Let $\displaystyle Y$ be a vector field on a curve $\displaystyle \alpha$. If $\displaystyle \alpha (h)$ is a reparametrization of $\displaystyle \alpha$, show that the reparametrization $\displaystyle Y(h)$ is a vector field on $\displaystyle \alpha (h)$.

I'm a bit stuck and would appreciate some help.