Final answer:
Yes, two objects with different velocities can have the same kinetic energy if they end up with the same final velocity after a collision.
Step-by-step explanation:
In a collision between two objects, the kinetic energy is conserved if both the objects have the same final velocity after the collision. Therefore, it is possible for two objects with different initial velocities to have the same kinetic energy if they end up with the same final velocity.
For example, consider two billiard balls colliding. If one ball is initially at rest and the other has a certain velocity, after the collision, the moving ball will stop and the initially stationary ball will move with the same velocity as the other originally had. In this case, the kinetic energy of both balls before and after the collision will be the same.