Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Problem Statement:**
Suppose the position of an object moving in a straight line is given by \( s(t) = t^2 + 6t + 5 \). Find the instantaneous velocity when \( t = 6 \).
**Solution:**
To find the instantaneous velocity, we need to take the derivative of the position function, \( s(t) \), with respect to time \( t \), giving us the velocity function \( v(t) \).
The position function is:
\[ s(t) = t^2 + 6t + 5 \]
The derivative, or velocity function, is:
\[ v(t) = \frac{d}{dt}(t^2 + 6t + 5) = 2t + 6 \]
Substituting \( t = 6 \) into the velocity function:
\[ v(6) = 2(6) + 6 = 12 + 6 = 18 \]
Therefore, the instantaneous velocity at \( t = 6 \) is \( 18 \) units per time interval.](https://content.bartleby.com/qna-images/question/56289daf-944e-4934-ac7e-546f2acb04ad/7ca29697-382a-4fc5-8e5c-186b9d7f9a30/mxwo137_processed.jpeg)
Transcribed Image Text:**Problem Statement:**
Suppose the position of an object moving in a straight line is given by \( s(t) = t^2 + 6t + 5 \). Find the instantaneous velocity when \( t = 6 \).
**Solution:**
To find the instantaneous velocity, we need to take the derivative of the position function, \( s(t) \), with respect to time \( t \), giving us the velocity function \( v(t) \).
The position function is:
\[ s(t) = t^2 + 6t + 5 \]
The derivative, or velocity function, is:
\[ v(t) = \frac{d}{dt}(t^2 + 6t + 5) = 2t + 6 \]
Substituting \( t = 6 \) into the velocity function:
\[ v(6) = 2(6) + 6 = 12 + 6 = 18 \]
Therefore, the instantaneous velocity at \( t = 6 \) is \( 18 \) units per time interval.
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