deletions | additions       diff --git a/Delta_Subsituting_vec_v_t__.tex b/Delta_Subsituting_vec_v_t__.tex  index 4185fe8..6e250a3 100644  --- a/Delta_Subsituting_vec_v_t__.tex  +++ b/Delta_Subsituting_vec_v_t__.tex 
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$\Delta$:  Subsituting $\vec{v}(t)$ from (2) into (1):  $$\vec{v}(t) = \vec{v}(t - \Delta t) + \frac{\vec{a}(t - \Delta t) + \vec{a}(t)}{2} \Delta t$$