If an object far away from convex mirror moves towards the mirror, the image also moves. Does it moves faster, slower or at the same speed as compared to the object?

let a object is placed at  distance from convex mirror of focal length f....

applying mirror formula

              1/v+1/u=1/f...................1

differentiating eq 1 wrt to time

           dv/dt (-1/v^2) -du/dt(1/u^2)=0..........2

  velocity of image =dv/dt=Vi

  velocity of object=du/dt=Uo

 from eq 2

           Vi=Vo(-v^2/u^2)                 (-v/u=m(magnification))

           Vi=-m^2Vo...............3

now here are two cases when magnification is equal to 1 and <1

if at any instant particle is at 2f then its image will have same speed but other than this position image will be slower than object speed because m<1 for other positions....

Approved