Let $S$ be an orientable surface with negative Euler characteristic. Can somebody provide a reference for the following well-known results:

the cyclic subgroup generated by a pseudo-Anosov element in the mapping class $MCG(S)$ is undistorted in the mapping class group.

the cyclic subgroup generated by a Dehn twist of the mapping class group is undistorted.

$\pi_1(S)$ is exponentially distorted in the mapping class group.

Thank you in advance.