for a perfectly elastic collision, +=2+2, or alternatively. 2. If object 2 is initially at rest, then u = 0. Then U - 1 = However, for a partially elastic collision the relative velocity after the collision will have a smaller magnitude than the relative velocity before the collision. We can express this mathematically as U-2=-, wherer (a number less than one) is called the coefficient of restitution. For some kinds of bodies, the coefficient r is a constant, independent of and . Show that in this case the final kinetic energy of the motion relative to the center of mass is less than the initial kinetic energy of this motion by a factor of r. Furthermore, derive expressions for vi and 12 in terms of us and r. (6 marks)