Question

how to derive the second law of motion

Answer 1

Answer:

the second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

Answer 2

                  Second Law of Motion

According to second law of motion the rate of change of momentum of a body is directly proposnal to the force applied.

                                      Derivation

$Force\propto\dfrac{Change\:in\:Momentum}{Time\:Taken}$

Change in Momentum = P₁ = mu

                                        p₂ = mv

∴ Change in Momentum =  P₂ - P₁

$=F\propto\dfrac{mv-mu}{t}\\\\=F\propto\dfrac{m(v-u)}{t}\\\\We\:know\:that\:\dfrac{v-u}{t}=a\\\\\therefore F\propto ma\\\\\Rightarrow F=Kma\\\\K\:is\:constent\:proportion\:and\:its\:\\\\value\:is\:1.\\\\\therefore F=ma$