Question

how and why the rate of change in momentum is directly proportional to unbalanced force

Answer 1

because of Newton's ll law of motion. The unbalanced Force applied on the object is directly proportional to the Rate of change of momentum. Hence , we found that Rate of change of momentum is equal to Force applied on the object.

hope helps ☺️☺️

Answer 2

According to Newton's 2nd law
The rate of change of an object is directly proportional to the force applied on it .

so
force = rate of change of momententum