A $1\mathrm{.}50$ kg object slides to the right on a surface having a coefficient of kinetic friction $0\mathrm{.}250($Fig$.$ P$7\mathrm{.}54).$ The object has a speed of vi $=3\mathrm{.}10$ m$/$s when it makes contact with a light spring that has a force constant of $50\mathrm{.}0$ N$/$m$.$ The object comes to rest after the spring has been compressed a distance d$.$ The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. The object finally comes to rest a distance D to the left of the unstretched spring

a$)$ find the distance of compression d

b$)$find the speed v at the unstretched position when the object is moving to the left

c$)$ find the distance D where the object comes to rest