A $500$ gram cart$($cart $1)$ moves with a velocity of $+0\mathrm{.}75$ m$/$s and collides with a second stationary cart $($cart $2).$ After the collision, cart $1$ is observed to have a velocity of $-0\mathrm{.}50$ m$/$s$.$ You can assume that the collision is either completely elastic to completely inelastic $($only one of these choices is reasonable$).$ Determine the mass of Cart $2$ and its velocity following the collision.