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Newton's 2nd law of motion  states that the rate of change of momentum of a body is proportional to the force producing it and takes place in the direction of force.

The momentum of a body ,

           P = mass* velocity = mv

Let   initial velocity = u  

         Initial momentum = mu 

Final velocity = v 

 final momentum  = mv 

Change in velocity = m(v - u) 

Rate of change of momementum = m(v - u) / t = m(v- u)/t = ma 

where t = time interval 

           a = acceleration 

The instantaneous rate of change of momentum = dP/dt = (d/dt)(mv) = m(dv/dt) = ma

Let the force acting on the body be F and from the second law " Force is proportional to  proportional to momentum "

= ie , F = k ma,  ( k = constant)    

Thus the directions of the Acceleration and the Force producing it are the same. 

The  Unit Force (Newton) is defined as the  force which when acts on a body of Unit Mass (1 kg) produces Unit Acceleration (1 m/s²). This means, Unit Force = k (Unit Mass)*(Unit Acceleration)     ie , => k = 1

and 

                     F = ma