Question

newtons second law of motion express it mathematically and find SI unit of force from it

Answer 1

Newton second law is
force proportional to rate of change in motion
i.e.
F  proportional to mv-mu/t
F=km(v-u)/t
here k is constant
so,
F=m(v-u)/t
and v-u/t =a (acceleration)
so,F=ma
Si unit is N or kgm/s²

Answer 2

The rate of flow charge of momentum of an object is proportional to the net force applied on the object.The direction of momentum is the same as the direction of the net force.
consider a body of mass 'm' moving with certain velocity 'u' in a certain direction.If a force 'F' is applied on it in the same direction ,it's velocity increases.
After a small interval of time't' and it's velocity will be 'v'.
initial momentum of the body = mass * initial velocity = m*u
final momentum of the body   = mass * final velocity  = m*v
The momentum changes from 'mu to mv' in a time interval of 't'
    According to NEWTON'S SECOND LAW OF MOTION , the rate of charge of         momentum of a body is directly proportional to the applied force.
hence, F∞mv-mu÷t = F∞m(v-u)÷t
but v-u÷t = a (acceleration)
∴F∞ma
  F=K ma (where k is constant)
if the value of K is taken as unity then,
                          ∴F = ma 
 UNITS OF FORCE-
C.G.S. SYSTEM----->  gcm/s.sq = 1 dyne
S.I. SYSTEM----------->kgm/s.sq  = 1 newton