When two objects collide, their kinetic energy, momentum, and velocity can change depending on the type of collision they experience. In the case of an elastic collision, in which the objects bounce off each other without any loss of kinetic energy, the final velocities of the objects can be calculated using the conservation of momentum and the coefficient of restitution.

In an inelastic collision, on the other hand, some of the kinetic energy is converted into other forms of energy, such as heat or sound. This means that the final velocities of the objects will be different from those in an elastic collision.

In your case, since you have provided the coefficient of restitution, it appears that the collision between the two objects is elastic. To determine their final velocities, we can use the following formula:

Final velocity of first object = (initial velocity of first object * (mass of first object - mass of second object) + 2 * mass of second object * initial velocity of second object) / (mass of first object + mass of second object)

Final velocity of second object = (initial velocity of second object * (mass of second object - mass of first object) + 2 * mass of first object * initial velocity of first object) / (mass of first object + mass of second object)

In your case, the initial velocities of the two objects are 7 m/s and 20 m/s, respectively, and the masses are 20 kg and 12 kg. Plugging these values into the above formula, we get the following:

Final velocity of first object = (7 m/s * (20 kg - 12 kg) + 2 * 12 kg * 20 m/s) / (20 kg + 12 kg) = 5.6 m/s

Final velocity of second object = (20 m/s * (12 kg - 20 kg) + 2 * 20 kg * 7 m/s) / (20 kg + 12 kg) = -14.4 m/s

Therefore, the velocities of the two objects after the collision are 5.6 m/s and -14.4 m/s, respectively.