The PSNI say officers spotted a red Renault car travelling at speed along the Springfield Road shortly before 9.30 pm on Friday and signalled for it to stop.
They said the car failed to stop and police followed it through the Cluain Mor Estate.
It was later found on Beechmount Parade.
A 35-year-old man appeared in Belfast Magistrates’ Court on Saturday charged with dangerous driving, driving while disqualified and failing to stop for police.
He was remanded in custody after a judge refused to grant him bail.
A 33-year-old man has been charged with disorderly behaviour and obstructing police.
He is expected to appear before Belfast Magistrates’ Court on 16 September. Police said he has also been returned to prison after his licence was revoked.
A 16-year-old girl has been charged with assault on police and resisting police.
She is expected to appear before Belfast Youth Court on 14 September.
All charges will be reviewed by the PPS.