Generic Person is pushing a crate $($m $=50\mathrm{.}0$ kg$)$ into a spring as shown in the illustration below. They push parallel to the floor with a force of $100$ N$.$  At the instant shown the spring is compressed $0\mathrm{.}500$ meters, and the crate is experiencing an acceleration of $2\mathrm{.}00$ m$/$s$2$ to the left as shown. There is no friction between the surface of the crate and the floor.

What is the spring constant of the spring?