A luminous point is moving at speed $v_0$ toward a spherical mirror with radius of curvature $r,$ along the central axis of the mirror. Assume the mirror is concave, with $r=25cm,$ and let $v_0=5\mathrm{.}4c\frac{m}{s}.$ Find $v_1($the speed of the image of the point$)$ when $($a$)p=37cm($far outside the focal point$),($b$)p=13cm($just outside the focal point$),$ and $($c$)p=9\mathrm{.}8mm($very near the mirror$).$

$($a$)$ Number $$ Units

$($b$)$ Number $$ Units

$($c$)$ Number $$ Units $$