The given figure shows the $x-t$ plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for $t < 0$ and on a parabolic path for $t > 0$? If not,suggest a suitable physical context for this graph.

(N/A) No,it is not correct. The $x-t$ graph of a particle moving in a straight line for $t < 0$ and on a parabolic path for $t > 0$ cannot be represented by the given graph.
This is because the graph shows the particle at rest $(x = 0)$ for $t < 0$,and then it starts moving with acceleration for $t > 0$.
$A$ suitable physical context for this graph is a ball held at a height $x = 0$ and released at $t = 0$ to fall freely under gravity.