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(Solved): EXAMPLE 6 A particle moves in a straight line and has acceleration given by a(t) = 12t+4. Its initia ...
EXAMPLE 6 A particle moves in a straight line and has acceleration given by a(t) = 12t+4. Its initial velocity is v(0) = -4 cm/s and its initial displacement is s(0) = 8 cm. Find its position function, s(t). SOLUTION Since v'(t) = a(t) = 12t+4, antidifferentiation gives v(t) = Note that v(0) = C. But we are given that v(0) = -4, so C = v(t) = Since v(t) = s'(t), s is the antiderivative of v: |) + 4( [ s(t) = = + 4t + C = ( s(t) = + D. This gives s(0) = D. We are given that s(0) = 8, so D = is + C. - 4t+ D and and the required position function
EXAMPLE 6 A particle moves in a straight line and has acceleration given by a(t)=12t+4. Its initial velocity is v(0)=?4cm/s and its initial displacement is s(0)=8cm. Find its position function, s(t). SOLUTION Since v?(t)=a(t)=12t+4, antidifferentiation gives v(t)=+4t+c=+C. Note that v(0)=C. But we are given that v(0)=?4, so C= and v(t)= Since v(t)=s?(t), s is the antiderivative of v : s(t)?=6()+4()?4t+D=+D.? This gives s(0)=D. We are given that s(0)=8, so D= and the required position function is s(t)=