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 ($\vec{p}_f$).

Momentum Principle

The Momentum Principle is Newton's Second Law - a fundamental principle of physics.  It is used to predict the behavior of objects, restating Newton's First Law in a form that is measurable and causal.  $$\Delta\vec{p} = \vec{F}_{net}\Delta t$$This equation simply states that:  The change in momentum ($\Delta\vec{p}$) is equal to the net force ($\vec{F}_{net}$) times the elapsed time ($\Delta t$).

This is only effective if the net force is nearly constant.  So, either the net force must be constant, or the measurement used in increments of time that are small enough to model nearly constant force.

For instance, if we had a net force that changed at $t=3$ and $t=7$, respectively, we could make the measurement from $t=0$, $\Delta\vec{p} = \vec{F}_{net}\times3$, and then again from $t=3$ as $\Delta\vec{p} = \vec{F}_{net}\times4$ to conclude at $t=7$.