Linear motion problem

Question

A kid is standing on a

merry-go-round 0.825 m from

the center. Starting from rest,

they reach 1.08 rad/s in 3.47 s.

What was his linear acceleration?

Can someone answer this throughly ?

Answer 1

His linear acceleration equals his radial acceleration times his distance from the center (which is the radius of the merry-go-round). Since he reaches 1.08 rad/s from rest in 3.47 s, his radial acceleration is (1.08 rad/s)/(3.47 s) = 0.311 rad/s². Hence, his linear acceleration is (0.825 m)(0.311 rad/s²) = 0.257 m/s².