Hi,

The proof for F=ma is as follows:

According to Newton's second law of motion, force is equal to rate of change of momentum,

so, consider a mass m, moving with the initial velocity u,and after a certain time t, the velocity changes to v.

So, initial momentum, p ₁ = m × u

final momentum,p ₂ = m × v

Rate of change of momentum will be,

p ₂ – p ₁ = (m × v) – (m × u)

p ₂ – p ₁ = m (v – u)

We know that rate of change of momentum is directly proportional to force,

F ∝ [m (v – u)]/t

F ∝ m × a  [v-u/t=a]

Therefore, we get F=kma where k=1

thus F=ma

I hope this helped you.