Special cases
Case I: When the mass of both the particles are equal i.e., m_{1} = m_{2} then from equation 8 and 9 , v_{2}=u_{1} and v_{1}=u_{2}. Thus if two bodies of equal masses suffer head on elastic collision then the particles will exchange their velocities. Exchange of momentum between two particles suffering head on elastic collision is maximum when mass of both the particles is same.
Case II: when the target particle is at rest i,e u_{2}=0
From equation (8) and (9)
Hence some part of the KE which is transformed into second particle would be
when m_{1}=m_{2},then in this condition v_{0}=0 and v_{2}=u_{1} and part of the KE transferred would be
=1
Therefore after collisom first particle moving with initial velocity u_{1} would come to rest and the second particle which was at rest would start moving with the velocity of first particle.Hence in this case when m_{1}=m_{2} transfer of energy is 100%.if m_{1} > m_{2} or
m_{1} < m_{2} ,then energy transformation is not 100%
Case III:
if m_{2} >>>> m_{1} and u_{2}=0 then from equation (10) and (11)
v_{1} ≅ -u_{1} and v_{2}=0 (13)
For example when a ball thrown upwards collide with earth
Case IV:
if m_{1} >>>> m_{2} and u_{2}=0 then from equation (10) and (11)
v_{1} ≅ u_{1} and v_{2}=2u_{1} (14)
Therefore when a heavy particle collide with a very light particle at rest ,then the heavy particle keeps on moving with the same velocity and the light particle come in motion with a velocity double that of heavy particle