Force = ma
We know, the unit that the S.I. unit of mass is Kg.
We also know that a = (v - u)/t.
We know that v = d/t and u = d/t and the S.I. unit of t(time) is s.
We know that the S.I. unit of d(displacement) is m.
So, the S.I. unit of v is m/s and the S.I. unit of u is m/s and the S.I. unit of t is s.
So, the S.I. unit of a is m/s×s or m/s²
So, the unit of force is
(unit of m) × (unit of a)
= kg × (m/s²)
= kg.m/s²
=
Or more simply,
F = ma
=> F = m{(v-u)/t}
Putting units,
Newton = kg[{(m/s) - (m/s)}/s]
=> Newton = kg{(m/s)/s}
=> Newton = kg(m/s²)
=> Newton = kg.m/s²
=> Newton = kg.m.(s^-2)