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Assignment MasteringPhysics: Print View http://session.masteringphysics.com/myct/assignmentPrint?assig... [ Print View ] PH1110A2008 Assignment 3 Due at 11:59pm on Saturday, September 6, 2008 View Grading Details Analyzing Position versus Time Graphs: Conceptual Question Two cars travel on the parallel lanes of a two-lane road. The cars motions are represented by the position versus time graph shown in the figure. Answer the questions using the times from the graph indicated by letters. Part A At which of the times do the two cars pass each other? Hint A.1 Two cars passing Hint not displayed ANSWER: Part B Are the two cars traveling in the same direction when they pass each other? ANSWER: yes no Part C At which of the lettered times, if any, does car #1 momentarily stop? Hint C.1 Determining velocity from a position versus time graph Hint not displayed ANSWER: Part D At which of the lettered times, if any, does car #2 momentarily stop? Hint D.1 Determining velocity from a position versus time graph Hint not displayed ANSWER: 1 of 7 10/13/2008 8:00 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assig... Part E At which of the lettered times are the cars moving with nearly identical velocity? Hint E.1 Determining Velocity from a Position versus Time Graph Hint not displayed ANSWER: 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. 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, the car 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. Answer not displayed Notice that the first and second options are always true, regardless of the values of Frequently, you will be able to pick your coordinate system. In such cases, making , , and . The last option, however, is only true when is often a good choice. . Part B Run the simulation, paying close attention to the graph of position. Press reset and change the value of graph. How does varying affect the graph of position? ANSWER: . Run the simulation again, noting any changes in the Increasing Increasing Increasing Increasing Increasing Changing 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 position? Choose the best answer. ANSWER: Increasing increases the width of the graph, whereas decreasing decreases the width. , but don't use any positive values. Note any changes in the graph. How does varying affect the graph of 2 of 7 10/13/2008 8:00 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assig... Increasing Increasing Increasing Increasing Changing shifts the graph to the right and upward, whereas decreasing it shifts the graph to the left and downward. shifts the graph to the left and upward, whereas decreasing it shifts the graph to the right and downward. shifts the graph to the right and downward, whereas decreasing it shifts the graph to the left and upward. shifts the graph to the left and downward, whereas decreasing it shifts the graph to the right and upward. 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 with the qualities of the graph that you have in the equation, would it move the graph upward? , initial velocity , and acceleration . identified. For instance, if you increase Express your answer in terms of time , initial position ANSWER: = 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: is the velocity equal to zero? Express your answer in seconds to the nearest integer. ANSWER: 3 , , and . The units of time in the graph are seconds. At what time Notice that the position graph has a minimum when velocity equals zero. This should make sense to you. Since 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 19.2 and accelerates with a constant acceleration of 4.15 . At what time is the velocity the of car ? Use the applet to be certain that your answer is reasonable. Choose the kinematic equation Part not displayed Part G.1 Hint G.2 Using the applet to check your answer Hint not displayed Express your answer in seconds to three significant figures. 3 of 7 10/13/2008 8:00 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assig... ANSWER: = 4.63 Part H For the same initial conditions as in the last part, what is the car's position reasonable. Part H.1 Choose the kinematic equation at time 4.05 ? Again, be sure to use the applet to check that your answer is 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. 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. Clear the Runway To take off from the ground, an airplane must reach a sufficiently high speed. The velocity required for the takeoff, the takeoff velocity, depends on several factors, including the weight of the aircraft and the wind velocity. Part A A plane accelerates from rest at a constant rate of 5.00 the end of the runway. What is the time Hint A.1 along a runway that is 1800 long. Assume that the plane reaches the required takeoff velocity at needed to take off? How to approach the problem As the plane travels along the runway, it has constant acceleration. To solve the problem, you'll need to use the kinematics equations for such motion. In particular, you need to use the equation relating the distance traveled and time. Part A.2 Find the equation for the distance traveled by the plane traveled by the plane during a certain interval of time ? Let and be, respectively, the initial position Which expression best describes the distance and speed of the plane, and use ANSWER: for the acceleration of the plane. Remember that the plane accelerates from rest. = Express your answer in seconds. 4 of 7 10/13/2008 8:00 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assig... ANSWER: = 26.83 Part B What is the speed Hint B.1 of the plane as it takes off? How to approach the problem Hint not displayed Part B.2 Find the equation for the velocity of the plane of the plane after a certain interval of time ? Let be the initial velocity of the plane, and use for the Which expression best describes the velocity acceleration of the plane. Remember that the plane starts from rest. ANSWER: = Alternatively, you can use the relation Express your answer numerically at meters per second. ANSWER: = 134 (recalling that in this case ). Part C What is the distance Hint C.1 traveled by the plane in the first second of its run? How to approach the problem Apply the same equation that you used to solve Part A. Express your answer numerically in meters. ANSWER: = 2.50 Part D What is the distance Hint D.1 traveled by the plane in the last second before taking off? How to approach the problem Use the equation that gives the distance traveled as a function of time. Note that you are looking for the distance traveled in the last second before the plane takes off, which can be expressed as the length of the runway minus the distance traveled by the plane up to that last second. Express your answer numerically in meters. ANSWER: = 132 Since the plane is accelerating, the average speed of the plane during the last second of its run is greater than its average speed during the first second of the run. Not surprisingly, so is the distance traveled. Part E 5 of 7 10/13/2008 8:00 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assig... What percentage of the takeoff velocity did the plane gain when it reached the midpoint of the runway? Hint E.1 How to approach the problem You need to find the velocity of the plane by the time it covers half the length of the runway and compare it with the takeoff velocity. Apply the same method that you used to determine the takeoff velocity. Express your answer numerically. ANSWER: 70 This is a "rule of thumb" generally used by pilots. Since the takeoff velocity for a particular aircraft can be computed before the flight, a pilot can determine whether the plane will successfully take off before the end of the runway by verifying that the plane has gained 70% of the takeoff velocity by the time it reaches half the length of the runway. If the plane hasn't reached that velocity, the pilot knows that there isn't enough time to reach the needed takeoff velocity before the plane reaches the end of the runaway. At that point, applying the brakes and aborting the takeoff is the safest course of action. Direction of Velocity at Various Times in Flight for Projectile Motion Conceptual Question For each of the motions described below, determine the algebraic sign (positive, negative, or zero) of the x component and y component of velocity of the object at the time specified. For all of the motions, the positive x axis points to the right and the positive y axis points upward. Alex, a mountaineer, must leap across a wide crevasse. The other side of the crevasse is below the point from which he leaps, as shown in the figure. Alex leaps horizontally and successfully makes the jump. Part A Determine the algebraic sign of Alex's x velocity and y velocity at the instant he leaves the ground at the beginning of the jump. Hint A.1 Algebraic sign of velocity Hint not displayed Part A.2 Sketch Alex's initial velocity Part not displayed Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). ANSWER: +,0 Part B Determine the algebraic signs of Alex's x velocity and y velocity the instant before he lands at the end of the jump. Part B.1 Sketch Alex's final velocity Part not displayed Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). ANSWER: +,- At the buzzer, a basketball player shoots a desperation shot. The ball goes in! 6 of 7 10/13/2008 8:00 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assig... Part C Determine the algebraic signs of the ball's x velocity and y velocity the instant after it leaves the player's hands. Part C.1 Sketch the basketball's initial velocity Part not displayed Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). ANSWER: +,+ Part D Determine the algebraic signs of the ball's x velocity and y velocity at the ball's maximum height. Part D.1 Sketch the basketball's velocity at maximum height Part not displayed Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). ANSWER: +,0 Summary 4 of 4 items complete (96.48% avg. score) 38.59 of 40 points 7 of 7 10/13/2008 8:00 PM ... View Full Document