Momentum Update Formula

The Momentum Update Formula is simply a rearrangement of the Momentum Principle:$$\Delta\vec{p} = \vec{p}_f - \vec{p}_i = \vec{F}_{net}\Delta t$$$$\vec{p}_f = \vec{p}_i + \vec{F}_{net} \Delta t$$If you know the initial momentum ($\vec{p}_i$) of an object and the net force ($\vec{F}_{net}$) over a period of time ($\Delta t$) short enough to make it approximately constant, you can predict the final momentum ($\vec{p}_f$).

Impulse

Impulse is the product of the force ($\vec{F}$) and change in time ($\Delta t$).  $$Impulse = \vec{F}\Delta t$$The impulse differs from the Momentum Principle in that it is distinct in forces.  The change in momentum ($\Delta\vec{p}$) is equal to the sum of the impulses applied, or:  $$\Delta\vec{p} = \sum\limits_{i=1}^n \vec{F}_i\Delta t$$