Our teacher suggested that Newtonian Mechanics only applies in cartesian coordinates. Is this true?

He gave this example.

Suppose there a train moving with constant velocity $\vec{v}=v_0\hat{x}$, with initial position vector $\vec{r}=(0, y_0)$, where $v_0,y_0$ are constants. He argued that Newton's second law would not hold in polar coordinates. Any ideas  ?

(We can assume 2D or 3D cases as well, so spherical or polar, it doesn't really matter)

Our teacher suggested that Newtonian Mechanics only applies in cartesian coordinates. Is this true?

He gave this example.

Suppose there a train moving with constant velocity $\vec{v}=v_0\hat{x}$, with initial position vector $\vec{r}=(0, y_0)$, where $v_0,y_0$ are constants. He argued that Newton's second law would not hold in polar coordinates. Any ideas?

(We can assume 2D or 3D cases as well, so spherical or polar, it doesn't really matter)