The conversation of momentum can be derived from newton's second law of motion .
F is a force acting on a body of mass m. giving it acceleration a . let it's velocity changes from V1 to V2 in time t. (P=mv ).
F = ma = m V2-V1 = mv2-mv1 = P2 - P1
t t t
if there is no net force then F=0
⇒P2 - P1 =0
⇒P2 - P1 = 0 .
THUS THE MOMENTUM OF THE PARTICLE DOES NOT CHANGE .
THIS IS THE LAW OF CONVERSATION OF MOMENTUM.