A 1.50-kg particle initially at rest and at the origin of an x–y coordinate system is subjected to a time-dependent force of
(a)
Find the time at which the particle’s speed will be
Answer to Problem 70PQ
The time at which the particle’s speed will be
Explanation of Solution
Write the equation for acceleration.
Here,
Substitute
To find the instantaneous velocity integrate the above equation.
In order to find the constant of integration consider the object is at rest and
Then,
Conclusion:
Substitute
The above equation can be factored as,
Then solution to the above equation to find t is,
Therefore, the time at which the particle’s speed will be
(b)
Find the distance at which the particle will travel with velocity
Answer to Problem 70PQ
The distance at which the particle will travel with velocity
Explanation of Solution
In order to find the position of the object the velocity equation should be integrated.
Conclusion:
Substitute
Therefore, the distance at which the particle will travel with velocity
(c)
Find the particle’s total displacement.
Answer to Problem 70PQ
The particle’s total displacement is
Explanation of Solution
Use the equation III to get the total displacement.
Conclusion:
Substitute
Therefore, the particle’s total displacement is
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Chapter 5 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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