If the final velocity of a cart is 12 m/s and it collides into another cart, the initial velocity of the second cart would depend on the specific circumstances of the collision.
If the second cart is initially stationary (at rest) and the first cart collides with it, then the initial velocity of the second cart would be 0 m/s. This assumes that the collision is perfectly elastic, meaning that kinetic energy is conserved and there is no loss of energy during the collision. In such a scenario, the momentum of the first cart is transferred to the second cart, causing it to move with the same velocity.
On the other hand, if the second cart is already in motion with a non-zero initial velocity before the collision, then its initial velocity would not be 0 m/s. In this case, the final velocity of the second cart would depend on the masses and initial velocities of both carts, as well as the nature of the collision (elastic or inelastic).
It's important to note that in real-world scenarios, collisions often involve complex factors such as energy loss due to friction or deformation of the objects involved. Therefore, the exact determination of velocities and outcomes would require more specific information about the masses, initial velocities, and the nature of the collision.