The plot represents the displacement `x` of a particle with respect to time `t`. By analyzing the shape of the plot, we can determine the type of motion the particle is undergoing.

Option 1: If the particle was moving with uniform velocity, the plot would have been a straight line with a constant slope. In this case, the plot shows a varying slope, so option 1 is not correct.

Option 2: The correct answer is option 2, which states that the particle is moving with acceleration. The plot shows a changing slope, indicating that the particle`s velocity is changing over time.

Option 3: If the particle was moving with deceleration, the plot would show a decreasing slope as time progresses. However, the plot does not exhibit a consistent decrease in slope, so option 3 is not correct.

Option 4: A periodic motion refers to a repetitive pattern of motion. The plot does not show any repetitive pattern or cycles, so option 4 is not correct.

In conclusion, the correct answer is option 2, which describes the particle as moving with acceleration based on the changing slope in the plot.