deletions | additions       diff --git a/vec_a_t_vec_a__.tex b/vec_a_t_vec_a__.tex  index 4cdaf43..28fa589 100644  --- a/vec_a_t_vec_a__.tex  +++ b/vec_a_t_vec_a__.tex 
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$$(\vec a(t) + \vec a(t+\Delta t))\Delta t^2= \vec x(t-\Delta t) - \vec x(t) + \vec{x}(t+2 \Delta t) - \vec x(t+\Delta t) $$ $$(\vec a(t) + \vec a(t+\Delta t))\Delta t^2= \vec{v}(t+\Delta t) 2 \Delta t - \vec{v}(t) 2 \Delta t $$  $$\frac{1}{2}(\vec a(t) + \vec a(t+\Delta t))\Delta t + \vec{v}(t) 2 \Delta t = \vec{v}(t+\Delta t) 2 \Delta t $$  Which is \textit{exactly} (2)