Concept explainers
A time-dependent force,
(a)
The time for which the object moves with a speed of
Answer to Problem 5.96CP
The time taken by the object is
Explanation of Solution
Given info: The time-dependent force vector is
From the Newton’s law of motion, the force on the object is,
Here,
Rearrange the above formula.
Substitute
The expression for the acceleration is,
Substitute
The expression for the velocity vector is,
Here,
Compare the above equation with equation (1), the
The magnitude of the velocity vector is,
Substitute
Substitute
Further solve the above equation.
In the above fraction of equation, second factor give the negative value of time and time cannot be negative so the value of time from first factor is,
Conclusion:
Therefore, the time taken by the object is
(b)
The position of an object from its initial position.
Answer to Problem 5.96CP
The position of an object from its initial position is
Explanation of Solution
From part (a), the expression for the velocity of the object is,
The expression for the velocity of the object is,
Here,
Substitute
The expression for the position vector from its initial position is,
Here,
Compare the above equation with equation (1), the
The magnitude of the velocity vector is,
Substitute
From part (a), the time taken by the object is,
Substitute
Conclusion:
Therefore, the position of an object from its initial position is
(c)
The total displacement of the object.
Answer to Problem 5.96CP
The total displacement of the object is
Explanation of Solution
From part (b), the position vector of the object is,
From part (a), the time taken by the object is,
Substitute
Conclusion:
Therefore, the total displacement of the object is
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Chapter 5 Solutions
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