(a). The box leaves position x - 0 with speed v ₀ . The box is slowed by a constant frictional force until 4 acmes to rest at position x - x ₁ .

Find F _f the magnitude of the average frictional force that Act on the box (Since you don't include it in your answer) Express the frictional force In terms of m, w, and x ₁ .

(b). Atter the box comes to rest at position x ₁ , a person starts pushing the box giving it a speed v ₁ .

When the box reaches position x ₂ (where x ₂ > x ₁ how much work Wp has the person done on the box? Assume that the box reaches x ₂ after the person Ms accelerated it from rest to sped v ₁ . Express the work in terms of m, w, x ₁ , x ₂ , and v ₁ .