a particle A moving with momentum p suffers a one dimensional collision with a particle B of the same mass but at rest.During the collision B imparts an impulse I to A.The coefficient of restitution is?please explain it`s answer

It is given in the question, initial momentum of the particle-A is `p`. Also, the momentum of particle -B will be zero due to its initial position at rest. Now, after the collision, assuming p1 and p2 be the linear momentum of the particles A and B. Now, Impulse imparted, I = change in momentum, `delta p`. Impulse for particle-B = I .....(i) Impulse for particle-A = p - p2 or p2 = p - I ..........(ii) (Final momentum - initial momentum for particle -A). Coefficient of restitution, Difference of final velocities after collision v2 - v1 mv1 - mv2 p1 - p2 e = -------------------------------------------------------- = --------- = ------------- = ---------- .....(iii) Difference of initial velocities u mu p (where, m is the mass of the each particle and `u` is the velocity of particle-A before collision and v1 and v2 be the velocities after collision of particle A` and `B`). Therefore, From eqns. (i), (ii) and (iii), we get to know, p1 - p + I I - p + I 2 I e = ................. = ............... = ..... - 1 p p p