Basically, you have defined the Newton.

Force is the vector product of mass and acceleration. For the purposes of this discussion, we'll just say that F = ma.

In the SI system, the unit of mass, m is the kilogram. Acceleration, a, is defined as the rate of change of velocity, and is expressed in meters per second squared, or m/s2.

Since F = ma, the unit of force, F, is the kilogram-meter per second squared, or kg-m/s2, which is known as a Newton, in honor of the great English scientist, Sir Isaac Newton.

So, it will take one Newton (of force) to accelerate a one-kilogram mass one meter per second squared.