homeworkphys - MasteringPhysics Assignment Print View 1 of...

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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 ] What Velocity vs. Time Graphs Can Tell You A 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 a single 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, respectively. Here is a plot of velocity versus time for a particle that travels along a straight line with a varying velocity. Refer to this plot to answer the following questions. Part A What is the initial velocity of the particle, ? Hint A.1 Initial velocity Hint not displayed Hint A.2 How to read a v vs. t graph Hint not displayed Express your answer in meters per second. ANSWER: = 0.5 Correct Part B What is the total distance traveled by the particle? Hint B.1 How to approach the problem Recall that 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 . Thus, to calculate the total distance, you need to find the area of the entire region under the v vs. t curve. In the case at hand, the entire region under the v vs. t curve is not an elementary geometrical figure, but rather a combination of triangles and rectangles. Hint B.2 Find the distance traveled in the first 20.0 seconds What is the distance traveled in the first 20 seconds of motion, between and ? Hint B.2.1 Area of the region under the v vs. t curve Hint not displayed Express your answer in meters. ANSWER: = 25 Correct Hint B.3 Find the distance traveled in the second 20.0 seconds Hint not displayed Hint B.4 Find the distance traveled in the last 10.0 seconds Hint not displayed Express your answer in meters. ANSWER: = 75 Correct Part C What is the average acceleration of the particle over the first 20.0 seconds? Hint C.1 Definition and graphical interpretation of average acceleration The average acceleration of a particle that travels along a straight line in a time interval is the ratio of the change in velocity experienced by the particle to the time interval , or . In a v vs. t graph, then, the average acceleration equals the slope of the line connecting the two points representing the initial and final velocities. MasteringPhysics: Assignment Print View ...
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