheet for Exploration 2.1: Compare Position vs. Time and Velocity vs. Time Graphs
Worksheet for Exploration 2.1: Compare Position vs. Time and Velocity vs. Time Graphs Shown are three different animations, each with three toy monster trucks moving to the right. Two ways to describe
More informationPhysics Midterm Review Packet January 2010
Physics Midterm Review Packet January 2010 This Packet is a Study Guide, not a replacement for studying from your notes, tests, quizzes, and textbook. Midterm Date: Thursday, January 28 th 8:1510:15 Room:
More information76: Solving Open Sentences Involving Absolute Value. 76: Solving Open Sentences Involving Absolute Value
OBJECTIVE: You will be able to solve open sentences involving absolute value and graph the solutions. We need to start with a discussion of what absolute value means. Absolute value is a means of determining
More informationInequalities  Absolute Value Inequalities
3.3 Inequalities  Absolute Value Inequalities Objective: Solve, graph and give interval notation for the solution to inequalities with absolute values. When an inequality has an absolute value we will
More informationAP Calculus AB 2010 FreeResponse Questions Form B
AP Calculus AB 2010 FreeResponse Questions Form B The College Board The College Board is a notforprofit membership association whose mission is to connect students to college success and opportunity.
More informationExam 1 Review Questions PHY 2425  Exam 1
Exam 1 Review Questions PHY 2425  Exam 1 Exam 1H Rev Ques.doc  1  Section: 1 7 Topic: General Properties of Vectors Type: Conceptual 1 Given vector A, the vector 3 A A) has a magnitude 3 times that
More informationDerivatives as Rates of Change
Derivatives as Rates of Change OneDimensional Motion An object moving in a straight line For an object moving in more complicated ways, consider the motion of the object in just one of the three dimensions
More informationSection 2.5 Average Rate of Change
Section.5 Average Rate of Change Suppose that the revenue realized on the sale of a company s product can be modeled by the function R( x) 600x 0.3x, where x is the number of units sold and R( x ) is given
More informationAbsolute Value Equations and Inequalities
. Absolute Value Equations and Inequalities. OBJECTIVES 1. Solve an absolute value equation in one variable. Solve an absolute value inequality in one variable NOTE Technically we mean the distance between
More informationPhysics 1050 Experiment 2. Acceleration Due to Gravity
Acceleration Due to Gravity Prelab Questions These questions need to be completed before entering the lab. Please show all workings. Prelab 1: For a falling ball, which bounces, draw the expected shape
More information3.1 MAXIMUM, MINIMUM AND INFLECTION POINT & SKETCHING THE GRAPH. In Isaac Newton's day, one of the biggest problems was poor navigation at sea.
BA01 ENGINEERING MATHEMATICS 01 CHAPTER 3 APPLICATION OF DIFFERENTIATION 3.1 MAXIMUM, MINIMUM AND INFLECTION POINT & SKETCHING THE GRAPH Introduction to Applications of Differentiation In Isaac Newton's
More informationCh 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43
Ch 7 Kinetic Energy and Work Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Technical definition of energy a scalar quantity that is associated with that state of one or more objects The state
More informationPRACTICE FINAL. Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 10cm.
PRACTICE FINAL Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 1cm. Solution. Let x be the distance between the center of the circle
More informationPhysics 2048 Test 1 Solution (solutions to problems 25 are from student papers) Problem 1 (Short Answer: 20 points)
Physics 248 Test 1 Solution (solutions to problems 25 are from student papers) Problem 1 (Short Answer: 2 points) An object's motion is restricted to one dimension along the distance axis. Answer each
More informationFocused Learning Lesson Science Grades 912 PSHE2
Focused Learning Lesson Science Grades 912 PSHE2 Overview: This lesson is designed to review the basic relationships of speed, velocity, and acceleration. During the lesson, students will review the
More informationUnit 2 Kinematics Worksheet 1: Position vs. Time and Velocity vs. Time Graphs
Name Physics Honors Pd Date Unit 2 Kinematics Worksheet 1: Position vs. Time and Velocity vs. Time Graphs Sketch velocity vs. time graphs corresponding to the following descriptions of the motion of an
More informationDespite its enormous mass (425 to 900 kg), the Cape buffalo is capable of running at a top speed of about 55 km/h (34 mi/h).
Revised Pages PART ONE Mechanics CHAPTER Motion Along a Line 2 Despite its enormous mass (425 to 9 kg), the Cape buffalo is capable of running at a top speed of about 55 km/h (34 mi/h). Since the top speed
More informationChapter 6 Work and Energy
Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system
More informationCalculus Vocabulary without the Technical Mumbo Jumbo
Calculus Vocabulary without the Technical Mumbo Jumbo Limits and Continuity By: Markis Gardner Table of Contents Average Rate of Change... 4 Average Speed... 5 Connected Graph... 6 Continuity at a point...
More information5. Unable to determine. 6. 4 m correct. 7. None of these. 8. 1 m. 9. 1 m. 10. 2 m. 1. 1 m/s. 2. None of these. 3. Unable to determine. 4.
Version PREVIEW B One D Kine REVIEW burke (1111) 1 This printout should have 34 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. Jogging
More informationFREE FALL. Introduction. Reference Young and Freedman, University Physics, 12 th Edition: Chapter 2, section 2.5
Physics 161 FREE FALL Introduction This experiment is designed to study the motion of an object that is accelerated by the force of gravity. It also serves as an introduction to the data analysis capabilities
More informationAP Calculus AB 2004 Scoring Guidelines
AP Calculus AB 4 Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and eam preparation; permission for any other use must be sought from
More informationThe Basics of Physics with Calculus. AP Physics C
The Basics of Physics with Calculus AP Physics C Pythagoras started it all 6 th Century Pythagoras first got interested in music when he was walking past a forge and heard that the sounds of the blacksmiths'
More informationSPEED, VELOCITY, AND ACCELERATION
reflect Look at the picture of people running across a field. What words come to mind? Maybe you think about the word speed to describe how fast the people are running. You might think of the word acceleration
More informationLesson 8: Velocity. Displacement & Time
Lesson 8: Velocity Two branches in physics examine the motion of objects: Kinematics: describes the motion of objects, without looking at the cause of the motion (kinematics is the first unit of Physics
More informationGraphical Presentation of Data
Graphical Presentation of Data Guidelines for Making Graphs Titles should tell the reader exactly what is graphed Remove stray lines, legends, points, and any other unintended additions by the computer
More informationCHAPTER We find the average speed from average speed = d/t = (230 km)/(3.25 h) =
CHAPTER 1. We find the average speed from average speed = d/t = (30 km)/(3.5 h) = 70.8 km/h.. We find the time from average speed = d/t; 5 km/h = (15 km)/t, which gives t = 0.60 h (36 min). 3. We find
More informationAP Physics Energy and Springs
AP Physics Energy and Springs Another major potential energy area that AP Physics is enamored of is the spring (the wire coil deals, not the ones that produce water for thirsty humanoids). Now you ve seen
More informationACCELERATION DUE TO GRAVITY
EXPERIMENT 1 PHYSICS 107 ACCELERATION DUE TO GRAVITY Skills you will learn or practice: Calculate velocity and acceleration from experimental measurements of x vs t (spark positions) Find average velocities
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationENERGYand WORK (PART I and II) 9MAC
ENERGYand WORK (PART I and II) 9MAC Purpose: To understand work, potential energy, & kinetic energy. To understand conservation of energy and how energy is converted from one form to the other. Apparatus:
More informationSCALAR VS. VECTOR QUANTITIES
SCIENCE 1206 MOTION  Unit 3 Slideshow 2 SPEED CALCULATIONS NAME: TOPICS OUTLINE SCALAR VS. VECTOR SCALAR QUANTITIES DISTANCE TYPES OF SPEED SPEED CALCULATIONS DISTANCETIME GRAPHS SPEEDTIME GRAPHS SCALAR
More informationMathematics 31 Precalculus and Limits
Mathematics 31 Precalculus and Limits Overview After completing this section, students will be epected to have acquired reliability and fluency in the algebraic skills of factoring, operations with radicals
More informationACCELERATION OF HEAVY TRUCKS Woodrow M. Poplin, P.E.
ACCELERATION OF HEAVY TRUCKS Woodrow M. Poplin, P.E. Woodrow M. Poplin, P.E. is a consulting engineer specializing in the evaluation of vehicle and transportation accidents. Over the past 23 years he has
More informationAlgebra 2. Linear Functions as Models Unit 2.5. Name:
Algebra 2 Linear Functions as Models Unit 2.5 Name: 1 2 Name: Sec 4.4 Evaluating Linear Functions FORM A FORM B y = 5x 3 f (x) = 5x 3 Find y when x = 2 Find f (2). y = 5x 3 f (x) = 5x 3 y = 5(2) 3 f (2)
More informationSolving Quadratic Equations
9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation
More informationLab 4: Magnetic Force on Electrons
Lab 4: Magnetic Force on Electrons Introduction: Forces on particles are not limited to gravity and electricity. Magnetic forces also exist. This magnetic force is known as the Lorentz force and it is
More informationAstronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007. Name:
Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007 Name: Directions: Listed below are twenty (20) multiplechoice questions based on the material covered by the lectures this past week. Choose
More information1. What is the distance formula? Use it to find the distance between the points (5, 19) and ( 3, 7).
Precalculus Worksheet P. 1. What is the distance formula? Use it to find the distance between the points (5, 19) and ( 3, 7).. What is the midpoint formula? Use it to find the midpoint between the points
More informationProjectile motion simulator. http://www.walterfendt.de/ph11e/projectile.htm
More Chapter 3 Projectile motion simulator http://www.walterfendt.de/ph11e/projectile.htm The equations of motion for constant acceleration from chapter 2 are valid separately for both motion in the x
More informationItems related to expected use of graphing technology appear in bold italics.
 1  Items related to expected use of graphing technology appear in bold italics. Investigating the Graphs of Polynomial Functions determine, through investigation, using graphing calculators or graphing
More informationLesson 9: Graphing Standard Form Equations Lesson 2 of 2. Example 1
Lesson 9: Graphing Standard Form Equations Lesson 2 of 2 Method 2: Rewriting the equation in slope intercept form Use the same strategies that were used for solving equations: 1. 2. Your goal is to solve
More informationLinear Motion vs. Rotational Motion
Linear Motion vs. Rotational Motion Linear motion involves an object moving from one point to another in a straight line. Rotational motion involves an object rotating about an axis. Examples include a
More informationRegents Exam Questions A2.S.8: Correlation Coefficient
A2.S.8: Correlation Coefficient: Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship 1 Which statement regarding correlation
More information1. How long does it take the sound of thunder to go 1,600 meters (~1 mile) traveling at an average speed of 330 meters / sec? (4.
LHWHS Physics Unit One  Motion (Kinematics) HW #2...Sept 9 NAME ANSWERS 1. How long does it take the sound of thunder to go 1,600 meters (~1 mile) traveling at an average speed of 330 meters / sec? (4.85
More informationW i f(x i ) x. i=1. f(x i ) x = i=1
Work Force If an object is moving in a straight line with position function s(t), then the force F on the object at time t is the product of the mass of the object times its acceleration. F = m d2 s dt
More information8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight
1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s 0.333 m/s 4.24 m/s 2. What is the distance traveled
More informationAnswer Key for California State Standards: Algebra I
Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.
More informationHSC Mathematics  Extension 1. Workshop E4
HSC Mathematics  Extension 1 Workshop E4 Presented by Richard D. Kenderdine BSc, GradDipAppSc(IndMaths), SurvCert, MAppStat, GStat School of Mathematics and Applied Statistics University of Wollongong
More informationLab 11: Magnetic Fields Name:
Lab 11: Magnetic Fields Name: Group Members: Date: TA s Name: Objectives: To measure and understand the magnetic field of a bar magnet. To measure and understand the magnetic field of an electromagnet,
More informationHow can you write an equation of a line when you are given the slope and the yintercept of the line? ACTIVITY: Writing Equations of Lines
. Writing Equations in SlopeIntercept Form How can ou write an equation of a line when ou are given the slope and the intercept of the line? ACTIVITY: Writing Equations of Lines Work with a partner.
More informationExperiment 2 Free Fall and Projectile Motion
Name Partner(s): Experiment 2 Free Fall and Projectile Motion Objectives Preparation PreLab Learn how to solve projectile motion problems. Understand that the acceleration due to gravity is constant (9.8
More informationLinear functions Increasing Linear Functions. Decreasing Linear Functions
3.5 Increasing, Decreasing, Max, and Min So far we have been describing graphs using quantitative information. That s just a fancy way to say that we ve been using numbers. Specifically, we have described
More informationPhysics Section 3.2 Free Fall
Physics Section 3.2 Free Fall Aristotle Aristotle taught that the substances making up the Earth were different from the substance making up the heavens. He also taught that dynamics (the branch of physics
More informationChapter 11 Work. Chapter Goal: To develop a deeper understanding of energy and its conservation Pearson Education, Inc.
Chapter 11 Work Chapter Goal: To develop a deeper understanding of energy and its conservation. Motivation * * There are also ways to gain or lose energy that are thermal, but we will not study these in
More informationCHAPTER 3: Quadratic Functions and Equations; Inequalities
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 3: Quadratic Functions and Equations; Inequalities 3.1 The Complex Numbers 3.2 Quadratic Equations, Functions, Zeros, and
More informationwww.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x
Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity
More informationAP Calculus BC 2008 Scoring Guidelines
AP Calculus BC 8 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a notforprofit membership association whose mission is to connect students to college
More information6. LECTURE 6. Objectives
6. LECTURE 6 Objectives I understand how to use vectors to understand displacement. I can find the magnitude of a vector. I can sketch a vector. I can add and subtract vector. I can multiply a vector by
More information