The magnitude of an object's acceleration is proportional to the force acting on the object and inversely proportional to the mass of the object. The direction of the acceleration is the same as the direction of the resultant external force. From the perspective of physics, Newton's second law of motion can also be expressed as "the rate of change of momentum of an object over time is proportional to the sum of the external forces it is subject to", that is, the first-order derivative of momentum with respect to time is equal to the sum of the external forces.

Newton's second law states that at macroscopic low speeds, the proportional expression is: a∝F/m, F∝ma; it can be expressed mathematically as F=kma, where k is the proportional coefficient, which is a constant. However, since there was no regulation on the force unit at that time, the selection of the proportional coefficient k was somewhat arbitrary. If k=1, then F=ma, which is the mathematical expression of Newton's second law that we are familiar with today.