The K trip curve means it's designed for motor and transformer loads where inrush currents are higher than resistive loads — it holds through the start-up spike and trips on sustained overloads.
The K characteristic is the one to spec when the load is a small motor or a transformer bank; a C-curve would nuisance-trip on the same inrush, and a D-curve would let a sustained overload run too long. For a 4A motor branch circuit, this is the right curve.
