If area (a) velocity(V) and density(d) are base units, then the dimensional formula of force can be represented as

Force = Mass × Acceleration…(1)

Mass = Density × volume = density×area×distance = density×area×velocity×time …(2)

Acceleration = velocity / time …(3)

By substituting for mass and acceleration using eqns. (2) and (3) in (1), we get Force = density×area×(velocity)^{2}