**Second law of motion**

Tanusri Gururaj, Academic content writer of Physics at Edumarz

The impact produced by a body is dependent both on velocity and mass.

The formula for momentum is given by:

p = mv

Where p = momentum

v = velocity

m = mass

SI unit of momentum = kg ms-1

Newton’s second law of motion:

The rate of change of momentum of a body is directly proportional to the external force applied.

Derivation of Newton’s second law of motion:

Let us assume that a body is moving with mass ‘m’ and initial velocity ‘u.’

After accelerating the body uniformly in time interval ‘t,’ it now has a velocity ‘v.’

Initial momentum = p1 = mu

Final momentum = p2 = mv

Change in momentum = p2 – p1

Rate of change of momentum = (p2 – p1)/t

But, the rate of change of momentum is directly proportional to the applied force ‘F.’

F ∝ (p2 – p1)/t

F ∝ m(v – u)/t

F = km(v – u)/t

But, (v – u)/t = acceleration ‘a’

F = kma

Where k = constant of proportionality

SI unit of force = Newton or kg ms-2

First law using second law:

According to the second law F = ma or F = m(v – u)/t

So when F = 0, v = u.

This shows that when the external force is zero, the body continues moving with the same initial velocity.

Similarly, if u = 0 then, v will also be zero. Hence, the body remains at rest.