Halliday, Resnick & Walker — Center of Mass and Linear Momentum: Problem 10

A block on a horizontal floor is initially either stationary, sliding in the positive direction of an $x$ axis, or sliding in the negative direction of that axis. Then the block explodes into two pieces that slide along the $x$ axis. Assume the block and the two pieces form a closed, isolated system. Six choices for a graph of the momenta of the block and the pieces are given, all versus time $t$. Determine which choices represent physically impossible situations and explain why.