Decomposing a problem into parts, each amenable to solution using the S.I.M. approach.
Typical Decompositions
By Time or Position
A single body may undergo different interactions during different times or at different positions. For example, a car may travel at uniform velocity, then the driver may apply the brakes causing deceleration, then the car may collide with something, then come to a stop because the brakes are still applied. This example requires decomposition into four separate regions. There are three boundaries between the regions, and for each the position and velocity of the car are the same on each side of the boundary (but may change within each region due to the laws of motion or due to interactions specific to that region).
In general, the boundaries between to regions may be specified on the basis of position or time. For example, a road may be covered with ice for 20 m (e.g. over a bridge) but have bare pavement beyond that. Or the driver may continue at constant speed for a second and then apply the brakes (irrespective of how far the car traveled in that time).
Often the position and velocity are equal across the boundary, but sometimes one assumes that a quick event (such as a collision with a projectile) suddenly changed the velocity of the particle at a particular time or place.
Multiple Systems
If there are two bodies present it may be preferable to treat them separately, rather than one system. An example is a faster car that is overtaking a slower one. Until they collide, they will have different positions vs. time. Afterwards, they may have different positions vs. time, or they may stick together so they have the same position vs. time.