SOLUTION: Please help me solve my homework question: A particle moves in a straight line and has a acceleration given by a(t)=7t + 8. Its initial velocity is V(0)= 9 cm/s and its displace

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Question 877658: Please help me solve my homework question:
A particle moves in a straight line and has a acceleration given by a(t)=7t + 8. Its initial velocity is V(0)= 9 cm/s and its displacement is s(0)=10 cm. Find its position function s(t).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Acceleration is the second derivative of position and the first derivative of velocity.
Integrate with respect to time.
V%28t%29=int%28a%28t%29%2Cdt%29=int%28%287t%2B8%29%2Cdt%29
V%28t%29=%287%2F2%29t%5E2%2B8t%2BC
Using the intial condition,
V%280%29=%287%2F2%29%280%29%5E2%2B8%280%29%2BC=9
C=9
V%28t%29=%287%2F2%29t%5E2%2B8t%2B9
Integrating again with respect to t.
S%28t%29=%287%2F6%29t%5E3%2B4t%5E2%2B9t%2BC
Again use the initial condition to solve for C.
S%280%29=%287%2F6%29%280%29%5E3%2B4%280%29%5E2%2B9%280%29%2BC=10
C=10
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S%28t%29=%287%2F6%29t%5E3%2B4t%5E2%2B9t%2B10