Question

Derive first and third laws of Newton from 2nd Law​

Answer 1

Newtons 2nd law states that , the rate of change of momentum is proportional to force .

Δp= mΔv [mass is constant for any body , hence if momentum changes then v must change ]

Δp = m (v - u ) [ here v is final velocity and u is initial velocity ]

now rate of Δp = m (v-u)/t = ma [°•° a = v-u/t ]

•°• rate of Δp = F [°•° F = ma ]

now at rest F = 0 N

then , Δp = 0 => mv= 0 •°• m=0[not possible] ; v=0

if v = 0 then body is at rest ..

hence , if force is not applied for a body in rest it will b in rest

now in motion F= x N

then , then , Δp =x => mv= x •°• m = y [suppose ] and v = β [suppose]

if v = β then body is at motion

this proves newtons 1st law which states that if a body is in state of rest it will b in rest unless any ext force is applied and if a body is in state of motion it will retain its state unless application of any ext force takes place .. ..