Newton's Second Law Of Motion And Momentum

Momentum:

"Momentum is simply defined as mass in motion or when a force is applied on an object of mass M then the object changes its position in the direction of force."

➡Momentum = mass X velocity

Newton's second law of motion:

" Newton's second law of motion is defined as the rate of change of momentum is directly proportional to the net force acting on an object and takes place in the direction of net force. "

➡Derivation of F = ma 

Consider an object of mass m having an initial velocity u.

Therefore its initial momentum is p1  = mu 

Let the final velocity of an object is v 

Therefore its final Momentum is p2 = mv 

Change in momentum = p2 - p1

Rate of change of momentum 

= p2 - p1/Δt 

= mv - mu /Δ t

= m(v - u)/Δ t

= mΔv / Δ t 

From Newton's second law of motion,

F  ∝ mΔv/Δt 

Since acceleration a = Δv/Δt 

F ∝ ma 

F = k ma 

When unit of force is considered acting on a unit mass then concept of proportionality K is equals to 1

                   F = ma