Expected squared distance after 16 random unit steps

A remote-control skateboard starts at the origin of the plane. Every second it chooses a direction uniformly at random from $[0,2\pi)$, independently of the past, and travels $1$ foot that way. After $16$ seconds, find the mean of the square of its distance from where it started.

$16$. Write the position as a sum of $16$ independent unit vectors with mean zero. The squared length expands into $16$ terms equal to $1$ plus cross terms $\mathbf u_i\cdot\mathbf u_j$ with zero mean, so $E[D^2]=16$.