Efter opvarmningen går jeg videre til motionscyklen, fordi mit knæ stadig er lidt ømt.

This is because Danish main clauses follow the V2 rule: the finite verb must come in the second position.

So when Efter opvarmningen is placed first, that takes the first slot, and the verb går must come next:

Efter opvarmningen går jeg videre ...

If you started with the subject instead, you would get:

Jeg går videre til motionscyklen efter opvarmningen.

Both are grammatical, but the word order changes because of the V2 rule.

Opvarmningen is the definite form and means the warm-up.

In this sentence, the speaker is referring to a specific warm-up that has just happened, so the definite form sounds natural:

Efter opvarmningen = after the warm-up

If you said efter opvarmning, it would sound more general, more like after warming up or after warm-up in general.

Not necessarily. Danish gå can mean go, proceed, or move on, not only walk.

Here, går videre is best understood as:

move on
continue on
go on to the next thing

So the sentence is not focusing on the physical act of walking. It is focusing on the next step in the workout.

Videre means further/on, and til means to.

Together, gå videre til means:

move on to
continue on to

So:

går jeg videre til motionscyklen
means something like
I move on to the exercise bike

It is a very natural way to describe the next stage in a sequence.

Because Danish usually writes compound nouns as one word.

So:

motion + cykel = motionscykel

This is very common in Danish. English often uses separate words where Danish uses compounds.

Examples: motionscykel = exercise bike
fodboldbane = football field
arbejdsdag = workday

In this sentence, motionscyklen is the definite singular form:

en motionscykel = an exercise bike
motionscyklen = the exercise bike

The definite form motionscyklen suggests a specific bike, or at least the bike that is relevant in the situation.

That is natural if the speaker means:

• the exercise bike at the gym they normally use
• the next machine in their routine
• the bike both speaker and listener can identify from context

If you said en motionscykel, it would mean an exercise bike, with less focus on a specific one.

Because knæ is a neuter noun in Danish.

For singular possessives:

• min is used with common-gender nouns
• mit is used with neuter nouns

So: min arm = my arm
mit knæ = my knee

This is something you simply have to learn together with the noun’s gender.

Because the adjective agrees with the noun.

Knæ is neuter, so the adjective takes -t in the singular neuter form:

et ømt knæ = a sore knee
mit knæ er ømt = my knee is sore

Compare: min arm er øm = my arm is sore
mit knæ er ømt = my knee is sore
mine ben er ømme = my legs are sore

So ømt matches the neuter noun knæ.

Stadig means still.

So:

mit knæ stadig er lidt ømt
means
my knee is still a little sore

Its position is connected to subordinate clause word order. In a clause introduced by fordi, words like stadig, ikke, ofte, and similar adverbs usually come before the finite verb:

fordi mit knæ stadig er lidt ømt

In a main clause, you would more naturally say:

Mit knæ er stadig lidt ømt.

Because fordi introduces a subordinate clause, and subordinate clauses follow different word order patterns from main clauses.

Main clause: Efter opvarmningen går jeg videre ...

Subordinate clause: fordi mit knæ stadig er lidt ømt

In standard Danish subordinate clauses, the order is typically:

subject + adverb + finite verb

So: mit knæ = subject
stadig = adverb
er = finite verb

That is why you get mit knæ stadig er rather than mit knæ er stadig in this clause.

Because fordi introduces a subordinate clause.

In Danish, many learners are taught to write a comma before subordinate clauses like this:

..., fordi mit knæ stadig er lidt ømt.

That said, modern Danish has two accepted comma systems, so you may also see sentences without this comma depending on the style being used. But the version with the comma is very common and perfectly correct.

Not in the same meaning.

Til motionscyklen is used because the speaker is moving toward the bike as the next activity.

På motionscyklen would describe being on the bike or exercising on it.

Compare: Jeg går videre til motionscyklen. = I move on to the exercise bike.
Jeg træner på motionscyklen. = I work out on the exercise bike.

So til is about direction or transition, while på is about location or activity.

Lidt means a little or slightly, so lidt ømt means:

a little sore
slightly sore

This makes the statement softer than just saying the knee hurts badly. It suggests mild discomfort rather than serious pain.

Also, øm often describes soreness or tenderness, especially after exercise or strain. It is not exactly the same as sharp pain.