deletions | additions       diff --git a/Subsituting_vec_v_t_from__.tex b/Subsituting_vec_v_t_from__.tex  index 6e250a3..8126c4b 100644  --- a/Subsituting_vec_v_t_from__.tex  +++ b/Subsituting_vec_v_t_from__.tex 
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Subsituting $\vec{v}(t)$ from (2) (4)  into (1):$$\vec{v}(t) = \vec{v}(t - \Delta t) + \frac{\vec{a}(t - \Delta t) + \vec{a}(t)}{2} \Delta t$$  $$\vec{x}(t + \Delta t) = \vec{x}(t) + (\vec{v}(t - \Delta t) + \frac{\vec{a}(t - \Delta t) + \vec{a}(t)}{2} \Delta t) \Delta t + \frac{1}{2} \vec{a}(t) \Delta t^2$$