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.