Concept explainers
(a)
The velocity as the function of time for the given time interval.
(a)
Answer to Problem 111P
The velocity as the function of time interval is
Explanation of Solution
Given:
The acceleration of the particle is given by
The velocity of particle at
The position of particle at
Formula used:
Write expression for the acceleration of the particle.
Here,
Substitute
Simplify above expression.
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the velocity as the function of time interval is
(b)
The position as function of time for the given time interval.
(b)
Answer to Problem 111P
The position as function of time for the given interval is
Explanation of Solution
Given:
The acceleration of the particle is given by
The velocity of particle at
The position of particle at
Formula used:
Write expression for the velocity of the particle as function of time for given time period.
Write expression for velocity of the particle.
Here,
Rearrange above expression for
Calculation:
Substitute
Simplify above expression.
........(3)
Substitute
Substitute
Substitute
Conclusion:
Thus, the position as function of time for the given interval is
(c)
The average velocity for the given time interval and compare to the average of instantaneous velocities of starting and ending times.
(c)
Answer to Problem 111P
The average velocity for the given time interval is
Explanation of Solution
Given:
The acceleration of the particle is given by
The velocity of particle at
The position of particle at
Formula used:
Write expression for average velocity of the particle.
Write expression for instantaneous velocity of the particle.
........(5)
Write expression for average of instantaneous velocities for
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the average velocity for the given time interval is
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Chapter 2 Solutions
Physics for Scientists and Engineers
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