 # State Newton's second law of motion and shown that the first law of motion can be mathematically started from the Newton's seconds law.

Newton’s second law of motion can be stated as the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v.Here we see that, the initial momentum

p1 = m × u

the final momentum

p2 = m × v

The change in momentum is

p2 – p1 = (m × v) – (m × u)

p2 – p1 = m (v – u)

The rate of change of momentum with respect to time is proportional to the applied force. The applied force is

F ∝ m (v – u)/t

or

F ∝ m × a

a = Rate of change of velocity/Time

F = k × m × a

k = proportionality constant.

Hence from the second law of motion, we get force is the product of mass and acceleration i.e F = ma.