Help with odd partial derivatives in velocity $\bar v^2 = \dot x ^2+\dot y^2$ I am doing a physics -course Tfy-0.2061. My teacher claims that this is velocity squared, $\bar v^2 = \dot x ^2+\dot y^2$. I cannot understand why it is not $\bar v^2 = (\dot x +\dot y)^2$. 
If distance is $\bar d = \bar x + \bar y$. Then velocity is $\partial_t \bar d = \dot x + \dot y$. Now just square it to get 
$$\bar v^2 = \dot x^2 +2\dot x\dot y +\dot y^2 \not = \dot x^2 +\dot y^2.$$
What does my teacher mean by velocity $\bar v^2 = \dot x ^2+\dot y^2$?
P.s. the goal was to do something called "nopeuden radiaalinen komponentti" that probably means radial component of velocity. I don't just understand what it means, some angular velocity? I am doing the exercise 3b here, sorry not in English.
Trial 1

The only way that my teacher can be correct is if $y_0=0$ and $x_0=0$ because



This is shorthand for
$$|v|^2=v\cdot v=\dot{x}^2+\dot{y}^2,$$
i.e. a statement about the length of the velocity vector whose components are $(\dot{x},\dot{y})$.
