Question

state Newton's second law of motion derive mathematical form of Newton's second law of motion​

Answer 1

Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system. Force applied is directly proportional to the product of mass and acceleration . ... Here, K is the proportionality constant.

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Answer 2

Newton's seconf law of motion :

The rate of change of momentum of a moving object is directly proportional / is equalto the the force applied.

Derivation :

F∝(dp/dt)−>Eq.1

since p=(m∗v)

=> dp=(m∗dv)−>Eq.2

replacing dp in Eq.1 from Eq.2

F∝(m∗dv)/dt=m∗(dv/dt)

Acceleration : Rate of change of velocity per unit time = (dv/dt)

F ∝m∗a

replacing proportionality using constant K

F=K∗m∗a

Experiments tells us that the value of constant is 1; Thus

F=ma

Hence proved

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