A clifd is riding a merry$-$go$-$round which is starts to spin up at t$(0)$ with angular acceleration $0\mathrm{.}05$ rad$/$s$?$ The child is standing $4\mathrm{.}65$ m from the center of the merry$-$go$-$round, After $5$ seconds,

a$)$ What is the angular speed of the child?

b$)$ What is the magnitude of the centripetal acceleration of the child?

c$)$ What is the magnitude of the tangential acceleration of the child?