The displacement of a particle a time t is given by where a, b and c are positive constants. Then the particle: is

The correct answer is Option 2. In physics, the motion of a particle is determined by the derivatives of its displacement function with respect to time (t).

To find the velocity (v), we take the first derivative of the displacement: v = dx/dt = a - 2bt. To find the acceleration (A), we take the second derivative: A = dv/dt = -2b.

Since the problem states that b is a positive constant, the acceleration A = -2b is a constant negative value. In kinematics, a negative acceleration acting opposite to the direction of motion (or simply a negative constant acceleration in a linear context) represents deceleration.

• Option 2 is correct because the negative sign mathematically confirms the particle is decelerating.
• Options 1 and 4 are incorrect as they suggest acceleration (positive A).
• Option 3 is incorrect as the motion is typically defined along the x-axis (i-direction) in such standard equations.