Dynamics S2 slide 11: Is acceleration tangent to the path? (ENGR5004)

Dynamics S2 slide 11: Is acceleration tangent to the path?From lectureCurrent spec2:23 marks4 min

ENGR5004 Dynamics Session 2, slide 11 (Defining the acceleration vector in Cartesian coordinates)

The slide states that the instantaneous velocity vector is always tangent to the path, but that the "acceleration vector is NOT usually tangent to the path", followed by a red question mark.

Explain why the acceleration of a particle in curvilinear motion is not usually tangent to its path, and state when it is tangent.

Formulas you may need

$\mathbf a = \dfrac{d\mathbf v}{dt} = \lim_{\Delta t\to 0}\dfrac{\mathbf v' - \mathbf v}{\Delta t}$ (learn this)
n-t components (Session 3): $\mathbf a = \dot v\,\mathbf u_t + \dfrac{v^2}{\rho}\,\mathbf u_n$ (learn this)