The nature of displacement-time graph is parabolic if the acceleration is constant(uniform).
When acceleration is constant, displacement is directly proportional to the square of time which results into a parabolic structure of graph.
Chat with our AI personalities
The question is based on a misconception. The displacement-time graph of a point travelling from the origin (O), in a straight line at a constant velocity (v) is a straight line through the origin with gradient = v. The graph for an object going from O to a point A and returning immediately is a triangle. If that object spends some time at A, then the graph is a trapezium. The graph for an object travelling in a circle around O - at a constant or variable angular velocity - is a horizontal line. None of these graphs could be described as parabolas.
Displacement is the area under the v-t graph.
It is the instantaneous speed in the direction in which the displacement is measured.
Any equation where variable a = some multiple of variable b2 + constant will graph a parabola.
As, in the velocity-time graph, curves passes through zero means 'when time is zero velocity is zero'. Velocity is time derivative of displacement. So displacement is maximum or minimum when time is zero in position-time graph.
It is time.