As a child, the Nobel Prize-winning physicist Richard Feynman asked his father why a ball in his toy wagon moved backward whenever he pulled the wagon forward. His father said that the answer lay in the tendency of moving things to keep moving, and of stationary things to stay put. "This tendency is called inertia," said Feynman senior. Then, with uncommon wisdom, he added: "But nobody knows why it is true."
Accelerating forward pushes the ball backward.
Accelerating backward pushes the ball forward.
Decelerating pushes the ball forward.
Curving pushes the ball sideways to opposite direction of turning.
The word ball can be replaced with the word body.
Pushing forward with the supporting foot accelerates the mass of the body and a force tends your body to bend backward, because of inertia. Body flight can be demonstrated in slow motion by asking somebody to push you against your chest while you are taking first forward step. The pushing will hold your moving foot not to fall on the floor. On walking the push of the supporting feet accelerates your body and the mysterious inertia takes care to push against your chest and other accelerating parts of the body to let your body to flight.
Deceleration is decreasing of velocity, ex. by braking. When the pushing of the supporting foot ends and the moving foot hits the floor, decelerates the mass of the body causing by inertia a forward force witch pushes the body on the new supporting foot.
When turning the body tends to fall to the opposite direction and must be balanced by the sway, like a cyclist does while curving.
Momentum is mass x velocity. Momentum must be increased by impulse to keep moving continuously. Impulse is force x time. Impulse accelerates the velocity. It should be interesting to discuss at what moment of the step and time of the beat the impulse takes place. I think during the beat one if the step takes two beats, in some dances.