The variation of displacement [d] with time [t] in the case of a particle falling freely under gravity from rest is correctly

For a particle released from rest and undergoing free fall, the kinematic displacement equation is s = ut + ½at^2. With initial velocity u = 0 and acceleration a = g (gravity), displacement varies as s = ½ g t^2, i.e., proportional to t^2, producing a parabola that starts at the origin with zero initial slope. Free-fall is exactly the case of one-dimensional motion with constant acceleration g when an object is dropped (initial velocity zero), so the time dependence is quadratic rather than linear or other forms [1]. Therefore the graph that shows d ∝ t^2 (parabolic rise from origin) is the correct choice.

Sources

1. [1] https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/03%3A_Motion_Along_a_Straight_Line/3.07%3A_Free_Fall