For motion with constant nonzero acceleration, the position versus time graph has the shape of a parabola. This occurs because the position of an object undergoing constant acceleration changes at an increasing rate over time.
When an object accelerates uniformly, its velocity increases linearly with time. The equation that describes the position of the object can be represented as:
x(t) = x_0 + v_0 t + rac{1}{2} a t^2Here, x(t) is the position at time t, x_0 is the initial position, v_0 is the initial velocity, and a is the constant acceleration. The t^2 term indicates that the position changes quadratically with time, which results in a parabolic curve when graphed.
As a result, when you plot position against time for an object in motion under constant acceleration, you get a curved graph opening in the direction of the acceleration. If the acceleration is positive, the parabola opens upwards, and if the acceleration is negative (deceleration), it opens downwards.