Question

how you can show that Newton's third law of motion follows Newton's second law of motion​

Answer 1

Newton's Second Law of Motion states that force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration, i.e. F = m*a. Learn about the Acceleration in detail here.Newton's Third Law of Motion states that for every action there is an equal and opposite reaction.

Answer 2

According to Newton's 2 nd law of motion

Force is the product of mass and acceleration

F = m×a

Also we know acceleration a = {final(v) - initial velocity(u)}/time

And Newton 3rd law of motion states that,to every action there is an equal and opposite reaction.

Thus F₁ = -F₂ ------(A)

From 2nd law of motion we get

F= ma= m(v-u)/t ------(B)

Reducing B in A we get,

m₁(v₁-u₁)/t = -{m₂(v₂-u₂)/t}

m₁v₁ - m₁u₁ =m₂u₂ - m₂v₂

m₁v₁+ m₂v₂ = m₂u₂ + m₁u₁