Consider a one-dimensional collision involving a body of mass $m_1$ moving in the positive $x$ direction with speed $v_0$ and a second body of mass $m_2$ initially at rest. The collision can be completely inelastic,completely elastic,or partially inelastic. After the collision,$m_1$ moves with velocity $v_1$ and $m_2$ moves with velocity $v_2$. Determine the range of final velocity $v_1$ for the following cases:
$(A)$ If $m_1 > m_2$
$(B)$ If $m_1 < m_2$

• A
  $ -v_0 < v_1 < 0$ ; $ -v_0 < v_1 < 0$
• B
  $v_0 < v_1 < 2v_0$ ; $0 < v_1 < v_0$
• C
  $0 < v_1 < 2v_0$ ; $0 < v_1 < v_0/2$
• D
  $0 < v_1 < v_0$ ; $-v_0 < v_1 < v_0/2$