As long as the force exerted by a gravitational field, such as Earth’s, is the only force on an object, then Newton’s Second Law can be used in the form a = F/m_inertial. But the force due to the field is given by F = m_{gravitationalg}. And, as has been tested by experiment and explained by Einstein’s theory, m_inertial = m_{gravitational}, so a = g.

There is one more thing to question. The acceleration a is measured in meters per second squared, while the gravitational field strength is measured in newtons per kilogram. How can these two quantities be equal? The answer can be found by looking at Newton’s Second Law again. In the form F_net = ma, you can see that the units of force, newtons, must be equal to the units in which m times a are measured. The mass, m, is measured in kilograms and the acceleration in meters per second squared. Therefore a newton must be a kilogram times a meter per second squared. Thus a newton per kilogram (N/kg) is a meter per second squared (m/s²).