EXAMPLE 6 A particle moves in a straight line and has acceleration given by a(t) = 12t + 10. Its initial velocity is v(0) = -6 cm/s and its initial displacement is s(0) = 8 cm. Find its position function, s(t) = 12t 10, antidifferentiation gives Since v'(t) a(t) SOLUTION 6t2+10t v(t) +C 12 2 10t C = Note that v(0) = C. But we are given that v(0) = -6, so C = -6 and 6t210t-6 v(t) = s'(t), s is the antiderivative of v: Since v(t) 6t D +10 s(t) 6 2 2p3 D. This gives s(0) and the required position = D. We are given that s(0) = 8, so D = function is s(t) =

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