Question

Is it possible for a particle to describe a curved path if no force acts on it? Does your answer depend on the frame of reference chosen to view the particle?

Answer 1

If no force acts on the particle it cannot change its direction. So, it is not possible for a particle to describe a curved path if no force acts on it.
Yes, the answer depends on the frame of reference chosen to view the particle if the frame of reference describes a curved path.