Concept explainers
The Acela is an electric train on the Washington–New York–Boston run, carrying passengers at 170 mi/h. A velocity–time graph for the Acela is shown in Figure P2.46. (a) Describe the train’s motion in each successive time interval. (b) Find the train’s peak positive acceleration in the motion graphed. (c) Find the train’s displacement in miles between t = 0 and t = 200 s.
Figure P2.46 Velocity versus time graph for the Acela.
(a)
The description of the train’s motion in each successive time interval.
Answer to Problem 46P
Initially A is moving at constant positive velocity in the
Explanation of Solution
In the given velocity versus time graph of A, the curve is parallel to the time axis in the interval
From around
Conclusion:
Thus, initially A is moving at constant positive velocity in the
(b)
The train’s peak positive acceleration in the motion graphed.
Answer to Problem 46P
The train’s peak positive acceleration in the motion graphed is
Explanation of Solution
The slope of the graph in a given interval gives the acceleration of the object during it. The region of steepest slope in the
Write the equation for the acceleration of the object.
Here,
Write the equation for the slope.
Here,
Put the above equation in equation (I).
Conclusion:
Substitute
Therefore, the train’s peak positive acceleration in the motion graphed is
(c)
The train’s displacement in miles between
Answer to Problem 46P
The train’s displacement in miles between
Explanation of Solution
The cumulative area under the velocity versus time graph between
The velocity versus time graph is shown below.
Write the equation for the area of a rectangle.
Here,
Write the equation for the area of a triangle.
Here,
The area from
In figure 1, the length of the rectangle from
Substitute
Here,
The area from
In figure 1, the length of the rectangle from
Substitute
Here,
In figure 1, the base of the triangle from
Substitute
Here,
The area from
In figure 1, the length of the rectangle from
Substitute
Here,
In figure 1, the base of the triangle from
Substitute
Here,
Write the equation for the net displacement.
Here,
Conclusion:
Substitute
Therefore, the train’s displacement in miles between
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Chapter 2 Solutions
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