Concept explainers
(a)
To find: The magnitude of displacement in meters for the shaded box.
(a)
Answer to Problem 104P
The magnitude of displacement for the shaded region is
Explanation of Solution
Given:
The initial velocity on the box is
The final velocity on the box is
The time interval covered in one box is
Formula used:
The area of the velocity-time graph gives the displacement of the body.
Write the expression for the area of the shaded region.
Here,
Calculation:
Substitute
Conclusion:
Thus, the magnitude of displacement for the shaded region is
(b)
To find:The displacement between the two given time intervals of
(b)
Answer to Problem 104P
The displacement of the particle for the given
Explanation of Solution
Given:
The first
The second
Formula used:
The area of one block of the graph is
Write the expression for the displacement.
Here,
Calculation:
Substitute
Here,
Substitute
Here,
Conclusion:
Thus, the displacement of the particle for the given
(c)
To find:The average velocity of the particle for given time interval.
(c)
Answer to Problem 104P
The average velocity of the particle for the given time period is
Explanation of Solution
Given:
The distance covered in the first interval is
The distance covered in the second interval is
Formula used:
The area of one block of the graph is
The average velocity is defined as the total displacement in the given time period.
Write expression for total displacement of the particle.
…... (3)
Here,
Write the expression for the average velocity of the particle.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the average velocity of the particle for the given time period is
(d)
To explain: The average displacement of the particle for the given time period and compare it with the answer of part (b) and to compare the average velocity to the mean of initial and final velocity of the particle.
(d)
Answer to Problem 104P
The displacement of the particle for the interval
Explanation of Solution
Given:
The equation of curve is
The time interval is
Formula used:
Write the expression for the velocity of particle.
Rearrange the above expression for
Integrate the above expression from
Write an expression for the mean of initial and final velocity.
Calculation:
Substitute
Substitute
Conclusion:
Thus, the displacement of the particle for the interval
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Chapter 2 Solutions
Physics For Scientists And Engineers
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