Difference between revisions of "009A Sample Midterm 1, Problem 5"

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Line 35: Line 35:
 
& = & \displaystyle{0-\frac{1}{4}(-1)}\\
 
& = & \displaystyle{0-\frac{1}{4}(-1)}\\
 
&&\\
 
&&\\
&= & \displaystyle{\frac{1}{4} \text{ foot}.}
+
&= & \displaystyle{\frac{1}{4} \text{ ft}.}
 
\end{array}</math>
 
\end{array}</math>
 
|}
 
|}
Line 61: Line 61:
 
& = & \displaystyle{-4(-1)+0}\\
 
& = & \displaystyle{-4(-1)+0}\\
 
&&\\
 
&&\\
& = & \displaystyle{4 \text{ feet/second}.}
+
& = & \displaystyle{4 \text{ ft/sec}.}
 
\end{array}</math>
 
\end{array}</math>
 
|}
 
|}
Line 69: Line 69:
 
!Final Answer: &nbsp;  
 
!Final Answer: &nbsp;  
 
|-
 
|-
|&nbsp; &nbsp; &nbsp; &nbsp; position is &nbsp;<math>\frac{1}{4} \text{ foot}.</math>
+
|&nbsp; &nbsp; &nbsp; &nbsp; position is &nbsp;<math>\frac{1}{4} \text{ ft}.</math>
 
|-
 
|-
|&nbsp; &nbsp; &nbsp; &nbsp; velocity is &nbsp;<math>4 \text{ feet/second}.</math>
+
|&nbsp; &nbsp; &nbsp; &nbsp; velocity is &nbsp;<math>4 \text{ ft/sec}.</math>
 
|}
 
|}
 
[[009A_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]

Revision as of 19:27, 13 April 2017

The displacement from equilibrium of an object in harmonic motion on the end of a spring is:

where    is measured in feet and    is the time in seconds.

Determine the position and velocity of the object when  


Foundations:  
What is the relationship between the position    and the velocity    of an object?
       


Solution:

Step 1:  
To find the position of the object at  
we need to plug    into the equation  
Thus, we have
       
Step 2:  
Now, to find the velocity function, we need to take the derivative of the position function.
Thus, we have
       
Therefore, the velocity of the object at time    is
       


Final Answer:  
        position is  
        velocity is  

Return to Sample Exam