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

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

a straight line
a circle
a parabola
any curve depending upon initial conditions
This question was previously asked in
UPSC NDA-1 – 2015
The correct option is C. The displacement-time graph of a particle acted upon by a constant force is a parabola.
According to Newton’s second law, a constant force (F) acting on a particle of constant mass (m) results in constant acceleration (a), where F = ma.
For motion under constant acceleration, the displacement (s) of a particle from its initial position as a function of time (t) is given by the kinematic equation: s = ut + (1/2)at², where u is the initial velocity and a is the constant acceleration.
This equation is a quadratic function of time (t).
The general form of the displacement-time graph for constant acceleration is a parabola. If the initial velocity is zero (u=0), the equation simplifies to s = (1/2)at², which is clearly a parabola passing through the origin. If there is an initial velocity, the parabola is shifted and possibly rotated, but remains a parabola. A straight line graph represents constant velocity (zero acceleration, thus zero net force).