Newtons first law says:
every body has a uniform velocity (0 or some value). It is changed only by an external force.
Here how much is the force, how much velocity changes is not described or calculated. At this point how much is the numerical value of force - also is not known. we want to find a formula. We know velocity and acceleration.
Let us define momentum = product of mass and velocity. p = m v
Newtons 2nd law:
Rate of change of p is directly proportional to F.
Newton has observed this in experiments from data. He applied same external agent/push/pull on different objects and found that this is so. But he did not know the actual quantity of F in numbers. No one knows yet.
From data he found: (p2 - p1 ) / (t2 - t1) is same on different bodies of different masses.
So F α Δp / Δt F = k Δp / Δt
k is called the constant of proportionality. we have to find what k is.
as Δt -> 0, this becomes F = k dp/dt = k d [m v ] / dt
so F = k m d v / dt so F = k m a as we know a = dv/dt or (v2-v1)/(t2-t1)
Now so far no system exists that tells what F is numerically. For convenience, we can choose k = 1. We can choose k = 10 or 100000 or 3465 also. We can make its units to be cm or sec or kg etc. also. This is because F is not decided yet.
As we choose k = 1 and dimensionless, for making calculations easier,
So F = m a
So units of force is now kg m/sec². ( or gm cm / sec²). we called this as 1 newton.
If k is chosen as 987 volts sec / meter, then unit for force would be
F = 987 volts sec /meter * kg * meter /sec² = 987 volts kg / sec.
If u discovered this formula, you can call that unit for force as 1 Lily = 987 volts kg /sec