A firework with mass m that is initially at rest explodes and breaks into two fragments. One fragment has mass m$/3$ and the other fragment has mass $2$m$/3.$ If the lighter fragment moves in the positive x$-$direction with speed v$,$ what is the velocity of the heavier fragment?

Group of answer choices

speed v$/2,$ moving in the positive x$-$direction

speed $2$v$,$ moving in the negative x$-$direction

speed v$/2,$ moving in the negative x$-$direction

speed $2$v$,$ moving in the positive x$-$direction

speed v$/3,$ moving in the negative x$-$direction

speed v$/3,$ moving in the positive x$-$direction