I think the answer is periodic motion.
Since the stone is travelling, the displacement cannot be constant. This leaves the last 2 choices as possibilities. Now consider the acceleration that can act on the stone. Acceleration due to gravity is the only one. That means the horizontal component of the stone has to be constant since there is no acceleration in the horizontal direction.
Answer:
The answer is given below
Explanation:
u is the initial velocity, v is the final velocity. Given that:

a)
The final velocity of cart 1 after collision is given as:

The final velocity of cart 2 after collision is given as:

b) Using the law of conservation of energy:

You can't. Velocity and acceleration measure two different things, so their units are incompatible. It's like asking, "How many meters does this book weigh?"
Maybe you mean "find" acceleration using given velocities, or a velocity function?