the acceleration of an object is directly proportional to the force 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 net external force. from a physical point of view, newton's second law of motion can also be expressed as "the rate of change of an object's momentum over time is proportional to the sum of the external forces it experiences." that is, the first derivative of momentum with respect to time is equal to the sum of the external forces.

newton's second law explains that at macroscopic low speeds, the proportional expression is: a∝f/m, f∝ma; using mathematical expressions, it can be written as f=kma, where k is the proportional coefficient, which is a constant. however, since the force was not specified as the unit of force at that time, the selection of the proportional coefficient k was somewhat arbitrary. if k=1, f=ma is obtained. this is the mathematical expression of newton’s second law that we are familiar with today. mode.