deletions | additions       diff --git a/vec_a_t_vec_a__.tex b/vec_a_t_vec_a__.tex  index 28fa589..d55b360 100644  --- a/vec_a_t_vec_a__.tex  +++ b/vec_a_t_vec_a__.tex 
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$$(\vec a(t) + \vec a(t+\Delta t))\Delta t^2= \vec{v}(t+\Delta t) 2 \Delta t - \vec{v}(t) 2 \Delta t $$  $$\frac{1}{2}(\vec $$ \vec{v}(t+\Delta t) = \vec{v}(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)