a.
To calculate: The value of time when the particle moves forward, backward, increase in speed, decrease in speed.
a.
Answer to Problem 9E
The particle moves forward from
Explanation of Solution
Given information:
The graph of the velocity verses time
Concept used:
The displacement of the particle is final distance minus initial distance.
Calculation:
When the particle is in positive
In the given graph, the particle is in positive
In the given graph, the particle is in positive
When the slope is positive that is the line is moving upward from left to right then the speed of the particle will increase and if the slope is negative that is line is moving downwards from left to right then the speed of the particle will decrease.
The slope of the line is positive from
The slope of the line is negative from
Conclusion: The particle moves forward from
b.
To calculate: The time when acceleration is positive, negative and constant.
b.
Answer to Problem 9E
The time of positive acceleration is from
Explanation of Solution
Given information:
The graph of the velocity verses time
Calculation:
When the slope is positive, then the acceleration will be positive.
The acceleration of the particle is positive from
When the slope is negative, then the acceleration will be negative.
The acceleration of the particle is negative from
The acceleration of the particle will be zero when the velocity is constant.
So the acceleration will be constant from
Conclusion: The time of positive acceleration is from
c.
To calculate: The greatest speed of the particle.
c.
Answer to Problem 9E
The value of time is
Explanation of Solution
Given information:
The graph of velocity verses time is shown below.
Concept used:
The speed is always a positive quantity.
Calculation:
The speed is greatest at
Conclusion: The value of time is
d.
To calculate:. The value of time
d.
Answer to Problem 9E
The time is from
Explanation of Solution
Given information:
The function is
Calculation:
The particle is standing still from
Conclusion: The time is from
Chapter 2 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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