The displacement-time graph of a particle acted upon by a constant force is

According to Newton's second law of motion, when a constant net force is applied to an object with constant mass, it experiences constant acceleration. In kinematics, the relationship between displacement (s) and time (t) for an object undergoing constant acceleration is described by the second equation of motion: s = ut + 1/2 at², where 'u' is initial velocity and 'a' is acceleration. Mathematically, this equation represents a quadratic relationship where displacement is proportional to the square of time [1]. Consequently, the displacement-time (s-t) graph for such motion is a parabola. While a straight line on an s-t graph indicates constant velocity (zero acceleration), a curved parabolic path specifically characterizes motion under a constant force [1].

Sources

1. [1] https://en.wikipedia.org/wiki/Equations_of_motion