What acceleration does a person sitting 2.5m from the center of the merry-go-round undergo?

There is no acceleration if an object is at rest. However he or she maybe sitting in a vehicle traveling at constant velocity such as 5 m/s or 10 m/s. There is an acceleration if your talking about its relative motion to the earth and the earth speed is 30 km/s around the sun if that were you talking about. Hope this helps

2. they have negligible mass.