Final answer:
The speed of the first object after the collision is 0.30 m/s.
Step-by-step explanation:
To find the final velocity of the first object after the collision, we can use the principle of conservation of momentum. The initial momentum of the first object is given by its mass (0.16 kg) multiplied by its initial velocity (0.50 m/s). Since the second object is at rest, its initial momentum is 0. After the collision, the momentum of the second object is given by its mass (0.10 kg) multiplied by its final velocity (0.50 m/s).
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can set up the equation: (0.16 kg) * (0.50 m/s) = (0.10 kg) * (0.50 m/s) + (0.16 kg) * (vf).
Solving for vf, we find that the speed of the first object after the collision is 0.30 m/s.