Final answer:
Using the law of conservation of momentum, the mass of the second car is calculated to be 1 kg. The initial momentum of the first car (5 kg·m/s) equals the final momentum of the second car since the first car stops and the second car moves at 5 m/s.
Step-by-step explanation:
To determine the unknown mass of the second car after the collision, we can use the law of conservation of momentum, which states that in a closed system, the total momentum before the collision is equal to the total momentum after the collision. The first car of 1 kg, traveling at 5 m/s, has an initial momentum of 1 kg × 5 m/s = 5 kg·m/s. Since the first car stops after the collision, its final momentum is 0 kg·m/s. The second car, initially at rest, starts to move at 5 m/s after the collision.
To conserve momentum, the initial momentum of the first car must equal the final momentum of the second car:
(Mass of Car 2) × (Velocity of Car 2) = Momentum of Car 1
This gives us the equation:
(Mass of Car 2) × 5 m/s = 5 kg·m/s
By dividing both sides by 5 m/s, we find:
Mass of Car 2 = 1 kg
Thus, the mass of the second car is 1 kg. It has the same mass as the first car due to the conservation of momentum and the identical velocities after the collision.