Newton's second law with equation

Newton's second Law of Motion states that The rate of change of momentum is directly proportional to the force applied in the direction of force.

Let mass of an moving object = m.

Let the velocity of the object changes from 'u'

; to 'v' in the interval of time 't'

This means,
Initial velocity of the object = u

.Final velocity of the object = v

.We know that momentum (p) = Mass x velocity

Therefore,
Momentum (p) of the object at its initial velocity u=m×u=mu

Momentum (p) of the object at its final velocity v=m×v=mv
The change in momentum =mv−mu
Rate of change of momentum =(mv−mu)/t-----(i)
According to the Newton’s Second Law of motion force is directly proportional to the rate of change of momentum.

This means, Force ∝ Rate of change of momentum

After substituting the value of rate of change of momentum from equation (i) we get.

Force (F) ∝mv−mu/t

⇒F∝m(v−u)/t
⇒F∝m v−u/t
⇒F∝ma
[∵ acceleration (a)=v−ut]
[Since, acceleration is the rate of change in velocity]
⇒F=k⋅m⋅a ----(ii)

Where k

is the proportionality constant

∵ 1 unit force is defined as the mass of 1kg object produces the acceleration of 1m/s2
∴ 1 unit of force =k×1kg×1m/s²

∴ by putting the value of k=1 in equation (ii)
F=m⋅a ----(iii)

⇒ Force = mass x acceleration

Thus Newton’s Second Law of Motion gives the relation between force, mass and acceleration of an object.