# Graphing Motion. Every Picture Tells A Story

Save this PDF as:

Size: px
Start display at page:

## 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 x-axis. 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 I-do 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 Y-axis Manipulated Independent X-axis 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 distance-time 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 position-time graph, is one in which position is Plotted on the y-axis and the time is on the x-axis. A position-time graph is similar to a distance-time Graph but has direction on the y-axis.

30 Although distance-time and position-time 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 distance-time graph is on the left.

31 The position-time 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 position-time 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 position-time 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 v-t 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 x-axis. A position-time 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 position-time 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

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 velocity-time graph

62 Calculating the distance on velocity-time 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 x-axis 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 velocity-time graphs; the shaded regions between the line and the timeaxis represents the displacement during the stated time interval.

68

69

70

71 The velocity-time graph for a two-stage 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 2-20 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 v-t 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/x-t02_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 y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (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

### Motion 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

### Vectors. Objectives. Assessment. Assessment. Equations. Physics terms 5/15/14. State the definition and give examples of vector and scalar variables.

Vectors Objectives State the definition and give examples of vector and scalar variables. Analyze and describe position and movement in two dimensions using graphs and Cartesian coordinates. Organize and

### SPEED, 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

### 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 1-D path speeding up and slowing down In order to describe motion you need to describe the following properties.

### Speed, velocity and acceleration

Chapter Speed, velocity and acceleration Figure.1 What determines the maximum height that a pole-vaulter can reach? 1 In this chapter we look at moving bodies, how their speeds can be measured and how

### Physics 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

### To 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

### Scalar 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

### 1.3.1 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

### Elements of a graph. Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section Elements of a graph Linear equations and their graphs What is slope? Slope and y-intercept in the equation of a line Comparing lines on

### 1 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

### Motion 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

### Worksheet 1. What You Need to Know About Motion Along the x-axis (Part 1)

Worksheet 1. What You Need to Know About Motion Along the x-axis (Part 1) In discussing motion, there are three closely related concepts that you need to keep straight. These are: If x(t) represents the

### Physics: 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

### 2After completing this chapter you should be able to

After completing this chapter you should be able to solve problems involving motion in a straight line with constant acceleration model an object moving vertically under gravity understand distance time

### Plot the following two points on a graph and draw the line that passes through those two points. Find the rise, run and slope of that line.

Objective # 6 Finding the slope of a line Material: page 117 to 121 Homework: worksheet NOTE: When we say line... we mean straight line! Slope of a line: It is a number that represents the slant of a line

### 1 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]

### Example SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross

CHAPTER 13 SECTION 13-1 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants X-AXIS - the horizontal

### Newton s Laws Quiz Review

Newton s Laws Quiz Review Name Hour To be properly prepared for this quiz you should be able to do the following: 1) state each of Newton s three laws of motion 2) pick out examples of the three laws from

### Physics 2048 Test 1 Solution (solutions to problems 2-5 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

### Exam 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

### 8. 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

### Physics 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

### Why should we learn this? One real-world connection is to find the rate of change in an airplane s altitude. The Slope of a Line VOCABULARY

Wh should we learn this? The Slope of a Line Objectives: To find slope of a line given two points, and to graph a line using the slope and the -intercept. One real-world connection is to find the rate

### Ground 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

### Graphing Linear Equations

Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope

### PLOTTING 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

### A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion

A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for

### Name Partners Date. Energy Diagrams I

Name Partners Date Visual Quantum Mechanics The Next Generation Energy Diagrams I Goal Changes in energy are a good way to describe an object s motion. Here you will construct energy diagrams for a toy

### FREE 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

### 2-1 Position, Displacement, and Distance

2-1 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:

### Physics 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

### Lesson 2.15: Physical Science Speed, Velocity & Acceleration

Weekly Focus: Reading for Comprehension Weekly Skill: Numeracy Skills in Science Lesson Summary: This week students will continue reading for comprehension with reading passages on speed, velocity, and

### Physics 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 8:15-10:15 Room:

### Conceptual Questions: Forces and Newton s Laws

Conceptual Questions: Forces and Newton s Laws 1. An object can have motion only if a net force acts on it. his statement is a. true b. false 2. And the reason for this (refer to previous question) is

### ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION

ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION This tutorial covers pre-requisite material and should be skipped if you are

### MOTION DIAGRAMS. Revised 9/05-1 - LC, tlo

MOTION DIAGRAMS When first applying kinematics (motion) principles, there is a tendency to use the wrong kinematics quantity - to inappropriately interchange quantities such as position, velocity, and

### LAB 6 - GRAVITATIONAL AND PASSIVE FORCES

L06-1 Name Date Partners LAB 6 - GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies

### Chapter 3 Falling Objects and Projectile Motion

Chapter 3 Falling Objects and Projectile Motion Gravity influences motion in a particular way. How does a dropped object behave?!does the object accelerate, or is the speed constant?!do two objects behave

### Bridging Units: Resource Pocket 3

Bridging Units: Resource Pocket 3 Graphs in real-life contexts Kinematics Graphs representing financial situations Most students will have some knowledge of how to calculate bills such as mobile phone

### ACCELERATION 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

### Acceleration Introduction: Objectives: Methods:

Acceleration Introduction: Acceleration is defined as the rate of change of velocity with respect to time, thus the concepts of velocity also apply to acceleration. In the velocity-time graph, acceleration

### http://www.webassign.net/v4cgikchowdary@evergreen/assignments/prev... 1 of 10 7/29/2014 7:28 AM 2 of 10 7/29/2014 7:28 AM

HW1 due 6 pm Day 3 (Wed. Jul. 30) 2. Question Details OSColPhys1 2.P.042.Tutorial.WA. [2707433] Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 (a) The graph below plots the position versus time

### Part 1: Background - Graphing

Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software 1 1.1 Graphing Part 1: Background - Graphing In science it is very important to find and

### Problem 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. 12-5: 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

### Determining the Acceleration Due to Gravity

Chabot College Physics Lab Scott Hildreth Determining the Acceleration Due to Gravity Introduction In this experiment, you ll determine the acceleration due to earth s gravitational force with three different

### Temperature Scales. The metric system that we are now using includes a unit that is specific for the representation of measured temperatures.

Temperature Scales INTRODUCTION The metric system that we are now using includes a unit that is specific for the representation of measured temperatures. The unit of temperature in the metric system is

### Despite 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

### Worksheet 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

### Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding

### Freely Falling Objects

Freely Falling Objects Physics 1425 Lecture 3 Michael Fowler, UVa. Today s Topics In the previous lecture, we analyzed onedimensional motion, defining displacement, velocity, and acceleration and finding

### LAB 6: GRAVITATIONAL AND PASSIVE FORCES

55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction

### FRICTION, WORK, AND THE INCLINED PLANE

FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle

### x x y y Then, my slope is =. Notice, if we use the slope formula, we ll get the same thing: m =

Slope and Lines The slope of a line is a ratio that measures the incline of the line. As a result, the smaller the incline, the closer the slope is to zero and the steeper the incline, the farther the

### EXPERIMENT 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 freely-falling body varies with time to investigate whether the velocity

### Elasticity. I. What is Elasticity?

Elasticity I. What is Elasticity? The purpose of this section is to develop some general rules about elasticity, which may them be applied to the four different specific types of elasticity discussed in

### Speed, Velocity and Acceleration Lab

Speed, Velocity and Acceleration Lab Name In this lab, you will compare and learn the differences between speed, velocity, and acceleration. You will have two days to complete the lab. There will be some

### EdExcel Decision Mathematics 1

EdExcel Decision Mathematics 1 Linear Programming Section 1: Formulating and solving graphically Notes and Examples These notes contain subsections on: Formulating LP problems Solving LP problems Minimisation

### The fairy tale Hansel and Gretel tells the story of a brother and sister who

Piecewise Functions Developing the Graph of a Piecewise Function Learning Goals In this lesson, you will: Develop the graph of a piecewise function from a contet with or without a table of values. Represent

### 1. Then f has a relative maximum at x = c if f(c) f(x) for all values of x in some

Section 3.1: First Derivative Test Definition. Let f be a function with domain D. 1. Then f has a relative maximum at x = c if f(c) f(x) for all values of x in some open interval containing c. The number

### GRAPH 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

### Week 1: Functions and Equations

Week 1: Functions and Equations Goals: Review functions Introduce modeling using linear and quadratic functions Solving equations and systems Suggested Textbook Readings: Chapter 2: 2.1-2.2, and Chapter

### Experiment 2 Free Fall and Projectile Motion

Name Partner(s): Experiment 2 Free Fall and Projectile Motion Objectives Preparation Pre-Lab Learn how to solve projectile motion problems. Understand that the acceleration due to gravity is constant (9.8

### Projectile motion simulator. http://www.walter-fendt.de/ph11e/projectile.htm

More Chapter 3 Projectile motion simulator http://www.walter-fendt.de/ph11e/projectile.htm The equations of motion for constant acceleration from chapter 2 are valid separately for both motion in the x

1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points

### ACCELERATION 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

### Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.

Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular

### SCALAR 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 DISTANCE-TIME GRAPHS SPEED-TIME GRAPHS SCALAR

### C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

### Research question: How does the velocity of the balloon depend on how much air is pumped into the balloon?

Katie Chang 3A For this balloon rocket experiment, we learned how to plan a controlled experiment that also deepened our understanding of the concepts of acceleration and force on an object. My partner

### Questions: Does it always take the same amount of force to lift a load? Where should you press to lift a load with the least amount of force?

Lifting A Load 1 NAME LIFTING A LOAD Questions: Does it always take the same amount of force to lift a load? Where should you press to lift a load with the least amount of force? Background Information:

### Scientific Graphing in Excel 2010

Scientific Graphing in Excel 2010 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.

### 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

### Credits. Copyright, Utah State Office of Education, 2013.

Credits Copyright, Utah State Office of Education, 2013. Unless otherwise noted, the contents of this book are licensed under the Creative Commons Attribution NonCommercial ShareAlike license. Detailed

### Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide)

Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) 2012 WARD S Science v.11/12 OVERVIEW Students will measure

### Speed (a scalar quantity) is the distance travelled every second.

SCALAR and VECTOR QUANTITIES The following are some of the quantities you will meet in the Intermediate Physics course: DISTANCE, DISPLACEMENT, SPEED, VELOCITY, TIME, FORCE. Quantities can be divided into

### Physics 11 Assignment KEY Dynamics Chapters 4 & 5

Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problem-solving questions, draw appropriate free body diagrams and use the aforementioned problem-solving method.. Define the following

### 1.7 Graphs of Functions

64 Relations and Functions 1.7 Graphs of Functions In Section 1.4 we defined a function as a special type of relation; one in which each x-coordinate was matched with only one y-coordinate. We spent most

### A synonym is a word that has the same or almost the same definition of

Slope-Intercept Form Determining the Rate of Change and y-intercept Learning Goals In this lesson, you will: Graph lines using the slope and y-intercept. Calculate the y-intercept of a line when given

### Force and motion. Science teaching unit

Science teaching unit Disclaimer The Department for Children, Schools and Families wishes to make it clear that the Department and its agents accept no responsibility for the actual content of any materials

### Section 1.1 Linear Equations: Slope and Equations of Lines

Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of

### Summary of important mathematical operations and formulas (from first tutorial):

EXCEL Intermediate Tutorial Summary of important mathematical operations and formulas (from first tutorial): Operation Key Addition + Subtraction - Multiplication * Division / Exponential ^ To enter a

### AP PHYSICS C Mechanics - SUMMER ASSIGNMENT FOR 2016-2017

AP PHYSICS C Mechanics - SUMMER ASSIGNMENT FOR 2016-2017 Dear Student: The AP physics course you have signed up for is designed to prepare you for a superior performance on the AP test. To complete material

### SQA CfE Higher Physics Unit 1: Our Dynamic Universe

SCHOLAR Study Guide SQA CfE Higher Physics Unit 1: Our Dynamic Universe Authored by: Ian Holton Previously authored by: Douglas Gavin John McCabe Andrew Tookey Campbell White Reviewed by: Grant McAllister

### What are the place values to the left of the decimal point and their associated powers of ten?

The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

### Map Patterns and Finding the Strike and Dip from a Mapped Outcrop of a Planar Surface

Map Patterns and Finding the Strike and Dip from a Mapped Outcrop of a Planar Surface Topographic maps represent the complex curves of earth s surface with contour lines that represent the intersection

### One- and Two-dimensional Motion

PHYS-101 LAB-02 One- and Two-dimensional Motion 1. Objective The objectives of this experiment are: to measure the acceleration of gravity using one-dimensional motion to demonstrate the independence of

### Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}

Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### Tennessee State University

Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

### Mathematical goals. Starting points. Materials required. Time needed

Level A6 of challenge: C A6 Mathematical goals Starting points Materials required Time needed Interpreting distance time graphs To enable learners to: interpret and construct distance time graphs, including:

### -2- Reason: This is harder. I'll give an argument in an Addendum to this handout.

LINES Slope The slope of a nonvertical line in a coordinate plane is defined as follows: Let P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) be any two points on the line. Then slope of the line = y 2 y 1 change in

### Intermediate PowerPoint

Intermediate PowerPoint Charts and Templates By: Jim Waddell Last modified: January 2002 Topics to be covered: Creating Charts 2 Creating the chart. 2 Line Charts and Scatter Plots 4 Making a Line Chart.

### (I) s(t) = s 0 v 0 (t t 0 ) + 1 2 a (t t 0) 2 (II). t 2 = t 0 + 2 v 0. At the time. E kin = 1 2 m v2 = 1 2 m (a (t t 0) v 0 ) 2

Mechanics Translational motions of a mass point One-dimensional motions on the linear air track LD Physics Leaflets P1.3.3.8 Uniformly accelerated motion with reversal of direction Recording and evaluating

### Chapter 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

### Physics Lab Report Guidelines

Physics Lab Report Guidelines Summary The following is an outline of the requirements for a physics lab report. A. Experimental Description 1. Provide a statement of the physical theory or principle observed

### Acceleration of Gravity Lab Basic Version

Acceleration of Gravity Lab Basic Version In this lab you will explore the motion of falling objects. As an object begins to fall, it moves faster and faster (its velocity increases) due to the acceleration