Final answer:
In elastic collisions, the final velocity of a cart can be determined using conservation of momentum and kinetic energy. For equal mass carts, if one is initially at rest, it will take on the initial velocity of the moving cart post-collision. If both carts are moving, their final velocities can be calculated based on initial velocities and the conservation laws.
Step-by-step explanation:
In elastic collisions, momentum and kinetic energy are conserved. For two carts of equal mass (such as Cart A and Cart B) colliding elastically, the one-dimensional formulas for conservation of momentum and kinetic energy can be applied to find the final velocities after the collision.
If Cart A is moving with a velocity of +v in the positive direction towards Cart B, which is initially at rest, and they have an elastic collision, the final velocity of Cart A after the collision can be deduced using the conservation laws. Since both carts are of equal mass and assuming there's no external force acting on the system, the velocity of Cart A after the collision will be 0 m/s, and Cart B will move forward with the initial velocity of Cart A, which is +v m/s.
However, in the scenario where both Cart A and Cart B are moving with different velocities in opposite directions along the x-axis, we can use these velocities and the conservation laws to calculate their velocities after the collision. For example, if Cart A is moving with a velocity of +15 m/s and Cart B with a velocity of -10 m/s, one possible final velocity for Cart A, if Cart B's final velocity equals the initial velocity of Cart A in the opposite direction, would be -10 m/s. This result assumes that the mass of Cart A is equal to the mass of Cart B, and we use the equations for perfectly elastic collisions.