No, it is not correct to say that the particle moves in a straight linefor $t < 0$ and on a parabolic path for t > 0 as the x-t graph does not show thetrajectory of the path of a particle. The graph shows that at time$t = 0, x = 0$Context : The suitable context is a body dropped from a tower i.e. free fallof a body $\text{i.e. } x = 0 \text{ at } t = 0$