deletions | additions       diff --git a/vec_x_t_Delta_t__1.tex b/vec_x_t_Delta_t__1.tex  index f65afcf..3bb9a46 100644  --- a/vec_x_t_Delta_t__1.tex  +++ b/vec_x_t_Delta_t__1.tex 
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$$\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t) \Delta t + \frac{1}{2} \vec{a}(t) \Delta t^2$$  $$\vec{x}(t) = \vec{x}(t - \Delta t) $$\vec{x}(t  +\vec{v}(t-  \Delta t) - \vec{x}(t) = \vec{v}(t)  \Delta t + \frac{1}{2} \vec{a}(t- \Delta t) \vec{a}(t)  \Delta t^2$$