A to B.
That's all.

A motion verb doesn't just involve movement. It describes going from one place to another. That destination is everything. When you pair a motion verb with a two-way preposition, the destination makes the case Akkusativ. No destination, no Akkusativ.

Also: This article builds directly on two-way prepositions. See Same preposition. The verb decides.

The test

One question separates a motion verb from every other verb: does the action go from A to B?

gehen goes from A to B. fahren goes from A to B. fliegen goes from A to B. These are motion verbs.

tanzen does not go from A to B. You move, but you stay in the same place. spielen is the same. Physical activity, no destination. Not a motion verb.

The verbs

Verb	Meaning	A to B?
gehen	to go (on foot)	yes
fahren	to drive / travel	yes
fliegen	to fly	yes
laufen	to run / walk	yes
rennen	to run (fast)	yes
kommen	to come	yes
reisen	to travel	yes
wandern	to hike	yes
tanzen	to dance	no
spielen	to play	no
arbeiten	to work	no
schlafen	to sleep	no

Note that schwimmen can go either way. Ich schwimme imSee means you're swimming around in the lake. No destination, Dativ. Ich schwimme indenSee means you're swimming into the lake from outside. Destination, Akkusativ. The verb doesn't decide. The context does.

Why tanzen is not a motion verb

When you dance, your body moves. When you play football, you run constantly. Neither is a motion verb. The reason: neither verb describes going somewhere. You dance in a place. You play on a pitch. The location stays the same from start to finish.

A motion verb changes your location. It starts somewhere and ends somewhere else. That's the only criterion that matters.

The bridge to two-way prepositions

Two-way prepositions like in, auf, and an can take either Dativ or Akkusativ. The verb decides which one. The shortcut question is Wo? (where?) or Wohin? (where to?).

A motion verb always answers Wohin. It has a destination. That triggers Akkusativ. A non-movement verb answers Wo. It describes a position. That triggers Dativ.

Example	Verb type	Question	Case
Ich gehe indenPark.	motion verb	Wohin?	Akkusativ
Ich tanze imPark.	no destination	Wo?	Dativ
Er fährt aufdieAutobahn.	motion verb	Wohin?	Akkusativ
Er spielt aufdemPlatz.	no destination	Wo?	Dativ
Wir fliegen überdenAtlantik.	motion verb	Wohin?	Akkusativ
Wir arbeiten überdemCafé.	no destination	Wo?	Dativ

The same preposition, two different sentences

Look at in and tanzen versus gehen again. The preposition doesn't change. The verb doesn't change the preposition. But the verb type changes the case of the noun that follows.

That's the full picture for two-way prepositions: the preposition alone tells you nothing. You need to know whether the verb has a destination.