Resultant force being zero: motion implications (Newton’s first law) The resultant of all forces acting on a body is zero. Which of the following kinematic states must be true for the body in classical mechanics?

Introduction / Context:
Newton’s first law states that if the net external force on a body is zero, the body either remains at rest or continues to move with uniform velocity in a straight line. Many test questions probe recognition of these allowable states versus those that necessarily require a nonzero resultant force.

Given Data / Assumptions:

• Classical particle mechanics; rotational dynamics not specifically included in the options except implicitly.
• Resultant force equals zero.
• No constraints forcing curved motion by other means (e.g., tension providing centripetal force).

Concept / Approach:

Zero net force implies zero linear acceleration. Two states are compatible: rest and uniform straight-line motion. The listed options do not include constant-velocity straight motion, but “does not move at all” is compatible with the condition and is the only correct option among those provided. Variable velocity, curved paths, or speeding up inherently require nonzero net force (tangential or normal components). Rotation with angular acceleration requires a net moment; for a particle this also implies forces not balancing in effect.

Step-by-Step Solution:

Verification / Alternative check:

Consider uniform circular motion: even with constant speed, direction changes so a_n = v^2/R ≠ 0, hence a net force is required; this contradicts F_res = 0.

Why Other Options Are Wrong:

(a), (b), (c), and (e) imply nonzero linear acceleration or change of direction; they cannot occur with zero resultant force.

Common Pitfalls:

Forgetting that constant velocity straight motion would also be acceptable, but since it is not listed, choosing the compatible state “at rest” is correct.

Final Answer:

It does not move at all (can be at rest).