The displacement x of a particle in a straight line motion is given by x = 1 - t^2 . The correct representation of the motion is

Step-by-step solution

Given x = 1 - t^2 At t = 0 : x = 1 , so the graph must start at a positive value on the x -axis. This eliminates graph (1) which starts at the origin. Velocity: v = dx dt = -2t . At t = 0 , v = 0 , so the slope of the x - t graph must be zero (horizontal) at the start. This eliminates graph (4) which has a positive initial slope. Acceleration: a = dv dt = -2 , a negative constant, so the x - t graph must be a downward-opening parabola. This eliminates graph (3) which opens upward. Graph (2) starts at a positive x -