Property of for same acceleration

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Does the property that two bodies connected together and if one of them is accelerating with some acceleration the second also accelerates with the same acceleration, have a name? Like for example, if there is a person in an elevator and the elevator is accelerating with acceleration ##a##, then the person also accelerates with acceleration ##a##. Is there a name for this property? Or is not a property because it is so logical that it is said so because it makes sense?
 
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Dr. Courtney said:
When to masses are connected with a rope or string, the condition is that the rope or string not stretch.

More generally, there needs to be a fixed distance and orientation between the two objects the for their acceleration to be the same.
What about the case for a person inside an accelerating elevator?