# Math Help - Arclength parameterisation

1. ## Arclength parameterisation

Let $\underline{r} (s):=(f(s),g(s))$ be the arclength parameterisation of a plane curve $\Gamma \subset \mathbb{R}^2$.

Given $\alpha, \beta \in \mathbb{R}$ such that $\alpha^2+\beta^2=1$, let $\underline{R}(s):=(f(\alpha s), g(\alpha s), \beta s)$ be a parameterisation of a space curve $C \subset \mathbb{R}^3$.
a). Show that $\underline{R}$ is the arclength parameterisation of C.
I'm not really sure how to show this. Firstly, in my book it has $\int_0^t v( \tau)~dt$ which I can't see how i'm supposed to apply.

Does anyone have any pointers?