The second law of motion states that the force exerted on a a body is proportional to the rate of change of momentum of that body.
Let mass of body be m
initial velocity be u and final velocity be v
and time taken for the momentum change be t
Thus rate of change of momentum: m(v-u)/t = ma
here a = (v-u)/t = rate of change of velocity.
thus Force, F = kma
here k is the constant of proportionality.
its value if selected as 1 by keeping the units of other parameters in accordance.
thus F = ma