A.1.RI:5.1 - Associate two moving objects and retain an unresolved alternative
Consider two persistent point objects with independent motion on one axis; their paths may cross. Each object is observed once at each end of a one-second interval. Positions are assumed known in one common frame. Initially A is at 0 cm and B at 10 cm. Later R is at 1 cm and S at 9 cm.
The motion account limits speed to 2 cm/s. Construct the complete associations:
| Association | Required displacement magnitudes | Result under the speed bound |
|---|---|---|
| A to R; B to S | 1 cm each | Admissible; the two straight paths give a joint realization. |
| A to S; B to R | 9 cm each | Excluded; each exceeds the permitted displacement. |
Under these premises, R observes the continuing A and S the continuing B. A’s displacement is +1 cm and B’s is -1 cm.
Now allow speed up to 10 cm/s. Both associations have admissible straight paths. The observations leave A’s displacement as either +1 or +9 cm; choosing the shorter path adds a preference absent from the speed-bound premise.
Suppose the next question is instead the mean position of these two objects. It was 5 cm and is still 5 cm under both associations. That calculation can proceed without another observation. If a following action must address A individually, look for a discriminator that matters to that action or use an explicitly permitted provisional association.
If the motion premise changes again to a bound below 1 cm/s, neither complete association fits. Reconsider the bound or the observation account before asserting an identification.