A spring with a force constant of $500\frac{N}{m}$ is resting on a frictionless surface and mounted horizontally on a wall.

A $2\mathrm{.}5kg$ box is pushed against the spring, compressing it $10\mathrm{.}0cm$ from equilibrium. When released, the spring

pushes the box across the floor.

a$.$ How much force must be exerted on the spring to compress it $10\mathrm{.}0cm?$

b$.$ How much work is done on the spring to compress it $10\mathrm{.}0cm?$

c$.$ How much elastic potential energy is stored in the spring while it is compressed?

d$.$ Once released, what maximum speed will the box attain?