## Calculus: Early Transcendentals 8th Edition

$s(t) = -3cost + 2sint + 2t + 3$
Given: $a(t)=3cos t-2sin t$ Thus we have: $v(t) = 3sint - 2(-cost)+C$ $v(t) = 3sint + 2cost + C$ $v(0) = 3sin(0) + 2cos(0) + C$ $v(0) = 3(0) + 2(1) + C$ Given: $v(0) = 4$ $4 = 2+ C$ $2 = C$ Plug in the value of $C$ in the function of $v(t)$. $v(t) = 3sint + 2cost + 2$ $s(t) = 3(-cost) + 2sint + 2t + C$ $s(t) = -3cost + 2sint + 2t + C$ $s(0) = -3cos(0) + 2sin(0) + 2(0) + C$ $s(0) = -3(1) + 2(0) + 2(0) + C$ $s(0) = -3 + C$ Given $s(0) = 0$ $0 = -3 + C$ $C = 3$ Plug in the value of $C$: $s(t) = -3cost + 2sint + 2t + 3$