Ответ: S(3)=112 м.

Объяснение:

[tex]\displaystyle\\a(t)=12t^2+4\\\\v(t)=\int(12t^2+4)dt=\frac{12t^3}{3} +4t+C=4t^3+4t+C.\\\\v(1)=4*1^3+4*1+C=10\\\\4+4+C=10\\\\C=2.\ \ \ \ \ \ \Rightarrow\\\\v(t)=4t^3+4t+2.\\\\S(t)=\int(4t^3+4t+2)dt=\frac{4t^4}{4}+\frac{4t^2}{2}+2t+C=t^4+2t^2+2t+C\\\\ S(1)=1^4+2*1^2+2*1+C=12\\\\1+2+2+C=12\\\\C=7.\ \ \ \ \ \ \Rightarrow\\\\S(t)=t^4+2t^2+2t+7.\\\\S(3)=3^4+2*3^2+2*3+7=81+18+6+7=112.[/tex]