
ungebremst
unbraked
Without braking; at full speed and without reducing speed.
Das Auto fuhr ungebremst in die Mauer.
The car drove into the wall without braking.
unbraked / unchecked
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unbraked
Without braking; at full speed and without reducing speed.
Das Auto fuhr ungebremst in die Mauer.
The car drove into the wall without braking.

unchecked
In a figurative sense: without inhibition, restriction, or control; unhindered.
Die Digitalisierung setzt ihren ungebremsten Vormarsch fort.
Digitalization continues its unchecked advance.
The word is the past participle of 'bremsen' (to brake) with the negative prefix 'un-'. So it literally means 'nicht gebremst' (not braked) and describes an action without a reduction in speed.
Der Radfahrer stürzte ungebremst vom Weg ab.
The cyclist went off the path without braking.
'Ungebremst' is very often used like an adverb to describe a verb of motion. In this case, it is not declined and usually appears at the end of the sentence or before a prepositional complement.
Der LKW raste ungebremst über die rote Ampel.
The truck raced through the red light without braking.
The literal meaning refers to vehicles and physical movement. You can recognize the figurative meaning from abstract nouns such as 'Wachstum' (growth), 'Konsum' (consumption), 'Fortschritt' (progress), or 'Ehrgeiz' (ambition).
Der ungebremste Konsum von Ressourcen schadet der Umwelt.
The unchecked consumption of resources harms the environment.
In the figurative meaning, 'ungebremst' (unchecked) is often combined with developments or processes. Common phrases are 'ungebremstes Wachstum' (unchecked growth), 'ungebremster Fortschritt' (unchecked progress), or 'ungebremste Kauflust' (unrestrained desire to shop).
Sein ungebremster Ehrgeiz machte ihn bei den Kollegen nicht beliebt.
His unchecked ambition made him unpopular with his colleagues.
uncontrolled
When describing a development, unkontrolliert and ungebremst can both express a lack of limitation. Unkontrolliert emphasizes that it is not being directed or controlled, while ungebremst mainly highlights its continuing unabated without slowing down. Choose unkontrolliert when there is no control, and ungebremst when there is no damping or slowing effect.

Trotz der neuen Maßnahmen stiegen die Preise auf dem Markt ungebremst weiter.
Despite the new measures, prices on the market continued to rise unchecked.
Ohne klare Regeln stiegen die Preise auf dem Markt unkontrolliert weiter.
Without clear rules, prices on the market continued to rise uncontrollably.