SOLUTION: Determine the position function if the acceleration function is a(t) = t^2+1, the initial velocity is v(0) = 4 and the initial position is s(0) = 0 .

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Question 1103834: Determine the position function if the acceleration function is a(t) = t^2+1, the initial velocity is v(0) = 4 and the initial position is s(0) = 0 .
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Integrate to get the velocity,
v%28t%29=t%5E3%2F3%2Bt%2BC%5B1%5D
Integrate again to get the position,
s%28t%29=t%5E4%2F12%2Bt%5E2%2F2%2BC%5B1%5D%2At%2BC%5B2%5D
Solving for C%5B1%5D,
0%5E3%2F3%2B0%2BC%5B1%5D=4
C%5B1%5D=4
Solving for C%5B2%5D,
0%5E4%2F12%2B0%5E2%2F2%2B4%280%29%2BC%5B2%5D=0
C%5B2%5D=0
.
.
highlight%28s%28t%29=t%5E4%2F12%2Bt%5E2%2F2%2B4t%29