%% formulation
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\begin{document}
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\begin{align*}
\min_{u(t),x(t),v(t),t_f} \quad & t_f \\
\text{subject to:} \quad & \begin{bmatrix}
\dot{x} \\ \dot{v}
\end{bmatrix} = \begin{bmatrix}
v \\
0.001 u - 0.0025 \cos(3x) \\
\end{bmatrix} \\
& (x,v)(0) = (-0.5,0) \\
& x(t_f) = 0.5 \\
& |u(t)| \leq 1 \\
& v(t_f) \geq 0
\end{align*}
}}
\end{document}

%% solution