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Concept explainers
(a)
The instantaneous velocity as a function of time.
(a)
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Answer to Problem 112P
The instantaneous velocity as the function of time is given as
Explanation of Solution
Given:
The acceleration of the particle is
The position of particle is
Formula used:
Write expression for the acceleration of the particle.
Here,
Rearrange above expression for
Calculation:
Substitute
Conclusion:
Thus, the instantaneous velocity as the function of time is given as
(b)
The position of particle as function of time.
(b)
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Answer to Problem 112P
The position of particle as a function of time is given by
Explanation of Solution
Given:
The acceleration of the particle is
The position of particle is
Formula used:
Write expression for the instantaneous velocity of the particle.
Write expression for the velocity of the particle.
Rearrange above expression for
Calculation:
Substitute
Conclusion:
Thus, the position of particle as a function of time is given by
(c)
The average velocity for the time interval
(c)
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Answer to Problem 112P
The average velocity for the given time interval is given by
Explanation of Solution
Given:
The acceleration of the particle is
The position of particle is
Formula used:
Write expression for average velocity of the particle.
Calculation:
Substitute
Conclusion:
Thus, the average velocity for the given time interval is given by
(d)
The average of initial and final velocity and compare with part (c)
(d)
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Answer to Problem 112P
The average of the initial and final velocities is given by
Explanation of Solution
Given:
The acceleration of the particle is
The position of particle is
Formula used:
Write expression for the average instantaneous velocity of the particle.
Calculation:
Substitute
Conclusion:
Thus, the average of the initial and final velocities is given by
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Chapter 2 Solutions
Physics for Scientists and Engineers
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