\documentclass[12pt]{article}

\begin{document}

$$
  v(t+\frac{\Delta t}{2}) = v(t) + \frac{\Delta t}{2}\cdot a(t),
$$

$$
  r(t+\Delta t) = r(t) + \Delta t\cdot v(t+\frac{\Delta t}{2}),
$$

$$
  a(t+\Delta t) = \frac{1}{m}\cdot F\left[ r(t+\Delta t), v(t) +\lambda \cdot \Delta t\cdot a(t)\right],
$$

$$
  v(t+\Delta t) = v(t+\frac{\Delta t}{2}) + \frac{\Delta t}{2}\cdot a(t+\Delta t)
$$

\end{document}
