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Assignment MasteringPhysics: Print View
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[ Print View ]
Physics 2211-001, Fall 2008
basic kinematics
Due at 11:00pm on Sunday, August 24, 2008
[ Print ]
View Grading Details
Given Positions, Find Velocity and Acceleration
Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordinate of a moving object. The position is tabulated at 1-s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes. time (s) x (m) 0 0 1 1 2 4 3 9 4 16 5 24 6 32 7 40 8 46 9 48
Part A Which graph best represents the function , describing the object's position vs. time?
Hint A.1 Meaning of a bounded and nonspiky acceleration Hint not displayed ANSWER: 1 2 3 4
Part B
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MasteringPhysics: Assignment Print View
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Which of the following graphs best represents the function time?
, describing the object's velocity as a function of
Part B.1 Find the velocity toward the end of the motion Part not displayed Part B.2 What are the implications of zero velocity? Part not displayed Part B.3 Specify the characteristics of the velocity function Part not displayed ANSWER: 1 2 3 4
In principle, you could also just compute and plot the average velocity. The expression for the average velocity is . The notation emphasizes that this is not an instantaneous velocity, but rather an average over an
interval. After you compute this, you must put a single point on the graph of velocity vs. time. The most accurate place to plot the average velocity is at the middle of the time interval over which the average was computed. Also, you could work back and find the position from the velocity graph. The position of an object is the integral of its velocity. That is, the area under the graph of velocity vs. time from up to time must equal the position of the object at time . Check that the correct velocity vs. time graph gives you the correct position according to this method.
Part C
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MasteringPhysics: Assignment Print View
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Which of the following graphs best represents the function
, describing the acceleration of this object?
Part C.1 Find the acceleration toward the end of the motion Part not displayed Part C.2 Calculate the acceleration in the region of constant velocity Part not displayed Part C.3 Find the initial acceleration Part not displayed ANSWER: 1 2 3 4
In one dimension, a linear increase or decrease in the velocity of an object over a given time interval implies constant acceleration over that particular time interval. You can find the magnitude of the acceleration using the formula for average acceleration over a time interval: . When the acceleration is constant over an extended interval, you can choose any value of interval to compute the average. and within the
What x vs. t Graphs Can Tell You
To describe the motion of a particle along a straight line, it is often convenient to draw a graph representing the position of the particle at different times. This type of graph is usually referred to as an x vs. t graph. To draw such a graph, choose an axis system in which time is plotted on the horizontal axis and position on the vertical axis. Then, indicate the values of at various times . Mathematically, this corresponds to plotting the variable as a function of . An example of a graph of position as a function of time for a particle traveling along a straight line is shown below. Note that an x vs. t graph like this does not represent the path of the particle in space.
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MasteringPhysics: Assignment Print View
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Now let's study the graph shown in the figure in more detail. Refer to this graph to answer Parts A, B, and C.
Part A What is the total distance traveled by the particle?
Hint A.1 Total distance The total distance and the position at traveled by the particle is given by the difference between the initial position . In symbols, . Hint A.2 How to read an x vs. t graph Remember that in an x vs. t graph, time is plotted on the horizontal axis and position example, in the plot shown in the figure, Express your answer in meters. ANSWER: = 30 at . on the vertical axis. For at
Part B What is the average velocity of the particle over the time interval ?
Hint B.1 Definition and graphical interpretation of average velocity The average velocity as . In an x vs. t graph, then, the average velocity equals the slope of the line connecting the initial and final positions. Hint B.2 Slope of a line Hint not displayed of a particle that travels a distance along a straight line in a time interval is defined
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MasteringPhysics: Assignment Print View
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Express your answer in meters per second. ANSWER: = 0.600
The average velocity of a particle between two positions is equal to the slope of the line connecting the two corresponding points in an x vs. t graph. Part C What is the instantaneous velocity of the particle at ?
Hint C.1 Graphical interpretation of instantaneous velocity The velocity of a particle at any given instant of time or at any point in its path is called instantaneous velocity. In an x vs. t graph of the particle's motion, you can determine the instantaneous velocity of the particle at any point in the curve. The instantaneous velocity at any point is equal to the slope of the line tangent to the curve at that point. Express your answer in meters per second. ANSWER: = 0.600
The instantaneous velocity of a particle at any point on its x vs. t graph is the slope of the line tangent to the curve at that point. Since in the case at hand the curve is a straight line, the tangent line is the curve itself. Physically, this means that the instantaneous velocity of the particle is constant over the entire time interval of motion. This is true for any motion where distance increases linearly with time. Another common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time is plotted on the horizontal axis and velocity on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only one nonzero component in the direction of motion. Thus, in this problem, we will call the velocity and the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion. Part D Which of the graphs shown is the correct v vs. t plot for the motion described in the previous parts? Hint D.1 How to approach the problem Hint not displayed
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MasteringPhysics: Assignment Print View
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ANSWER:
Graph A Graph B Graph C Graph D
Whenever a particle moves with constant nonzero velocity, its x vs. t graph is a straight line with a nonzero slope, and its v vs. t curve is a horizontal line. Part E Shown in the figure is the v vs. t curve selected in the previous part. What is the area the curve? of the shaded region under
Hint E.1 How to approach the problem Hint not displayed Express your answer in meters.
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MasteringPhysics: Assignment Print View
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ANSWER:
= 30
Compare this result with what you found in Part A. As you can see, the area of the region under the v vs. t curve equals the total distance traveled by the particle. This is true for any velocity curve and any time interval: The area of the region that extends over a time interval under the v vs. t curve is always equal to the distance traveled in .
Problem 2.25
A particle moving along the x-axis has its position described by the function 2.00 4.00 2.00 , where is in s. At = 2.00, what are the particle's (a) position, (b) velocity, and (c) acceleration? Part A ANSWER: 10.0 m
Part B ANSWER:
20.0
Part C ANSWER:
24.0
Going for a Drive
Learning Goal: To gain a qualitative understanding of kinematics and how the qualitative nature of position and velocity versus time graphs relates to the equations of kinematics. In this problem, you will explore kinematics using an applet that simulates a car moving under constant acceleration. When you open the applet, you will see three sliders that allow you to adjust the initial position , the initial velocity , and the acceleration . Set the initial position to 0 , the initial velocity to and the acceleration to 5 .
Run the simulation. Notice that, as the movie proceeds, pictures of the car remain at certain points. Once the simulation is over, these pictures form a motion diagram--a representation of motion consisting of pictures taken at equal time intervals during the motion. In this case, the interval between pictures is one second. Below the movie, the position of the car as a function of time is graphed in green. Run the simulation several times, paying attention to how the graph and the motion diagram/movie of the car's motion relate to each other.
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MasteringPhysics: Assignment Print View
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Part A Which of the following describe the relationship between the motion diagram/movie and the graph? Check all that apply. ANSWER: When the slope of the graph is close to zero, the pictures in the motion diagram are close together. When the slope of the graph is steep, the car is moving quickly. When the slope of the graph is positive, the car is to the right of its starting position. When the x position on the graph is negative, the car moves backward. When the x position on the graph is positive, the car moves forward. When the x position on the graph is negative, the car moves slowly. When the x position on the graph is positive, car the moves quickly. When the x position on the graph is negative, the car is to the left of its starting position. When the x position on the graph is positive, the car is to the right of its starting position.
Notice that the first and second options are always true, regardless of the values of , , and . The last option, however, is only true when . Frequently, you will be able to pick your coordinate system. In such cases, making Part B Run the simulation, paying close attention to the graph of position. Press reset and change the value of simulation again, noting any changes in the graph. How does varying affect the graph of position? ANSWER: Increasing Increasing Increasing Increasing Increasing Changing . Run the is often a good choice.
increases the width of the graph, whereas decreasing decreases the width. shifts the graph to the right, whereas decreasing it shifts the graph to the left. shifts the graph to the left, whereas decreasing it shifts the graph to the right. shifts the graph upward, whereas decreasing it shifts the graph downward. shifts the graph downward, whereas decreasing it shifts the graph upward. does not affect the graph.
Part C Now, run the simulation with different values of , but don't use any positive values. Note any changes in the graph. How does varying affect the graph of position? Choose the best answer. ANSWER: Increasing increases the width of the graph, whereas decreasing decreases the width. Increasing shifts the graph to the right and upward, whereas decreasing it shifts the graph to the left and downward. Increasing shifts the graph to the left and upward, whereas decreasing it shifts the graph to the right and downward. Increasing shifts the graph to the right and downward, whereas decreasing it shifts the graph to the left and upward. Increasing shifts the graph to the left and downward, whereas decreasing it shifts the graph to the right and upward.
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MasteringPhysics: Assignment Print View
http://session.masteringphysics.com/myct/assignmentPrint?assignm...
Changing
does not affect the graph.
This behavior may be a bit difficult to understand by just looking at the equation for position vs. time that you know from kinematics. If you complete the square to get the equation into standard form for a parabola, this should become more apparent. Now that you've seen how affects the graph, run the simulation with a few different values of acceleration. You should see that increasing the acceleration decreases the width of the graph and decreasing the acceleration increases the width. (Decreasing the acceleration below 0 makes the parabola open downward instead of upward.)
Part D Enter the equation for position as a function of time. Before submitting your answer, check that it is consistent in the equation, would it , and with the qualities of the graph that you have identified. For instance, if you increase move the graph upward? Express your answer in terms of time , initial position acceleration ANSWER: . =
, initial velocity
Part E Now, open this applet. This applet looks like the previous applet, but when you run the simulation, you will now get graphs of both position and velocity. Run the simulation several times with different values of . How does changing affect the graph of velocity? ANSWER: Increasing Increasing Increasing Increasing Increasing Changing increases the slope of the graph, whereas decreasing decreases the slope. shifts the graph to the right, whereas decreasing it shifts the graph to the left. shifts the graph to the left, whereas decreasing it shifts the graph to the right. shifts the graph upward, whereas decreasing it shifts the graph downward. shifts the graph downward, whereas decreasing it shifts the graph upward. does not affect the graph.
Part F Run the simulation again, with the following settings: , , and . The units of time
in the graph are seconds. At what time is the velocity equal to zero? Express your answer in seconds to the nearest integer. ANSWER: 3
Notice that the position graph has a minimum when velocity equals zero. This should make sense to you. Since
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MasteringPhysics: Assignment Print View
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velocity is the derivative of position, position has a local minimum or maximum when velocity is zero. Part G Suppose that a car starts from rest at position what time is the velocity of the car 19.2 and accelerates with a constant acceleration of 4.15 ? Use the applet to be certain that your answer is reasonable. . At
Part G.1 Choose the kinematic equation Part not displayed Hint G.2 Using the applet to check your answer Hint not displayed Express your answer in seconds to three significant figures. ANSWER: = 4.63
Part H For the same initial conditions as in the last part, what is the car's position the applet to check that your answer is reasonable. Part H.1 Choose the kinematic equation You have seen a number of kinematic equations. Choose the one from the following list that will be the most useful in this problem. Again, is the acceleration, and are, respectively, velocity and position at time , while and are, respectively, the initial velocity and initial position. at time 4.05 ? Again, be sure to use
ANSWER:
Express your answer in meters to three significant figures. ANSWER: = 30.7
Any time that you are working a physics problem, you should check that your answer is reasonable. Even when you don't have an applet with which to check, you have a wealth of personal experience. For example, if you obtain an answer such as "the distance from New York to Los Angeles is 3.96 ," you know it must be wrong. You should always try to relate situations from physics class to real-life situations.
The Graph of a Sports Car's Velocity
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MasteringPhysics: Assignment Print View
http://session.masteringphysics.com/myct/assignmentPrint?assignm...
The graph in the figure shows the velocity following questions.
of a sports car as a function of time . Use the graph to answer the
Part A Find the maximum velocity of the car during the ten-second interval depicted in the graph.
Hint A.1 How to approach the problem Hint not displayed Express your answer in meters per second to the nearest integer. ANSWER: = 55
Part B During which time interval is the acceleration positive? Hint B.1 Finding acceleration from the graph Hint not displayed Indicate the best answer. ANSWER: to to to to to
Part C Find the maximum acceleration of the car.
Hint C.1 How to approach the problem Hint not displayed Part C.2 Find the final velocity on the interval with greatest acceleration Part not displayed Express your answer in meters per second per second to the nearest integer.
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MasteringPhysics: Assignment Print View
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ANSWER:
= 30
Part D Find the minimum magnitude of the acceleration Hint D.1 How to approach the problem Hint not displayed Express your answer in meters per second per second to the nearest integer. ANSWER: =0 of the car.
Part E Find the distance traveled by the car between and .
Hint E.1 How to approach the problem Hint not displayed Part E.2 Find the distance traveled in the first second Part not displayed Part E.3 Find the distance traveled in the second second Part not displayed Express your answer in meters to the nearest integer. ANSWER: = 55
Problem 2.61
A ball rolls along the smooth track shown in the figure with an initial speed of 8.70 all the corners smoothly, with no loss of speed. . Assume that the ball turns
Part A What is the ball's speed as it goes over the top?
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MasteringPhysics: Assignment Print View
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ANSWER:
7.49
Part B What is its speed when it reaches the level track on the right side? ANSWER: 8.70
Running and Walking
Tim and Rick both can run at speed and walk at speed , with . They set off together on a journey of distance . Rick walks half of the distance and runs the other half. Tim walks half of the time and runs the other half. Part A How long does it take Rick to cover the distance Part A.1 Compute midpoint for Rick Part not displayed Part A.2 Compute running time for Rick Part not displayed Hint A.3 What equation to use Hint not displayed Express the time taken by Rick in terms of ANSWER: = , , and . ?
Part B Find Rick's average speed for covering the distance Hint B.1 Calculate velocity using .
and time
You were given the total distance and have calculated the total time. Recall that average velocity is equal to total distance traveled divided by the amount of time it took to travel this distance. Express Rick's average speed in terms of ANSWER: = , , and .
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Part C How long does it take Tim to cover the distance? Part C.1 Calculate average speed Part not displayed Express the time taken by Tim in terms of ANSWER: = , , and .
Part D Who covers the distance more quickly?
Hint D.1 Consider the relative positions at the midpoint Hint not displayed Think logically, but without using the detailed answers in the previous parts. ANSWER: Rick Tim Neither. They cover the distance in the same amount of time.
Part E In terms of given quantities, by what amount of time, , does Tim beat Rick? . It will help you check your answer if you simplify it algebraically and check the special case Express the difference in time, ANSWER: = in terms of , , and .
Part F In the special case that , what would be Tim's margin of victory ?
Hint F.1 Think it through Hint not displayed ANSWER: 0
Problem 2.73
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A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.10 later. Part A What was the rocket's acceleration? ANSWER: 5.63
Summary
8 of 8 items complete (91.34% avg. score) 15.65 of 17 points
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Chapter 6 LoopsIn the last chapter, we introduced the idea of a control construct, a method by which Matlab will depart from its customary sequential processing. Initially, we accomplished this task through the use selection. That is, we used either

UVA - CS - 103

Chapter 7 User Defined FunctionsTo this point, the programs you have written have relied almost exclusively on sequential control. And while you have used control constructs such as loops and conditional statements to alter that sequential processi

UVA - CS - 103

Chapter 8 Data TypesEvery modern programming language provides means for storing numbers in variables, operating on them, and printing them. Matlab is no exception, and we have seen countless examples of numbers being stored, operated on, and print

UVA - CS - 103

This chapter introduces a fundamental new method of programming called recursion. Recursion is a powerful idea that makes it possible to solve some problems easily that would otherwise be quite difficult. Recursion cannot be used in all programming l

UVA - CS - 103

Chapter 10 Searching and SortingIn this chapter we will look at two closely related problems: searching and sorting. Both problems appear in applications involving databases, and without efficient solutions to these problems databases would be virtu

UVA - CS - 103

Chapter 11 Graphical User InterfacesBy default, Matlab runs through a command line interface. That is, individual commands, functions or scripts are executed by typing instructions into the command window and pressing enter. For many years, this was

UVA - CS - 103

Chapter 12 Symbolic MathematicsWhen mathematicians work, they use symbols, such as x and y, to represent numbersand the functional notation f(x) to represent a function of x. We have used the same symbols in Matlab, and yet the meanings are subtly

UVA - CS - 103

PrefaceThis book is meant for students of engineering or science who need both a useful programming language for solving problems in their disciplines and an introduction to ideas from the discipline of computer science. It is a provided free of cha

Genesee - BUS - 101

Corporate Scandals2007 Paxil Lawsuit GlaxoSmithKline promoted Paxil for prescription to children/ adolescents while withholding material information about the medication's safety for minors. More than 2 million prescriptions for youth in

UVA - CS - 103

Introduction to Programming With MatlabJ. Michael Fitzpatrick and John D. CrocettiIntroduction to Programming with MatlabJ. Michael Fitzpatrick and John D. Crocetti Department of Electrical Engineering and Computer Science School of Engineering

UChicago - ECON - 201

Lecture ScheduleWeekMondayTuesdayWednesdayThursdayFridayAssignments1Lecture 1 Chapter 1: IntroductionLecture 2 Chapter 3: Scarcity2TA Session 1: Chapter 2: Constrained MaximizationLecture 3 Chapter 4: Preferences and Utility

UChicago - ECON - 201

The University of Chicago Department of Economics Elements of Economic Analysis I Econ 200 Course SyllabusInstructor : V ictor O. Lima e mail : vlima@uchicago.edu of f ice : Rosenwald 229B TA : M arkP hillips email : mdp@uchicago.edu Course Logist

UChicago - ECON - 201

Beatrice Fineschi bfinesch@uchicago.edusOffice Hours. By appointment. BSLC Room 208 Emails are not a mean of getting concepts explained. Write only to set up appointments or to communicate things that cannot wait until office hours. Strongly recom

UChicago - ECON - 201

3Macromolecules and the Origin of Life3 Macromolecules and the Origin of Life 3.1 What Kinds of Molecules Characterize Living Things? 3.2 What Are the Chemical Structures and Functions of Proteins? 3.3 What Are the Chemical Structures and Fun

UChicago - ECON - 201

Kennesaw - CHEM - 1152

Practice 4 Alkane Conformation 1) (Your answers may look different and still be correct. If yours look different, hand write these answers and consider them carefully.)i) (H3C)2HC CH3 ii) (H3C)2HC CH2CH3 iii) H3CH2C CH2OH iv) (H3C)2HC CH2OHH3C H3

Kennesaw - CHEM - 1152

Practice - Lewis StructuresProvide Lewis structures for the following molecules, be sure to show all non-bonding electrons. Bear in mind that hydrogen and halogens can make only one bond at a time. a) CCl4 b) CH3Br c) H2NNH2 d) PH3 e) H2S f) CH3CH2

Kennesaw - CHEM - 1152

Practice 1 - Lewis StructuresProvide Lewis structures for the following molecules, be sure to show all non-bonding electrons. Cl a) CCl4 b) CH3Br c) H2NNH2 d) PH3 e) H2S f) CH3CH2OH g) HOCH2CH2OH H HP H HS H HH HCCOH HH l) CO2 m) CF4 O n) Cl2CO o)

Kennesaw - CHEM - 1152

-Provide IUPAC names for the following molecules:BrBr

Kennesaw - CHEM - 1152

Practice 2 - Naming AlkanesProvide IUPAC names for the following molecules:3-ethyl-2,5-dimethylheptane4-ethyl-6-methylnonane1,1-dimethylcyclopentane Br3,5-diethyl-2-methyldecane4-ethylnonane1-bromo-3-ethylcyclohexaneBr propylcyclohept

Kennesaw - CHEM - 1152

Practice - Balancing Combustion Equations Provide a balanced equation for the complete combustion of each substance:a)+ 7 O25 CO2 + 4 H2Ob)+ 11 O27 CO2 + 8 H2OOHc)+ 6 O24 CO2 + 5 H2Od)+ 15 O210 CO2 + 10 H2Oe)O+ 6 O24