Lupa käyttää tätä tietokonetta on voimassa vielä viikon.

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Questions & Answers about Lupa käyttää tätä tietokonetta on voimassa vielä viikon.

Why does the sentence start with Lupa? Is it the subject?

Yes. Lupa käyttää tätä tietokonetta is the full subject noun phrase: lupa (permission) + an infinitive clause describing what the permission is for (käyttää tätä tietokonetta = to use this computer).
Then the predicate is on voimassa (is valid/in force).

Why is it lupa käyttää and not something like lupa käyttämään?

After lupa (permission), Finnish commonly uses the A-infinitive (dictionary form) to express what you have permission to do: lupa tehdä (permission to do).
Käyttämään is the illative of the MA-infinitive and is used more with verbs of movement/aim or “go to do”, like mennä käyttämään (go to use), not as the most neutral “permission to”.

Why is tätä tietokonetta in the partitive case?

Because käyttää often takes a partitive object when the action is viewed as ongoing/indefinite rather than a single completed result. Permission to use something typically implies repeated or ongoing use, so tätä tietokonetta is natural.
A “total object” (like tämän tietokoneen) would more easily suggest a single, bounded action (or even “use it up”), which usually isn’t what you mean with general permission.

What’s the difference between tätä and tämän here?
  • tätä is partitive singular: it matches tietokonetta (also partitive). It fits the “ongoing/unspecified amount of using” idea.
  • tämän is genitive/accusative singular: it would typically go with a total object like tämän tietokoneen.

So tätä tietokonetta and tämän tietokoneen are a package: the demonstrative and the noun agree in case.

How does on voimassa work? Is voimassa an adjective?

Voimassa is not a normal adjective; it’s essentially an adverbial form meaning in force / valid.
The structure is a very common Finnish expression: olla voimassa = to be valid, to be in effect.
So Lupa … on voimassa literally reads like “The permission … is in force.”

Why is vielä placed before viikon?

Vielä means still / (for) another depending on context. Placing it before the time expression is typical: vielä viikon = still for a week / for another week.
You can also move vielä earlier for emphasis (e.g., on vielä voimassa viikon), but vielä viikon is a very common chunk.

Why is it viikon (genitive-looking form) and not viikkoa (partitive)?

With durations, Finnish often uses two patterns:

  • (vielä) viikon = for (another) a week (a bounded “one-week” period)
  • (vielä) viikkoa = for (another) week (often felt as “a week more” in an ongoing sense)

Both can be correct, but vielä viikon is very common when you mean the permission remains valid for one more full week as a unit.

Is viikon here genitive or accusative?

Formally it looks like genitive singular, but in many duration expressions it’s often described as an accusative-like total duration (sometimes called “accusative of measure” in descriptions).
Pragmatically: treat viikon as the normal “one-week duration” form you memorize.

Could you add ajan (time) like vielä viikon ajan? Would it change the meaning?

Yes: Lupa … on voimassa vielä viikon ajan is also correct and very clear.
ajan explicitly marks it as a time span (for the duration of a week). The meaning doesn’t really change; it just sounds slightly more explicit/formal.

Are there other natural ways to say the “permission to use” part?

Yes, a few common alternatives:

  • Lupa käyttää tätä tietokonetta (your sentence) = very natural and common
  • Lupa tämän tietokoneen käyttämiseen = literally “permission for the using of this computer” (more noun-like/official style)
  • Saat käyttää tätä tietokonetta = “You may/can use this computer” (changes the structure to a statement about what someone is allowed to do)