Second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the same direction as the force.
Suppose the velocity of a body of mass m changes from u to v in time t. The magnitudes of initial and final momentum of the body will be P1=mu and P2=mv. The change in momentum (P2-P1), takes place in time t. Then according to the law:
or F=kxm(v-u)/t where k is a constant ...(i)
Now (v-u)/t is the rate of change of velocity, which is acceleration á', so we have
We choose the units of force in such a manner that the value of k=1. So that
By the second law of motion we get to know that force is equal to the product of a body's mass and its acceleration.