Question

The position time graph of a body is parabolic then the body is __?

• A. In non uniform motion
• B. In uniform motion
• C. At rest with some initial distance covered
• D. None of these

Answer 1

Answer:

B. In uniform motion

• The body is undergoing uniformly accelerated motion (motion with constant acceleration).

• x=x_o+ v_o t+1/2at²

• This equation is a quadratic function of time, as it depends on $t^2$. In mathematics, the graph of a quadratic equation is a parabola.

• Slope and Velocity: In a position-time graph, the slope represents the instantaneous velocity of the object. For a parabolic curve, the slope is continuously changing, which means the velocity is changing (i.e., the object is accelerating). Since the graph is a smooth parabola, the rate of change of the slope (which is the acceleration) is constant (uniform).