Concept explainers
(a)
The general position function
(a)
Answer to Problem 110P
The position function for the given condition is
Explanation of Solution
Given:
The acceleration of the rocket is given by
The initial condition is given as
Formula Used:
Write the expression for the acceleration of the rocket.
Here,
Substitute
Simplify the above expression.
Write expression for position of the rocket.
Substitute
Integrate the above expression.
Simplify the above expression.
Calculation:
Substitute
Initially, the velocity of the rocket is zero. Substitute
Substitute
Initially, position of rocket is
Express
Conclusion:
Thus, the position function for the given condition is
(b)
The position and velocity of the rocket for the given conditions.
(b)
Answer to Problem 110P
The position is
Explanation of Solution
Given:
The initial position or rocket is
The initial velocity of the rocket is
The time is
The value of
Formula Used:
Write the expression of position function
Calculation:
Substitute
Substitute
Conclusion:
Thus, the position is
(c)
The average velocity for the given conditions and compare it with instantaneous velocity.
(c)
Answer to Problem 110P
The average velocity for the given condition is
Explanation of Solution
Given:
The time period is
Concept used:
Write expression for average velocity of the rocket.
Write expression for instantaneous velocity of the rocket.
Calculation:
Substitute,
Substitute
Substitute
Conclusion:
Thus, the average velocity for the given condition is
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Chapter 2 Solutions
Physics for Scientists and Engineers
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