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13 Nov 2019
My Notes Ask Your Teacher EXAMPLE 6 A particle moves in a straight line and has acceleration given by a(t) = 18t + 10, Its initial velocity is v(0) =-6 cm/s and its initial displacement is s(0) = 7 cm. Find its position function, s(t). SOLUTION Since v'(t) = a(t)-18t + 10, antidifferentiation gives v(t) = +10t + C = Note that v(0)= C. But we are given that v(0)=-6, so C= v(t) = Since v(t) = s'(t), s is the antiderivative of v: to- s(t) = 9 + 10 6t +D + D This gives s(0) = D, we are given that s(0)= 7, so D = and the required position function is s(t) =
My Notes Ask Your Teacher EXAMPLE 6 A particle moves in a straight line and has acceleration given by a(t) = 18t + 10, Its initial velocity is v(0) =-6 cm/s and its initial displacement is s(0) = 7 cm. Find its position function, s(t). SOLUTION Since v'(t) = a(t)-18t + 10, antidifferentiation gives v(t) = +10t + C = Note that v(0)= C. But we are given that v(0)=-6, so C= v(t) = Since v(t) = s'(t), s is the antiderivative of v: to- s(t) = 9 + 10 6t +D + D This gives s(0) = D, we are given that s(0)= 7, so D = and the required position function is s(t) =
Nestor RutherfordLv2
4 Feb 2019