Concept explainers
(a)
The instantaneous velocity as a function of time.
(a)
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)
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)
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)
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, Vol. 3
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