Question

Prove  Force = Mass × Acceleration

Answer 1

F = Mass X Acceleration
Where F directly proportional to rate of change of momentum
F is proportional to (v-u) / t

If we are removing the proportional then there would be a constant added lets assume the constant as K

F=k(v-u/t)

k is constant so k=1
momentum=mv
f=k(-u/t)mv
f=mk(v-u/t)  since v-u/t =a
f=kma where k is constant
f=ma

Answer 2

by newtons 2nd law of motion,
momentum is directly proportional to F
hence dp/dt proportional to F
F=k(dp/dt)
in si unit k=1
F=dp/dt=d(mv)/dt
since m is const.
Hence F=ma