Newton's second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force and the motion of the change must take place in the same direction of the force.
Mathematically,
F=K(mv-mu)/t where K is the constant of proportionality and it is enperimetaly proven to be 1
mu = initial momentum
mv=final momentum
⇒ F=( mv-mu)/t by factorization,
F= m( v-u)/t but v-u/t = a
⇒ F = ma
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