Is it mandatory to maintain a minimum distance of at least 100 metres from the vehicle in front on a road marked in this manner?

In the picture, the blue rectangular sign with a symbol of two roadways and a flyover is D-9 "motorway". On a road marked in this way, a minimum distance of at least 100 m from the vehicle in front is not required. The answer is: no.

The Regulation on road signs and signals states that sign D-9 marks the beginning or continuation of a motorway. The Road Traffic Act requires a driver travelling on a motorway or an expressway to keep a minimum distance from the vehicle in front of them in the same lane, which in metres must be no less than half the number showing the speed in km/h; this rule does not apply when overtaking. So there is no single value of "100 m": when driving at 140 km/h, you must keep at least 70 m, at 100 km/h - 50 m, at 80 km/h - 40 m. A hundred metres would correspond to a speed of 200 km/h, which you are not allowed to reach on Polish motorways. The rule was introduced because too short a distance is one of the main causes of multiple pile-ups on motorways - at 140 km/h, one second of reaction time means almost 40 m. The distance required by the Act is the minimum on a dry road; on a wet road you double it.

Legal basis: Art. 19 para. 3a of the Road Traffic Act (Prawo o ruchu drogowym); § 48 para. 2 of the Regulation on road signs and signals