
rasant
fast
Very fast, happening at high speed or within a short time.
Das Auto beschleunigte mit rasanter Geschwindigkeit.
The car accelerated at a fast speed.
rapid / fast
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fast
Very fast, happening at high speed or within a short time.
Das Auto beschleunigte mit rasanter Geschwindigkeit.
The car accelerated at a fast speed.

rapid
Happening in an impressive, dynamic, or exciting way. Often refers to a development or change.
Die Technologie hat in den letzten Jahren eine rasante Entwicklung durchgemacht.
Technology has undergone rapid development in recent years.
'Rasant' (rapid/fast) is an expressive word that is often used in the press, advertising, or sports commentary to describe speed or change in a dynamic and impressive way.
Die Zeitung berichtete über den rasanten Aufstieg des jungen Politikers.
The newspaper reported on the young politician's rapid rise.
The meaning depends on the context. In connection with movement ('Fahrt' — ride/drive, 'Tempo' — pace/speed), 'rasant' means very fast. In connection with abstract nouns ('Entwicklung' — development, 'Wandel' — change), it means dynamic and impressive.
Der Skifahrer legte eine rasante Abfahrt hin.
The skier made a fast descent.
When it is about speed, 'rasant' is often combined with nouns such as 'Fahrt' (ride/drive), 'Tempo' (pace/speed), or 'Geschwindigkeit' (speed). It can also be used as an adverb, e.g. 'rasant zunehmen' (to increase rapidly).
Die Zahl der Anmeldungen ist rasant gestiegen.
The number of registrations has risen rapidly.
To describe a dynamic change, 'rasant' is frequently used with nouns such as 'Entwicklung' (development), 'Anstieg' (increase), 'Wachstum' (growth), or 'Wandel' (change).
Das Unternehmen erlebte ein rasantes Wachstum.
The company experienced rapid growth.
fast / quick
Schnell generally describes a high speed or a short duration. Rasant describes an especially high speed and can additionally portray a development as dynamic or impressive. Schnell is enough for an ordinary fast change; for an exceptional pace, rasant is more suitable.

Die Besucherzahl stieg nach der landesweiten Werbung rasant an und verdreifachte sich in zwei Tagen.
The number of visitors rose rapidly after the nationwide advertising campaign and tripled in two days.
Die Besucherzahl stieg nach der Werbung schnell an.
The number of visitors rose quickly after the advertising campaign.