A point object $P$ moves towards a convex mirror with a constant speed $V,$ along its optic axis. The speed of the image 

For a convex mirror , $\frac{1}{v}+\frac{1}{\left(-u\right)}=\frac{1}{f} \Rightarrow v = \frac{f}{1+{\displaystyle \frac{f}{u}}}. Here v = image dis\tan ce .$

Speed of image ,V = $\frac{dv}{dt}={\left(\frac{f}{u+f}\right)}^2\times \frac{du}{dt}$$<\frac{du}{dt}$

When the object moves from infinity to the pole of the mirror, the virtual image moves from focus to the pole.