A person says that he measured the acceleration of a particle to be non-zero even though no force was acting on the particle.
He is a liar.
His clock might have run slow.
His metre scale might have been longer than the standard.
He might have used a non-inertial frame.
He might have used a non-inertial frame
If no force is acting on a particle and yet, its acceleration is non-zero, it means the observer is in a non-inertial frame.