The force required to accelerate 1 kg of mass at 1 meter per second squared is 1 Newton.

This is directly derived from Newton's Second Law of Motion:

Force (F) = Mass (m) x Acceleration (a)

In this case:

* F = ? (what we want to find)

* m = 1 kg

* a = 1 m/s²

Therefore, F = 1 kg * 1 m/s² = 1 Newton.