A particle with momentum p₁ in one dimension makes an elastic collision with a second particle of momentum p₂ = −p₁ in the center-of-mass reference frame. After the collision its momentum is. Write the total initial and final energies in terms in terms of p₁ and p₁', and show that p₁' = ±p₁. If p₁' = -p₁, the particle is merely turned around by the collision and leaves with the speed it had initially. What is the significance of the plus sign in your solution?