I attach an explosive device to a cart in the lab and roll it along a track at a velocity of $+2\mathrm{.}30\frac{m}{s}.$ As it rolls along the track at that speed, I trigger the device and the cart explodes, breaking it into two parts, the first with a mass of $168$ g $,$ and the second a mass of $285$ g $.$ If the second piece of the cart is moving with a velocity of $+4\mathrm{.}76\frac{m}{s}$ after the explosion, what is the velocity of the first piece of the cart after the explosion?