Figure 3.21 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.
No.
x-t graph doesn’t represent the trajectory followed by the particle. It is formed by the points consist of both time and space coordinates.