An object is placed far beyond the centre of curvature of a concave mirror. The object then starts accelerating towards the mirror. Which one of the following is correct?

According to the mirror formula 1/v + 1/u = 1/f, for a concave mirror, the position of the image depends on the position of the object relative to the focus (F) and the centre of curvature (C). When an object is at infinity, the image is formed at F. As the object moves from infinity towards C, the image moves from F towards C. Since the object in the question is "far beyond" C and moving towards the mirror, the image must be moving from the vicinity of F towards C.

The velocity of the image (vi) is given by vi = -(v/u)2 × vo, where vo is the velocity of the object. Because the object is accelerating and the magnification factor (v/u)2 changes as the distances change, the image will also accelerate. Therefore, the image accelerates towards the centre of curvature.