deletions | additions       diff --git a/Now_we_need_to_show__.tex b/Now_we_need_to_show__.tex  index 7015036..bb048d0 100644  --- a/Now_we_need_to_show__.tex  +++ b/Now_we_need_to_show__.tex 
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Now Comparing (6) with (3),  we need to show only that $$ \vec{x}(t) - \vec{x}(t-\Delta t) = \vec{v}(t-\Delta t)\Delta t + \frac{1}{2} \vec{a}(t-\Delta t) \Delta t^2 $$  to prove that (6) (which is derived from (1), (2)) is equivalent to (3)  We can shift this equation $\Delta t$ forward in time:  $$ \vec{x}(t+\Delta t) - \vec{x}(t) = \vec{v}(t)\Delta t + \frac{1}{2} \vec{a}(t) \Delta t^2 $$