(i) No repetition of motion. Its a unidirectional, linear but non-uniform motion of the particle.
(ii) Motion repeats after every 2 s. Hence, periodic with time period 2 s.
(iii) Repetition of one position or a few positions (but not all) is not enough for motion to be periodic, the entire motion during one period must be repeated successively. Hence, the given x-t plot is not periodic, though there is repetition of a single position (x = 0 at every 3 s) but other positions are not repeated.
(iv) Clearly, the motion repeats itself after every 2 s. Hence, periodic having a time-period of 2 s.