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 P2.69. (a) Describe the train's motion in each successive lime interval, (b) Find the trains peak positive acceleration in the motion graphed, (c) Find the trains displacement in miles between t = 0 and t = 200 s.
(a)
The motion of train in each successive interval.
Answer to Problem 2.69AP
The train has positive constant velocity from
Explanation of Solution
Given Info: The velocity of the train is
For
The train has constant velocity of
For
The train has a linear increase in the velocity that shoes train is accelerating in the positive
For
The engineer applies brakes at
For
The train just after
Conclusion:
Therefore, the train has positive constant velocity from
(b)
The peak acceleration.
Answer to Problem 2.69AP
The peak acceleration of the train is
Explanation of Solution
Given Info: The velocity of the train is
The train has steepest acceleration from
The train starts acceleration from
The formula to calculate the acceleration of a body is,
Here,
Substitute
Conclusion:
Therefore, the peak acceleration of the train is
(c)
The train displacement between
Answer to Problem 2.69AP
The train displacement between
Explanation of Solution
Given Info: The velocity of the train is
Consider the figure given below.
Figure (1)
The area under the velocity time graph gives the displacement.
The net displacement form
From figure (1), the
The
The
The
The
The net displacement form
Substitute
Substitute
Further solve the above equation.
Conclusion:
Therefore, the net displacement is
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