Explanation

(a) According to mirror formula
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
Here $u\ = \ - 9\ m\ and\ f\ = \ - 1\ m$
$\frac{1}{( - 1)} - \frac{1}{( - 9)} = \frac{1}{v}$
$\Rightarrow v = \ - \frac{9}{8}m$
As the object moves at a constant speed of 5 m/s after 1 s the new position of image is
$u' = \ - 9\ m + 5\ m = \ - 4\ m$
$\therefore\frac{1}{( - 1)} - \frac{1}{( - 4)} = \frac{1}{v'}$
$\Rightarrow v' = \ - \frac{4}{3}m$
The shift in the position of image in 1 s is
$v - v'\ = \ - \frac{9}{8} + \frac{4}{3} = \frac{1}{5}$
$\therefore$ Average speed of image $= \frac{1}{5}m/s$