postponement / deferment
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postponement
The moving of an action, appointment, or deadline to a later point in time; a delay.
Wir haben für die Abgabe der Projektarbeit einen Aufschub von einer Woche erhalten.
We received a postponement of one week for submitting the project paper.
'Der Aufschub' (postponement/deferment) is the noun related to the separable verb 'aufschieben' (to postpone). When you postpone a task, you ask for an 'Aufschub' (postponement).
Ich kann diese Entscheidung nicht länger aufschieben.
I cannot postpone this decision any longer.
Common verbs in this context are 'einen Aufschub beantragen' (to request a postponement), 'einen Aufschub bekommen' (to get a postponement), or 'jemandem einen Aufschub gewähren' (to grant someone a postponement). It is often about a postponement for a deadline, a payment, or a task.
Der Student hat für seine Hausarbeit einen Aufschub beantragt.
The student requested a postponement for his term paper.
The duration of the 'Aufschub' (postponement) is often expressed with the preposition 'von' and the dative.
Wir haben einen Aufschub von zwei Wochen bekommen.
We got a postponement of two weeks.
This meaning is mainly used in official and legal language. Typical contexts are court proceedings or administrative orders.
Der Verurteilte erhielt einen Aufschub des Strafantritts aus gesundheitlichen Gründen.
The convicted person received a deferment of the start of his sentence for health reasons.
extension / extra time
'die Verlängerung' and 'der Aufschub' can both mean that you get more time. 'Verlängerung' (extension) is used when an existing deadline or period of validity becomes longer, for example with a contract or a permit. 'Aufschub' (postponement) more often means that an action, appointment, or obligation is moved to a later time. The words can be confused because both can push the end further back. As a guide: 'Verlängerung' makes a period of time longer, while 'Aufschub' postpones something that was actually supposed to happen now.
Für die Abgabe hat Mehmet einen Aufschub bekommen, weil er krank war.
Mehmet received a postponement for the submission because he was ill.
Vor dem Termin fragt sie, ob eine Verlängerung der Frist möglich ist.
Before the appointment, she asks whether an extension of the deadline is possible.