In this part, we’ll discuss about different varieties of this conservations.
Case 1:Imagine two objects are of same masses (m_1=m_2).m_1 is motionless that means u_1=0 & m_2 is in motion with an initial velocity of u_2 before collision.
Replace m_1 instead of m_2 in the formula of v_1 to get the velocity of m_1 after collision:
v_1=\frac{2m_1u_2+u_1(m_1-m_1)}{m_1+m_1}
Then you’ll get v_1=u_2
To get the velocity of m_2 after collision, put m_2=m_1 & u_1=0 in the formula of v_2:
v_2=\frac{2m_1*0+u_2(m_1-m_1)}{m_2+m_2}
then you will get v_2=0
That is, if a stationary marble is hit by a second marble (of equal mass), then the second marble will become stationary, the first one will move out with that velocity. You can check whether it is true or not.