deletions | additions       diff --git a/Let_s_reformulate_1_and__.tex b/Let_s_reformulate_1_and__.tex  index a4fda0b..29a4deb 100644  --- a/Let_s_reformulate_1_and__.tex  +++ b/Let_s_reformulate_1_and__.tex 
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Let's reformulate (1) and (2) for $t = t' t  - \Delta t$ $$\vec{v}(t') $$\vec{v}(t)  = \vec{v}(t' \vec{v}(t  - \Delta t) + \frac{\vec{a}(t' \frac{\vec{a}(t  - \Delta t) + \vec{a}(t')}{2} \vec{a}(t)}{2}  \Delta t$$ $$\vec{x}(t') $$\vec{x}(t)  = \vec{x}(t' \vec{x}(t  - \Delta t) + \vec{v}(t' \vec{v}(t  - \Delta t) \Delta t + \frac{1}{2} \vec{a}(t' \vec{a}(t  - \Delta t) \Delta t^2$$