I have a question on kinematics.
Say the path traced by a particle is given by a Koch curve or Koch snowflake.
Now consider the particle starts from some arbitrary point $A$ on the curve and continues moving with some acceleration. It moves a finite distance on the curve and reaches another point $B$ which is different from $A$ and the particle has not crossed the same point twice.
So there is a net finite displacement covered in a finite time. Hence the particle has a finite average velocity.
But the curve is not differentiable at any point, by definition of the curve. So the particle has no instantaneous velocity at all points of the path taken.
QUESTION: Can a particle have no instantaneous velocity at all points of the path taken but still a finite average velocity?
Is this possible? Can anyone explain this?