Position Update Formula

The position update formula simply states that given the initial position ($\vec{r}_i$) of an object, we can predict the final position ($\vec{r}_f$) using the average velocity ($\vec{v}_{avg}$) and change in time ($\Delta t$).

$$\Delta \vec{r} = \vec{v}_{avg} \Delta t$$
$$\vec{r}_f - \vec{r}_i = \vec{v}_{avg}(t_f - t_i)$$

Or just simply

$$\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t$$