EXAMPLE 6 A particle moves in a straight line and has acceleration given by a(t) = 5: + 5. Its initial velocity is v(0) = 4 chs and its initial displacement is 5(0) = 8 cm. Find its position function, 5(t). SOLUTION Since v'(t) = a(t) = 5t + 5, antidifferentiation gives v(t)= +5t+C= +C. Note that v(0) = C. But we are given that v(0) = -4, so C = \\:l and v(t) = Since v(t) = 5'(t), 5 is the an:iderivative of v: 5m =3ll:l )+5(l:l )_4HD = +0. This gives 5(0) = D. We are given that 5(0) = 8, so D = \\:l and the required position function is Slit) =