Newton’s second law is `\Sigma \vec{F} = \frac{d\vec{P}}{dt}`.  It describes the relationship between the net force acting on a system and the rate of change of the systems momentum with respect to time. When thinking about how to use Newton’s second law with an object, at this level we will typically work one of two problems.  If the forces acting on the object are constant and the mass of the object doesn’t change during the interaction, we will rewrite Newton’s second law as `\Sigma \vec{F} = m\vec{a}` and work a vector addition problem.  The vector diagram we will use to help us is a fee-body diagram showing the individual forces as they act on the object.

On the other hand, we might have a problem where the forces acting on the object are complicated or not well understood.  In addition, the details of the objects motion during the interaction may also be difficult to ascertain, so that we really only have information about how the object was moving just before the interaction and how it was moving just after it.  In problems like these, it is in our interest to use the impulse-momentum theorem and focus on what the net force does on average during the interaction.  This means we want to work a vector subtraction problem and our vector diagram should show the initial and final momentum vectors of the object.