Question

prove f=m a
$f=m a$

Answer 1

Now According to Newton’s 2nd Law of Motion:
F α dp/dt

F  = k dp/dt

F = k d(mv)/dt

F = k md(v)/dt

F = k ma

Experimentally k =1

F = k ma

Which is the required equation of force.

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Answer 2

initial momentum= mu
final momentum=mv
change in momentum=mv-mu
rate of change in momentum=mv-mu/t

according to second law of motion
F <mv-mu/t (<= DIRECTLY PROPORTIONAL)
F <m (v-u)/t
F <ma
F=kma (k=constant)
F=ma

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