Final answer:
Prolonged eye movement after spinning is due to the vestibulo-ocular reflex, which stabilizes vision during rapid head movements and can cause a sensation of vertigo.
Step-by-step explanation:
The prolonged eye movement observed in a child after being spun around 10 times describes a response involving the vestibulo-ocular reflex. This reflex helps to stabilize vision during head movement by producing eye movements in the opposite direction of head movement, thus maintaining the gaze on a stationary object.
When a person is spun around, the fluid in the inner ear continues to move for a short period after the spinning has stopped, which leads to the sensation of still spinning (vertigo) and causes the eyes to continue moving (nystagmus).