deletions | additions       diff --git a/Subsituting_4_into_1_vec__.tex b/Subsituting_4_into_1_vec__.tex  index 8126c4b..74ae65b 100644  --- a/Subsituting_4_into_1_vec__.tex  +++ b/Subsituting_4_into_1_vec__.tex 
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$$\vec{x}(t + \Delta t) = \vec{x}(t) + (\vec{v}(t - \Delta t) + \frac{\vec{a}(t - \Delta t) + \vec{a}(t)}{2} \Delta t) \Delta t + \frac{1}{2} \vec{a}(t) \Delta t^2$$  $$\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t - \Delta t) \Delta t + \frac{\vec{a}(t \frac{1}{2}\vec{a}(t  - \Delta t)}{2} t)  \Delta t^2 + \vec{a}(t) \Delta t^2$$