
(a)
The velocity of the mass with respect to time.
(a)

Answer to Problem 2.14P
The velocity of the mass with respect to time is
Explanation of Solution
Given, the force on the mass
Write the expression for
Substituting
Taking log on both sides
Conclusion:
Thus, the velocity of the mass with respect to time is
(b)
The time that takes to for the mass to come instantaneously to rest.
(b)

Answer to Problem 2.14P
The time that takes to for the mass to come instantaneously to rest is
Explanation of Solution
From part (a), the velocity of the mass with respect to time is
Therefore,
Conclusion:
Thus, the time that takes to for the mass to come instantaneously to rest is
(c)
The distance the mass travels before coming instantaneously to rest.
(c)

Answer to Problem 2.14P
The distance the mass travels before coming instantaneously to rest is
Explanation of Solution
From part (a), the velocity of the mass with respect to time is
Therefore, integrating the velocity will gives displacement of the mass.
For integration, consider
Solving the integration part in the above equation,
Let
The integration part becomes,
Substitute the above equation in equation (II)
Substitute the value of
Substitute the above integral in equation (I) and solving
From part (b), the time that takes to for the mass to come instantaneously to rest is
Therefore,
Conclusion:
Thus, the distance the mass travels before coming instantaneously to rest is
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Chapter 2 Solutions
Classical Mechanics
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