use newtons second law to explain a collision

Newton's second law states that the rate of change of momentum is proportional to the applied force and takes place at the direction in which the force acts.

i.e. F = m(v-u)/t
where F is the applied force
m is the mass
v and u are the initial and final velocities respectively
t is the time taken

thus, Ft = mv - mu

during a collision between 2 bodies, the impact F and time taken must be the same for both bodies, and from which the conservation of momentum is achieved.