If $c$ is a regular path in the plane with non-vanishing acceleration, we define the unit tangent $\mathbf{T}$ to be the normalized velocity, and we define the normal $\mathbf{N}$ to be the unit vector positively proportional to the derivative $\mathbf{T}'$. The curvature is $\kappa = |\mathbf{T}'|$.
Each demo shows a plane curve with its velocity and normalized velocity in blue, its unit normal vector and $\kappa\mathbf{N}$ in light blue, and the acceleration in light green.
The comma (less-than) and period (greater-than) keys move the frame backward and forward along the curve.