If a ball has zero initial velocity but is subject to the gravitational acceleration (g), its motion will resemble free fall. The ball will start from rest and continuously accelerate downward due to gravity. However, since the ball has no initial velocity, it will not possess any horizontal motion.
The motion of the ball can be described by the equations of motion under constant acceleration. The equation for the displacement (s) of the ball as a function of time (t) can be expressed as:
s = 0.5 * g * t^2
Where g represents the acceleration due to gravity. As time progresses, the displacement of the ball will increase quadratically.
Additionally, the velocity (v) of the ball at any given time can be obtained by integrating the equation for acceleration with respect to time:
v = g * t
The velocity of the ball will linearly increase with time due to the constant acceleration provided by gravity.
It's important to note that in the absence of any other forces or resistances, the ball will continue to accelerate until it hits the ground or encounters another object.