Which of the following statements about moving particle is correct?

Analyze the question: We need to find the one true statement about a moving particle, so we check each option against Newton's laws.

Concept:

• Newton's first law: if the resultant force on a body is zero, its velocity is constant (zero acceleration). A moving body in this state is in dynamic equilibrium. A body at rest in this state is in static equilibrium.
• Newton's second law: F = rate of change of momentum, so the resultant force and the rate of change of momentum point in the same direction.
• Free fall: the acceleration is constant (g), so the velocity keeps increasing.

Checking each option:

• A. If the resultant force is zero, the particle moves with constant velocity, which is dynamic equilibrium. Correct.
• B. If the resultant force is greater than zero, the particle accelerates, so it does not move with uniform velocity. False.
• C. By F = d(mv)/dt, the rate of change of momentum is in the direction of the resultant force, not necessarily opposite to the motion. False.
• D. A freely falling particle speeds up, using s = ½gt². It covers larger distances in successive equal time intervals (in the ratio 1 : 3 : 5 : ...). False.

Tip: Remember "Zero force means zero acceleration, not zero velocity." A moving body with zero resultant force is in dynamic equilibrium, and a stationary one is in static equilibrium. In free-fall questions, equal distances in equal times means constant velocity, which is wrong because free fall is accelerated motion.