Which equation represents Newton's Second Law?

Which equation represents Newton's Second Law?

• A. P = m v
• B. E = m c^2
• C. F = m a
• D. F = m g

Answer: (C)

Newton's Second Law describes how forces cause motion to change. The net external force acting on an object determines its acceleration, and the acceleration points in the same direction as that net force. The concise form is F_net = m a, with F_net as the net force, m as mass, and a as acceleration. This means doubling the force (for the same mass) doubles the acceleration, and increasing the mass (for the same force) lowers the acceleration. The relationship is vectorial, so both magnitude and direction matter. In many problems mass is constant, so this reduces to F = m a. If mass can change, the more general form is F_net = d p / d t, where p = m v is momentum; with constant mass, d p / d t becomes m a. The unit of force is the newton, equal to kg·m/s^2. The other expressions don’t capture the full link between force and motion: p = m v describes momentum, not the cause of motion change; E = m c^2 is mass–energy equivalence; F = m g represents weight under gravity, a specific case and not the general law relating all forces to acceleration.

Newton's Second Law describes how forces cause motion to change. The net external force acting on an object determines its acceleration, and the acceleration points in the same direction as that net force. The concise form is F_net = m a, with F_net as the net force, m as mass, and a as acceleration. This means doubling the force (for the same mass) doubles the acceleration, and increasing the mass (for the same force) lowers the acceleration. The relationship is vectorial, so both magnitude and direction matter.

In many problems mass is constant, so this reduces to F = m a. If mass can change, the more general form is F_net = d p / d t, where p = m v is momentum; with constant mass, d p / d t becomes m a. The unit of force is the newton, equal to kg·m/s^2.

The other expressions don’t capture the full link between force and motion: p = m v describes momentum, not the cause of motion change; E = m c^2 is mass–energy equivalence; F = m g represents weight under gravity, a specific case and not the general law relating all forces to acceleration.