Which equation expresses Newton's Second Law?

Which equation expresses Newton's Second Law?

• A. F = ma
• B. F = mv
• C. F = m a^2
• D. F = m/d

Answer: (A)

Net force acting on an object determines its acceleration. This is Newton's second law: the force applied to a mass causes it to accelerate, with the acceleration proportional to the force and inversely proportional to the mass. In symbols, F = m a. Here m is the mass (inertia), a is the acceleration (change in velocity per unit time), and F is the net force. This means doubling the force on a given mass doubles the acceleration, and doubling the mass for the same force halves the acceleration. The direction of acceleration matches the direction of the net force, since force is a vector and mass is a scalar. In SI units, a Newton equals 1 kg·m/s^2, so F = m a is dimensionally consistent. The other expressions don’t represent the force law. F = mv corresponds to momentum, not force (the force is the time rate of change of momentum, F = dp/dt). F = m a^2 would have incorrect units for force, and F = m/d has no basis in this fundamental relationship.

Net force acting on an object determines its acceleration. This is Newton's second law: the force applied to a mass causes it to accelerate, with the acceleration proportional to the force and inversely proportional to the mass. In symbols, F = m a. Here m is the mass (inertia), a is the acceleration (change in velocity per unit time), and F is the net force. This means doubling the force on a given mass doubles the acceleration, and doubling the mass for the same force halves the acceleration. The direction of acceleration matches the direction of the net force, since force is a vector and mass is a scalar. In SI units, a Newton equals 1 kg·m/s^2, so F = m a is dimensionally consistent.

The other expressions don’t represent the force law. F = mv corresponds to momentum, not force (the force is the time rate of change of momentum, F = dp/dt). F = m a^2 would have incorrect units for force, and F = m/d has no basis in this fundamental relationship.