Question

derive the mathematical form of second law of motion​

Answer 1

Answer:

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 . ... We know that, Momentum ( P) = mv . Let v be the final and u be the initial velocity .

Explanation:

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Answer 2

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Suppose an object of mass 'm' is moving along a straight line with initial velocity 'u'.It is uniformly accelerated to velocity'v' by the application of a constant force F throughout the time t.Let the initial and final momentum be P1 and P2.

The change in momentum       ∝P2-P1

                                                   ∝mv-mu

                                                   ∝m(v-u)

The rate of change of momentum∝m(v-u)/t

So,

F∝m(v-u)/t

F∝ ma

F= kma       k=constant

but k becomes 1

so, F=ma

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