The displacement of an object over a time interval is defined to be the change in position between the beginning and end of the interval.  Displacement is a vector from the object's starting point to its ending point. It doesn't matter what path the object took, only the starting and ending points matter.

If  you know that an object has made a successive series of displacements during the parts of a larger time interval, then the net or resultant displacement during the whole interval will be the vector sum of all the individual displacements made during that interval.   This is a vector relationship. However, because Andes accepts only scalar equations, you will be applying the principle component-wise to each of the components of the net displacement vector:

If an object has made a series of displacements d01 from T0 to T1, d12 from T1 to T2, d23 from T2 to T3 and so on, then the components of the net displacement dnet will be given by