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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.