Final answer:
In an elastic collision, the velocity of car A after the collision will be equal to the average of the two initial velocities, in its original direction, which is 12.5 m/s in the +x-direction.
Step-by-step explanation:
In an elastic collision, the velocities of the cars after the collision can be calculated using the conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. In this case, we have car A moving at 15 m/s in the +x-direction and car B moving at 10 m/s in the -x-direction. Since the cars have equal mass, their momenta before the collision are equal in magnitude but opposite in direction.
After the collision, the momenta of the cars are still equal in magnitude but their directions have changed. The velocity of car A after the collision will be equal to the average of the two velocities, in its original direction, which is 12.5 m/s in the +x-direction.