Graphing Motion. Every Picture Tells A Story


 Evelyn Summers
 11 months ago
 Views:
Transcription
1 Graphing Motion Every Picture Tells A Story
2 Read and interpret motion graphs Construct and draw motion graphs Determine speed, velocity and accleration from motion graphs
3
4 If you make a graph by hand it should always be on graph paper. The graph should fill the available space. Carefully choosing the best scale is necessary to achieve this.
5
6 The graph should always have a title.
7 Always label the x and y axes in 3 ways: title, numerical values, and units.
8 Always make a line graph line graphs are way more handy, because they tell you how one thing changes under the influence of some other variable.
9 The x axis is always the independent variable. If time is one of the measurements being graphed, it always goes on the xaxis. Independent Variable or Manipulated Variable is what you are testing. It is what causes things to change as you make changes to it. Some people nickname it the Ido variable.
10 The y axis is always the dependent variable. Y axis Dependent Variable or the Responding Variable is the effect and it may or may not change. It is observed during as well as at the end of the experiment.
11 Dependent Responing Yaxis Manipulated Independent Xaxis D = dependent variable R = responding variable Y = graph information on the vertical axis M = manipulated variable I = independent variable X = graph information on the horizontal axis
12 Example of a Bad Graph There's no title. What's it a graph of? Who knows? There are no labels on the x or y axis. What are those numbers? Who knows? There are no units on the x or y axis. Is this a graph of speed in miles per hour or a graph of temperature in Kelvins? Who can tell?
13 What s wrong with this graph? There's no title. What's it a graph of? Who knows? There are no increments on the axes, and there are no gridlines. There are no labels on the x or y axis. What are those numbers? Who knows? There are no units on the x or y axis. What size are the numbers: kilo, centi, or milli?
14
15 Definition of slope Numerical measure of a line's incline relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it ( slope equals rise over run ).
16 A displacement time graph with time along x axis and displacement on the y axis. Velocity is positive when the object moves in the positive direction. Since the position value is increasing, the graph slopes upward. Zero slope Velocity is zero when the position does not change. This line has zero slope. Velocity is negative when the object moves In the negative direction on the Axis system. This line has a negative Slope.
17 Types of Motion Graphs Distance vs Time Position vs Time Velocity vs Time Acceleration vs Time
18 Distance vs Time Graphs Speed is the distance an object travels per unit of time. You can graphically represent the speed or an object using a distancetime graph.
19
20
21 If the speed is constant, then the slope is constant (straight line).
22 Constant Speed A uniform distance is covered for each unit of time. A constant speed graph shows a constant & positive slope
23 The steeper the slope, the faster the speed.
24
25 If the speed is changing, then the slope is changing (curve).
26 Describe the motion in each section of the graph. Decelerating Stopped Accelerating Steady speed
27 Position vs time Graphs of Constant motion Position vs. time graphs give you an easy and obvious way of determining an object s displacement at any given time, and a subtler way of determining that object s velocity at any given time.
28
29 A positiontime graph, is one in which position is Plotted on the yaxis and the time is on the xaxis. A positiontime graph is similar to a distancetime Graph but has direction on the yaxis.
30 Although distancetime and positiontime graphs can show Similar graphs, this is not always the case. Below is a graph of a person who walked to a nearby store (10 km north) and back to the original reference point, this would mean the total travelled distance is 20 km (10 km to the store and 10 km back). The distancetime graph is on the left.
31 The positiontime graph looks different because the position changed when the person turned back from the store back to the original reference point.
32 Looking at the slope of a distance vs time or a position vs time graph... Slope = Velocity As slope goes, so does velocity. If the speed is constant, then the slope is constant (straight line). If the speed is changing, then the slope is changing (curve). If the velocity is positive, then the slope is positive (moving upward, towards the right). If the velocity is negative, then the slope is negative (moving downward, towards the right). The steeper the line/curve, the faster the speed.
33 Reading and interpreting positiontime graphs
34
35 s vs t  The object is standing still at a positive location. Time is going by but the position is not changing. Since the slope equals zero it has no movement.
36 s vs t  the object is traveling at a constant positive velocity. The locations of its position are increasingly positive.
37 s vs t  the object is traveling at a constant positive velocity but is traveling through a negative region.
38 s vs t  this slope represents a constant negative velocity since the object is traveling in a negative direction at a constant rate. Notice that the locations of its position are becoming less and less positive
39 s vs t  the object is traveling at a constant negative velocity through a negative region. The locations of its position are increasingly negative.
40 The meaning of slope on a positiontime graph! If calculated properly, it shows the velocity of the motion.
41 In this graph Car A moves for 5 seconds a distance of 10 meters. How can we figure out the velocity of the car from the graph? We can use the formula for the slope of a line to get the velocity.
42
43 Any point on this graph shows the position of the ant at a particular moment in time.
44 The point at (2, 2) show that, two seconds after it started moving, the ant was two centimeters to the left of its starting position. The point at (3,1) shows that, three seconds after it started moving, the ant is one centimeter to the right of its starting position.
45 For the first two seconds, the ant is moving to the left. The next second, it reverses its direction and moves quickly to y = 1. The ant then stays still for three seconds before it turns left again and moves back to where it started.
46 For any position vs. time graph, the velocity at time t is equal to the slope of the line at time t. In a graph made up of straight lines, like the one for the ant, the slope can easily be calculated at each point on the graph to show the instantaneous velocity at any given time.
47 Determine the ant s instantaneous velocity at any given point during the trip. Remember the instantaneous velocity shows the velocity of the ant at one point. The ant is cruising along at the fastest speed between t = 2 and t = 3, because the position vs. time graph is steepest between these points.
48 Calculate the ant s average velocity during this time interval is a simple matter of dividing rise by run. Remember average velocity is the total displacement divided by the total time. The average velocity here is zero because the total diaplacement is zero. 0/7 = 0 m/s
49 Stage 1: The car moves forwards from the origin to in the first 5 s. Calculate the velocity for the car after the first five seconds.
50 Stage 2: The car moves backwards, passes the origin, to in the next 5 s. Calculate the velocity of the car between five and ten seconds.
51 Stage 3: The car remains at rest in the last 5 s. Calculate the velocity of the car for the last five seconds.
52 Distance (km) Different Slopes Slope = Rise/Run = 1 km/1 hr = 1 km/hr Run = 1 hr Slope = Rise/Run = 0 km/1 hr = 0 km/hr Rise = 1 km Run = 1 hr Rise = 0 km Time (hr) Run = 1 hr Rise = 2 km Slope = Rise/Run = 2 km/1 hr = 2 km/hr
53 Position Time Graphs of Accelerated motion Position vs. time graphs give you an easy and obvious way of determining an object s displacement at any given time, and a subtler way of determining that object s velocity at any given time.
54 A very useful aspect of these graphs is that the area under the vt graph tells us the distance travelled during the motion.
55 Since the slope represents the speed, if the speed is increasing over time, the slope must be also be increasing over time. The graph is a curve that gets steeper as you move along The xaxis. A positiontime graph for a ball in free fall is shown below.
56 The graph of an object slowing down is also cuved. The example below show the positiontime graph for a car coming to a gradual stop at a red l ight. As time passes, the car s speed decreases. The slope must therefore decrease.
57
58 answers
59 Velocity vs Time Graphs d slope = velocity t slope = acceleration v area = distance t a area = velocity t
60 If the graph is a horizontal line, there is no change in velocity, therefore there is no acceleration (the slope is 0). If the acceleration is positive then the slope is positive (the line moves upward to the right). If the acceleration is negative, then the slope is negative (the line moves downward to the right).).
61 Calculating acceleration from a velocitytime graph
62 Calculating the distance on velocitytime graph.
63 An object is moving in the positive direction if the line is located in the positive region of the graph (whether it is sloping up or sloping down). An object is moving in the negative direction if the line is located in the negative region of the graph (whether it is sloping up or sloping down). If a line crosses over the xaxis from the positive region to the negative region of the graph (or vice versa), then the object has changed directions.
64 The object moves in the + direction at a constant speed  zero acceleration (interval A). The object then continues in the + direction while slowing down with a negative acceleration (interval B). Finally, the object moves at a constant speed in the + direction, slower than before (interval C).
65 The object moves in the + direction while slowing down; this involves a negative acceleration (interval A). It then remains at rest (interval B). The object then moves in the  direction while speeding up; this also involves a negative acceleration (interval C).
66 The object moves in the + direction with a constant velocity and zero acceleration (interval A). The object then slows down while moving in the + direction (i.e., it has a negative acceleration) until it finally reaches a 0 velocity (stops) (interval B). Then the object moves in the  direction while speeding up; this corresponds to a  acceleration (interval C).
67 a plot of velocity versus time can also be used to determine the displacement of an object. The diagram below shows three different velocitytime graphs; the shaded regions between the line and the timeaxis represents the displacement during the stated time interval.
68
69
70
71 The velocitytime graph for a twostage rocket is shown below. Use the graph and your understanding of slope calculations to determine the acceleration of the rocket during the listed time intervals. When finished, click the buttons to see the answers. 40 m/s 2 20 m/s 220 m/s 2
72 Constant positive (rightward) velocity
73 Constant negative (leftward) velocity
74 Rightward velocity with rightward acceleration.
75 Rightward Velocity and negative acceleration
76 Leftward velocity, leftward acceleration
77 Leftward velocity rightward acceleration
78 Acceleration Acceleration the rate at which velocity is changing Acceleration = v/ t Can increase or decrease (sometimes called deceleration) Think of traveling in a car, you can feel the acceleration 3 ways to accelerate in a car 1. Brake pedal slowing down; coming to a stop (changing speed) 2. Steering wheel going around a corner or curve (changing direction) 3. Gas pedal leaving from a stopped position (changing speed)
79
80 The object moves in the + direction at a constant speed  zero acceleration (interval A). The object then continues in the + direction while slowing down with a negative acceleration (interval B). Finally, the object moves at a constant speed in the + direction, slower than before (interval C).
81 The object moves in the + direction at a constant speed  zero acceleration (interval A). The object then continues in the + direction while slowing down with a negative acceleration (interval B). Finally, the object moves at a constant speed in the + direction, slower than before (interval C).
82 The object moves in the + direction while slowing down; this involves a negative acceleration (interval A). It then remains at rest (interval B). The object then moves in the  direction while speeding up; this also involves a negative acceleration (interval C).
83 Zero to 90s  On this graph we see a horizontal line that reads 5m/s for those same first 90 seconds. On a vt graph a flat line means constant velocity. Constant velocity means zero acceleration.
84
85 Graphs of Motion Uniform Velocity The area under a velocity vs time graph is the displacement of the object. Find the distance traveled by each object.
86 Acceleration Suppose you are traveling in a car and your speed goes from 10.km/h to 60.km/h in 2.0s. What is your acceleration? Suppose a car goes from 80.km/h to 15km/h in 5.0 seconds. What is the acceleration? A car is coasting backwards down a hill at a speed of 3.0m/s when the driver gets the engine started. After 2.5s, the car is moving uphill at 4.5m/s. Assuming that uphill is in the positive direction, what is the car s average acceleration?
87 Graphs of Motion Velocity vs time graphs: How can you tell if the object is accelerating or decelerating? Accelerating (speeding up) when the magnitude of the velocity is increasing Decelerating (slowing down) when the magnitude of the velocity is decreasing
88 Graph Practice
89 Which pair of graphs shows the same motion? Answer 1
90 pc.org/~clement/simulations/physlets/tst/position Time%20Graphs.html
91 anics/kin/motion_graph/xt02_e.html
92
93 Stage 1: The car moves forwards from the origin to in the first 5 s.
94
95 Stage 2: The car moves backwards, passes the origin, to in the next 5 s.
96 Stage 3: The car remains at rest in the last 5 s.
97
98
99
100
101
102
103
104
105
106 What is the velocity for each stage of the journey? b. What is the average (mean) velocity for the whole journey
107
108
109
110
111
112 Distance or Displacement Distance how far an object has traveled Indianapolis is about 45 miles away The distance to Indianapolis is 45 miles; the distance back to Bloomington is 45 miles the total distance traveled round trip is 90 miles Displacement how far an object is from its original position (direction matters) The displacement to Indianapolis is 45 miles north; the displacement back to Bloomington is 45 miles south the total displacement is 0 miles You can find displacement by Finding the area under a velocity time graph Using the equation d = v avg * t
113
114
115
116 Understanding the Connection Between Slope and Velocity The slope of a line for a distance vs. time graph represents the velocity for the object in motion. Slope can be determined using the following formula: The change in y values divided by the change in x values determines the average velocity for the object between any two points.
117 Pick two points on the line and determine their coordinates. Determine the difference in ycoordinates of these two points (rise). Determine the difference in xcoordinates for these two points (run). Divide the difference in ycoordinates by the difference in xcoordinates (rise/run or slope).
118 rise over run Calculate the velocity between 3 and 4 seconds. Note: This is a constant speed graph, so the velocity should be the same at all points.
119
M1. (a) (i) 4.5 allow 1 mark for correct substitution i.e. 9 2 2
M. (a) (i) 4.5 allow mark for correct substitution i.e. 9 (ii) m/s accept answer given in (a)(i) if not contradicted here (iii) (iv) speed straight line from the origin passing through (s, 9m/s) allow
More informationProblem Set 1 Solutions
Problem Set 1 Solutions Chapter 1: Representing Motion Questions: 6, 10, 1, 15 Exercises & Problems: 7, 10, 14, 17, 24, 4, 8, 44, 5 Q1.6: Give an example of a trip you might take in your car for which
More informationGLENCOE PHYSICS. Principles and Problems. Problems and Solutions Manual
GLENCOE PHYSICS Principles and Problems Problems and Solutions Manual GLENCOE PHYSICS Principles and Problems Student Edition Teacher Wraparound Edition Teacher Classroom Resources Transparency Package
More informationThis copy of the text was produced at 16:02 on 5/31/2009.
Calculus This work is licensed under the Creative Commons AttributionNonCommercialShareAlike License To view a copy of this license, visit http://creativecommonsorg/licenses/byncsa/30/ or send a letter
More informationChapter 11 Equilibrium
11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of
More information2 ONE DIMENSIONAL MOTION
2 ONE DIMENSIONAL MOTION Chapter 2 OneDimensional Motion Objectives After studying this chapter you should be able to derive and use formulae involving constant acceleration; be able to understand the
More informationMathematics Placement
Mathematics Placement The ACT COMPASS math test is a selfadaptive test, which potentially tests students within four different levels of math including prealgebra, algebra, college algebra, and trigonometry.
More informationIntro to Excel spreadsheets
Intro to Excel spreadsheets What are the objectives of this document? The objectives of document are: 1. Familiarize you with what a spreadsheet is, how it works, and what its capabilities are; 2. Using
More informationSection 3.7. Rolle s Theorem and the Mean Value Theorem. Difference Equations to Differential Equations
Difference Equations to Differential Equations Section.7 Rolle s Theorem and the Mean Value Theorem The two theorems which are at the heart of this section draw connections between the instantaneous rate
More informationHow Rockets Work Newton s Laws of Motion
How Rockets Work Whether flying a small model rocket or launching a giant cargo rocket to Mars, the principles of how rockets work are exactly the same. Understanding and applying these principles means
More informationNewton s Law of Motion
chapter 5 Newton s Law of Motion Static system 1. Hanging two identical masses Context in the textbook: Section 5.3, combination of forces, Example 4. Vertical motion without friction 2. Elevator: Decelerating
More informationThe Big Idea. Key Concepts
The Big Idea Acceleration is caused by force. All forces come in pairs because they arise in the interaction of two objects you can t hit without being hit back! The more force applied, the greater the
More informationCopyright 2010 ALFANO S.A. All rights reserved.
Manual of use 1 Copyright 2010 ALFANO S.A. All rights reserved. The reproduction, transfer, distribution or storage of part of or the totality of the contents of this document in whatever form is prohibited
More informationMathematics as Problem Solving The students will demonstrate the ability to gather information from a graphical representation of an equation.
Title: Another Way of Factoring Brief Overview: Students will find factors for quadratic equations with a leading coefficient of one. The students will then graph these equations using a graphing calculator
More informationAN INTRODUCTION TO PREMIUM TREND
AN INTRODUCTION TO PREMIUM TREND Burt D. Jones * February, 2002 Acknowledgement I would like to acknowledge the valuable assistance of Catherine Taylor, who was instrumental in the development of this
More informationStatistics Revision Sheet Question 6 of Paper 2
Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of
More informationIf A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?
Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question
More information( ) ( ) ( ) ( ) ( ) ( )
Problem (Q1): Evaluate each of the following to three significant figures and express each answer in SI units: (a) (0.631 Mm)/(8.60 kg) 2 (b) (35 mm) 2 *(48 kg) 3 (a) 0.631 Mm / 8.60 kg 2 6 0.631 10 m
More informationAP1 Dynamics. Answer: (D) foot applies 200 newton force to nose; nose applies an equal force to the foot. Basic application of Newton s 3rd Law.
1. A mixed martial artist kicks his opponent in the nose with a force of 200 newtons. Identify the actionreaction force pairs in this interchange. (A) foot applies 200 newton force to nose; nose applies
More informationFlorida Math for College Readiness
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourthyear math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness
More information85 Using the Distributive Property. Use the Distributive Property to factor each polynomial. 1. 21b 15a SOLUTION:
Use the Distributive Property to factor each polynomial. 1. 1b 15a The greatest common factor in each term is 3.. 14c + c The greatest common factor in each term is c. 3. 10g h + 9gh g h The greatest common
More informationChapter 1 Linear Models page Linear Models Part 1 2 Linear Models Activities 1 17 Linear Models Part 2 21 Linear Models Activities 2 28
Table of Contents Chapter 1 Linear Models page Linear Models Part 1 Linear Models Activities 1 17 Linear Models Part 1 Linear Models Activities 8 Chapter Linear Programming Linear Programming Part 1 34
More informationA) F = k x B) F = k C) F = x k D) F = x + k E) None of these.
CT161 Which of the following is necessary to make an object oscillate? i. a stable equilibrium ii. little or no friction iii. a disturbance A: i only B: ii only C: iii only D: i and iii E: All three Answer:
More informationExample 1: Suppose the demand function is p = 50 2q, and the supply function is p = 10 + 3q. a) Find the equilibrium point b) Sketch a graph
The Effect of Taxes on Equilibrium Example 1: Suppose the demand function is p = 50 2q, and the supply function is p = 10 + 3q. a) Find the equilibrium point b) Sketch a graph Solution to part a: Set the
More information1.3. Maximum or Minimum of a Quadratic Function. Investigate A
< P16 photo of a large arched bridge, similar to the one on page 292 or p 360361of the fish book> Maximum or Minimum of a Quadratic Function 1.3 Some bridge arches are defined by quadratic functions.
More informationRolle s Theorem. q( x) = 1
Lecture 1 :The Mean Value Theorem We know that constant functions have derivative zero. Is it possible for a more complicated function to have derivative zero? In this section we will answer this question
More informationChapter 2. Software: (preview draft) Getting Started with Stella and Vensim
Chapter. Software: (preview draft) Getting Started with Stella and Vensim Stella and Vensim are iconbased programs to support the construction and testing of system dynamics models. I use these programs
More informationMFF 3a: Charged Particle and a Straight CurrentCarrying Wire... 2
MFF 3a: Charged Particle and a Straight CurrentCarrying Wire... 2 MFF3a RT1: Charged Particle and a Straight CurrentCarrying Wire... 3 MFF3a RT2: Charged Particle and a Straight CurrentCarrying Wire...
More informationInternational Year of Light 2015 TechTalks BREGENZ: Mehmet Arik WellBeing in Office Applications Light Measurement & Quality Parameters
www.ledprofessional.com ISSN 1993890X Trends & Technologies for Future Lighting Solutions ReviewJan/Feb 2015 Issue LpR 47 International Year of Light 2015 TechTalks BREGENZ: Mehmet Arik WellBeing in
More informationFSAE i2 Data Analysis Seminar Software Download & Installation
FSAE i2 Data Analysis Seminar Software Download & Installation MoTeC software is available for download from the website at: http://www.motec.com.au/software/latestreleases com 1 i2 Standard vs i2 Pro
More informationBlue Pelican Alg II First Semester
Blue Pelican Alg II First Semester Teacher Version 1.01 Copyright 2009 by Charles E. Cook; Refugio, Tx (All rights reserved) Alg II Syllabus (First Semester) Unit 1: Solving linear equations and inequalities
More informationIndifference Curves: An Example (pp. 6579) 2005 Pearson Education, Inc.
Indifference Curves: An Example (pp. 6579) Market Basket A B D E G H Units of Food 20 10 40 30 10 10 Units of Clothing 30 50 20 40 20 40 Chapter 3 1 Indifference Curves: An Example (pp. 6579) Graph the
More informationThe Influence of Aerodynamics on the Design of HighPerformance Road Vehicles
The Influence of Aerodynamics on the Design of HighPerformance Road Vehicles Guido Buresti Department of Aerospace Engineering University of Pisa (Italy) 1 CONTENTS ELEMENTS OF AERODYNAMICS AERODYNAMICS
More informationAP Calculus BC 2012 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a missiondriven notforprofit organization that connects students to college success and opportunity. Founded in 9, the College
More informationFind the Relationship: An Exercise in Graphing Analysis
Find the Relationship: An Eercise in Graphing Analsis Computer 5 In several laborator investigations ou do this ear, a primar purpose will be to find the mathematical relationship between two variables.
More informationHow to make a line graph using Excel 2007
How to make a line graph using Excel 2007 Format your data sheet Make sure you have a title and each column of data has a title. If you are entering data by hand, use time or the independent variable in
More informationt hours This is the distance in miles travelled in 2 hours when the speed is 70mph. = 22 yards per second. = 110 yards.
The area under a graph often gives useful information. Velocittime graphs Constant velocit The sketch shows the velocittime graph for a car that is travelling along a motorwa at a stead 7 mph. 7 The
More information+ 4θ 4. We want to minimize this function, and we know that local minima occur when the derivative equals zero. Then consider
Math Xb Applications of Trig Derivatives 1. A woman at point A on the shore of a circular lake with radius 2 miles wants to arrive at the point C diametrically opposite A on the other side of the lake
More informationA) N > W B) N = W C) N < W. speed v. Answer: N = W
CTN12. Consider a person standing in an elevator that is moving upward at constant speed. The magnitude of the upward normal force, N, exerted by the elevator floor on the person's feet is (larger than/same
More informationInterpreting Data in Normal Distributions
Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,
More informationExam 1 Sample Question SOLUTIONS. y = 2x
Exam Sample Question SOLUTIONS. Eliminate the parameter to find a Cartesian equation for the curve: x e t, y e t. SOLUTION: You might look at the coordinates and notice that If you don t see it, we can
More informationManual Analysis Software AFD 1201
AFD 1200  AcoustiTube Manual Analysis Software AFD 1201 Measurement of Transmission loss acc. to Song and Bolton 1 Table of Contents Introduction  Analysis Software AFD 1201... 3 AFD 1200  AcoustiTube
More informationalways in a rush Are you Rushing to work Rushing home Rushing off on vacation?
Are you always in a rush? Rushing to work Rushing home Rushing off on vacation? Do you find yourself increasingly picking up the pace, racing against time? 75 100 50 125 25 150 HUILE 60 40 80 100 120 140
More informationAS COMPETITION PAPER 2007 SOLUTIONS
AS COMPETITION PAPER 2007 Total Mark/50 SOLUTIONS Section A: Multiple Choice 1. C 2. D 3. B 4. B 5. B 6. A 7. A 8. C 1 Section B: Written Answer Question 9. A mass M is attached to the end of a horizontal
More informationHandheld Shock Control Design Guide
Handheld Shock Control Design Guide Handheld Shock Control Design Guide Cushioning in Handheld Devices: Understanding Impact The Challenge: Protecting Handheld Devices from Cracks The most devastating
More informationExperiments with a CameraBased HumanComputer Interface System
Experiments with a CameraBased HumanComputer Interface System Robyn Cloud*, Margrit Betke**, and James Gips*** * Computer Science Department, Boston University, 111 Cummington Street, Boston, MA 02215,
More informationREFERENCE BOOK FOR: AREX WINDOWS GC SYSTEMS
REFERENCE BOOK FOR: AREX WINDOWS GC SYSTEMS AREX TEST SYSTEMS BV VENNESTRAAT 4B 2161 LE LISSE HOLLAND Product of: Arex Test Systems bv Vennestraat 4b 2161 LE Lisse Holland Tel: +31(0)252419151 Fax: +31(0)252420510
More informationCash Flow and Accounts Receivable Management for Dialysis
Dialysis & Transplantation, Volume 13, Number 4, April 1984, p. 201 Cash Flow and Accounts Receivable Management for Dialysis John A. Sargent, PhD, President; Albert Grutze, Systems Manager, Quantitative
More informationMaximum Range Explained range Figure 1 Figure 1: Trajectory Plot for AngledLaunched Projectiles Table 1
Maximum Range Explained A projectile is an airborne object that is under the sole influence of gravity. As it rises and falls, air resistance has a negligible effect. The distance traveled horizontally
More informationTrading With Properly Scaled Static Charts
Trading With Properly Scaled Static Charts Dr. Al Larson 2/17/2013 Stock, commodity, and currency traders who use most modern trading programs are missing some great opportunities. Why? Because most modern
More informationFor example, estimate the population of the United States as 3 times 10⁸ and the
CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number
More informationThe Influence of Aerodynamics on the Design of HighPerformance Road Vehicles
The Influence of Aerodynamics on the Design of HighPerformance Road Vehicles Guido Buresti Department of Aerospace Engineering University of Pisa (Italy) 1 CONTENTS ELEMENTS OF AERODYNAMICS AERODYNAMICS
More informationBX in ( u, v) basis in two ways. On the one hand, AN = u+
1. Let f(x) = 1 x +1. Find f (6) () (the value of the sixth derivative of the function f(x) at zero). Answer: 7. We expand the given function into a Taylor series at the point x = : f(x) = 1 x + x 4 x
More informationPerformance Analysis Outdoor
Assistive Technology & Seating Service Vancouver Coastal Health GF Strong Rehab Centre 4255 Laurel Street Vancouver BC V5Z 2G9 Overview Consumers with a broad spectrum of abilities are using power wheelchairs.
More informationExplore 3: Crash Test Dummies
Explore : Crash Test Dummies Type of Lesson: Learning Goal & Instructiona l Objectives Content with Process: Focus on constructing knowledge through active learning. Students investigate Newton s first
More informationA Road Crash Reconstruction Technique
A Road Crash Reconstruction Technique Mukherjee S, nonmember Chawla A 1, member Lalaram Patel, nonmember Abstract The purpose of reconstruction is to identify the critical factors involved in a road
More informationMaximizing Fleet Efficiencies with Predictive Analytics
PHH Arval  Trucks Maximizing Fleet Efficiencies with Predictive Analytics Neil Gaynor Manager of Business Development 29 December 2012 1 Maximizing Fleet Efficiencies with the use of Predictive Analytics
More informationInteractive Voting System. www.ivsystem.nl. IVSBasic IVSProfessional 4.4
Interactive Voting System www.ivsystem.nl IVSBasic IVSProfessional 4.4 Manual IVSBasic 4.4 IVSProfessional 4.4 1213 Interactive Voting System The Interactive Voting System (IVS ) is an interactive
More informationAtlanta, Georgia Road Test
1. When driving your car Into traffic from a parked position, you should: A. Sound your horn and pull Into the other lane. B. Signal and proceed when safe. C. Signal other traffic and pull directly into
More information6 WORK and ENERGY. 6.0 Introduction. 6.1 Work and kinetic energy. Objectives
6 WORK and ENERGY Chapter 6 Work and Energy Objectives After studying this chapter you should be able to calculate work done by a force; be able to calculate kinetic energy; be able to calculate power;
More informationComputer Animation: Art, Science and Criticism
Computer Animation: Art, Science and Criticism Tom Ellman Harry Roseman Lecture 4 Parametric Curve A procedure for distorting a straight line into a (possibly) curved line. The procedure lives in a black
More informationA: zero everywhere. B: positive everywhere. C: negative everywhere. D: depends on position.
A string is clamped at both ends and then plucked so that it vibrates in a standing wave between two extreme positions a and c. (Let upward motion correspond to positive velocities.) When the
More informationINDIANA DEPARTMENT OF TRANSPORTATION OFFICE OF MATERIALS MANAGEMENT. MEASUREMENT OF RETROREFLECTIVE PAVEMENT MARKING MATERIALS ITM No.
Revised 3/14/14 INDIANA DEPARTMENT OF TRANSPORTATION OFFICE OF MATERIALS MANAGEMENT MEASUREMENT OF RETROREFLECTIVE PAVEMENT MARKING MATERIALS ITM No. 93114T 1.0 SCOPE. 1.1 This test method covers the
More informationPoWTER Problem Packet A Phoney Deal? (Author: Peggy McCloskey)
PoWTER Problem Packet A Phoney Deal? (Author: Peggy McCloskey) 1. The Problem: A Phoney Deal? [Problem #3280] With cell phones being so common these days, the phone companies are all competing to earn
More informationTable of Contents INTRODUCTION... 3. Prerequisites... 3 Audience... 3 Report Metrics... 3
Table of Contents INTRODUCTION... 3 Prerequisites... 3 Audience... 3 Report Metrics... 3 IS MY TEST CONFIGURATION (DURATION / ITERATIONS SETTING ) APPROPRIATE?... 4 Request / Response Status Summary...
More informationTRAFFIC ENGINEERING.
Mechanical Engineering Department Carlos III University of Madrid. TRANSPORTATION INTRODUCTION Transport: change of geographical position of people or goods Traffic: transport related exclusively to vehicle
More informationChapter Fortyseven. RURAL TWOLANE/MULTILANE STATE HIGHWAYS (New Construction/Reconstruction) BUREAU OF DESIGN AND ENVIRONMENT MANUAL
Chapter Fortyseven RURAL TWOLANE/MULTILANE STATE HIGHWAYS (New Construction/Reconstruction) BUREAU OF DESIGN AND ENVIRONMENT MANUAL Illinois RURAL TWOLANE/MULTILANE STATE HIGHWAYS December 2009 2 Illinois
More informationOPRE 6201 : 2. Simplex Method
OPRE 6201 : 2. Simplex Method 1 The Graphical Method: An Example Consider the following linear program: Max 4x 1 +3x 2 Subject to: 2x 1 +3x 2 6 (1) 3x 1 +2x 2 3 (2) 2x 2 5 (3) 2x 1 +x 2 4 (4) x 1, x 2
More informationcar2go San Diego Parking Rules and FAQs
car2go San Diego Parking Rules and FAQs 1. WHERE CAN I END MY TRIP? ONLY END YOUR TRIP IN AUTHORIZED PARKING LOCATIONS When finished, you may leave your car2go in any Authorized Parking Location within
More informationTESTBOX SHAKE TABLE USER MANUAL
TESTBOX SHAKE TABLE USER MANUAL Writer: Eren AYDIN Date: 05.02.2014 Version: 1.0 Index 1. HARDWARE... 3 1.1 GENERAL OVERVİEW... 3 1.2 CONNECTİONS AND STARTUP... 3 2. SOFTWARE... 6 2.1 SETUP... 6 2.2 IP
More informationChapter 6 Quadratic Functions
Chapter 6 Quadratic Functions Determine the characteristics of quadratic functions Sketch Quadratics Solve problems modelled b Quadratics 6.1Quadratic Functions A quadratic function is of the form where
More informationChapter 6 Atmospheric Aerosol and Cloud Processes Spring 2015 Cloud Physics Initiation and development of cloud droplets Special interest: Explain how droplet formation results in rain in approximately
More informationTeaching Your Teen to Drive
MetLife Auto & Home Teaching Your Teen to Drive Without driving each other crazy! Dear Parent/Guardian, One of the best ways for you to influence your teen s driving habits is to sit in the copilot seat
More informationHelp File Version 1.0.14
Version 1.0.14 By engineering@optimumg.com www.optimumg.com Welcome Thank you for purchasing OptimumT the new benchmark in tire model fitting and analysis. This help file contains information about all
More informationEstimating the Average Value of a Function
Estimating the Average Value of a Function Problem: Determine the average value of the function f(x) over the interval [a, b]. Strategy: Choose sample points a = x 0 < x 1 < x 2 < < x n 1 < x n = b and
More informationExercise 1: How to Record and Present Your Data Graphically Using Excel Dr. Chris Paradise, edited by Steven J. Price
Biology 1 Exercise 1: How to Record and Present Your Data Graphically Using Excel Dr. Chris Paradise, edited by Steven J. Price Introduction In this world of high technology and information overload scientists
More informationDesigning Cell Phone Games. An 8thgrade unit on linear functions
Designing Cell Phone Games An 8thgrade unit on linear functions Designing Cell Phone Games Copyright 2006 by SRI International. This material is based upon work supported by the National Science Foundation
More informationTomTom HAD story How TomTom enables Highly Automated Driving
TomTom HAD story How TomTom enables Highly Automated Driving Automotive World Webinar 12 March 2015 JanMaarten de Vries VP Product Marketing TomTom Automotive Automated driving is real and it is big Image:
More informationHow to pass your driving. assessment... A Candidate s Guide to the Practical Driving Assessment
How to pass your driving assessment... A Candidate s Guide to the Practical Driving Assessment Prepared and published by Department of Transport, Driver and Vehicle Services. Disclaimer: The information
More informationINTRODUCTORY MICROECONOMICS
INTRODUCTORY MICROECONOMICS UNITI PRODUCTION POSSIBILITIES CURVE The production possibilities (PP) curve is a graphical medium of highlighting the central problem of 'what to produce'. To decide what
More informationIntroduction to Fuzzy Control
Introduction to Fuzzy Control Marcelo Godoy Simoes Colorado School of Mines Engineering Division 1610 Illinois Street Golden, Colorado 804011887 USA Abstract In the last few years the applications of
More informationCurrent Probes, More Useful Than You Think
Current Probes, More Useful Than You Think Training and design help in most areas of Electrical Engineering Copyright 1998 Institute of Electrical and Electronics Engineers. Reprinted from the IEEE 1998
More informationHewlettPackard 10BII Tutorial
This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,
More informationCurrent Loop Tuning Procedure. Servo Drive Current Loop Tuning Procedure (intended for Analog input PWM output servo drives) General Procedure AN015
Servo Drive Current Loop Tuning Procedure (intended for Analog input PWM output servo drives) The standard tuning values used in ADVANCED Motion Controls drives are conservative and work well in over 90%
More informationIntroduction to Differential Calculus. Christopher Thomas
Mathematics Learning Centre Introduction to Differential Calculus Christopher Thomas c 1997 University of Sydney Acknowledgements Some parts of this booklet appeared in a similar form in the booklet Review
More informationSOLUTIONS. f x = 6x 2 6xy 24x, f y = 3x 2 6y. To find the critical points, we solve
SOLUTIONS Problem. Find the critical points of the function f(x, y = 2x 3 3x 2 y 2x 2 3y 2 and determine their type i.e. local min/local max/saddle point. Are there any global min/max? Partial derivatives
More information1. Specific Differential Phase (KDP)
1. Specific Differential Phase (KDP) Instructor Notes: Welcome to the dual polarization radar course. I am Clark Payne with the Warning Decision Training Branch. This lesson is part of the dualpol products
More informationProgramming Your Calculator Casio fx7400g PLUS
Programming Your Calculator Casio fx7400g PLUS Barry Kissane Programming Your Calculator: Casio fx7400g PLUS Published by Shriro Australia Pty Limited 7274 Gibbes Street, Chatswood NSW 2067, Australia
More informationComputers in teaching science: To simulate or not to simulate?
Computers in teaching science: To simulate or not to simulate? Richard N. Steinberg City College of New York Phys. Ed. Res. Suppl. to Am. J. Phys. 68, S37S41 (2) Do computer simulations help students
More informationPROVA DINAMICA SU PALI IN ALTERNATIVA ALLA PROVA STATICA. Pile Dynamic Load test as alternative to Static Load test
PROVA DINAMICA SU PALI IN ALTERNATIVA ALLA PROVA STATICA Pile Dynamic Load test as alternative to Static Load test Gorazd Strnisa, B.Sc.Civ.Eng. SLP d.o.o. Ljubljana ABSTRACT Pile Dynamic test is test
More informationChapter 4 Specific Factors and Income Distribution
Chapter 4 Specific Factors and Income Distribution Chapter Organization Introduction The Specific Factors Model International Trade in the Specific Factors Model Income Distribution and the Gains from
More informationTVM 4155 Numerical modelling and hydraulics 10. March 2014. OpenFOAM homework
TVM 4155 Numerical modelling and hydraulics 10. March 2014 OpenFOAM homework OpenFOAM is the most popular opensource CFD program in the world today. In this homework we will use the program to determine
More informationStair Workouts Get in Shape: Step up
Stair Workouts Get in Shape: Step up Warning: If you feel any knee pain, refrain from continuing that particular exercise. Avoid the no pain, no gain motto and modify with regular walking or any activity
More information(x 3)3. (x 3)3 =U. 3. Factor completely the given polynomial. ENHANCED
Student: Instructor: Vicky Kauffman Assignment: Final problems Date: Course: Kauffman's Math 12 1 1. A Norman window consists of a rectangle surmounted by a semicircle. Find the area of the Norman window
More informationUsing UML Part Two Behavioral Modeling Diagrams
UML Tutorials Using UML Part Two Behavioral Modeling Diagrams by Sparx Systems All material Sparx Systems 2007 Sparx Systems 2007 Page 1 Trademarks Object Management Group, OMG, Unified Modeling Language,
More informationBlender 3D Animation
Bachelor Maths/Physics/Computer Science University ParisSud Digital Imaging Course Blender 3D Animation Christian Jacquemin Introduction to Computer Animation Animation Basics animation consists in changing
More informationFor further information, and additional background on the American Meteorological Society s Education Program, please contact:
Project ATMOSPHERE This guide is one of a series produced by Project ATMOSPHERE, an initiative of the American Meteorological Society. Project ATMOSPHERE has created and trained a network of resource agents
More informationGETTING STARTED WITH LABVIEW POINTBYPOINT VIS
USER GUIDE GETTING STARTED WITH LABVIEW POINTBYPOINT VIS Contents Using the LabVIEW PointByPoint VI Libraries... 2 Initializing PointByPoint VIs... 3 Frequently Asked Questions... 5 What Are the
More informationChapter 7. a. Plot Lauren Landlord's willingness to pay in Exhibit 1. Exhibit 1. Answer: See Exhibit 6. Exhibit 6
Chapter 7 1. The following information describes the value Lauren Landlord places on having her five houses repainted. She values the repainting of each house at a different amount depending on how badly
More informationStudy of Analysis System for Bridge Test
Study of Analysis System for Bridge Test Chen Ke, Lu JianMing, Research Institute of Highway, 100088, Beijing, China (chenkezi@163.com, lujianming@263.net) Summary Analysis System for Bridge Test (Chinese
More information