Question

what is newton's second law of motion.? derive its mathematical formula.​

Answer 1

Newton's second law of motion :

The rate of change of momentum is directly proportional to the applied force, and takes place in the direction in which the force acts.

$\implies\sf{ Force \propto\dfrac{Change \: in \: momentum}{Time \: taken} }$

Consider a body of mass m having an initial velocity u.The initial momentum of this body will be mu. Suppose a force F acts on this body for time t and causes the final velocity to become v. The final momentum of this body will be mv.Now the change in momentum of this body is mv - mu and the time taken for this changes t. So,according to Newton's second law of motion :

$\implies\sf{F \propto \dfrac{mv - mu}{t} }$

$\implies \sf{F\propto \dfrac{m(v - u)}{t} }$

$\implies \sf{ F\propto \: m \times a}$

Where k is constant,

$\implies\sf{F = k \times m \times a}$

The value of constant k in SI unit is 1,so the above equation becomes :

$\implies\sf{F = ma} \green\bigstar$

Answer 2

THE RATE OF CHANGE OF MOMENTUM WHICH IS DIRECTLY PROPORTIONAL TO FORCE APPLIED ON THE SYSTEM......

INITIAL MOMENTUM = mu

FINAL MOMENTUM = mv

CHANGE IN MOMENTUM = mv-mu

=m(v-u)

Time taken = t

RATE OF CHANGE OF MOMENTUM = change in momentum /time

=[m(v-u) /t]

hope it will help u.......