Question

explain newton’s second law of motion. also derive the relationship between the force applied and the acceleration produced in the body.

Answer 1

Newton’s second law;

Newton’s second law of motion states that the rate of change of momentum of an object is Proportional to the applied unbalanced force in the direction of force.

Prooving--

Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time t.

The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively.   
The change in momentum =  p2 – p1 
Then
change in momentum = mv – mu 
The change in momentum = m × (v – u). 
The rate of change of momentum = m × (v – u)/t    
the applied force,  F ∝ m × (v – u)/t   
F = km × (v – u)/t   = kma     --------------- (i)   

*Here a = [ (v – u)/t ] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality.

* The SI unit of force is kg m s-2 or newton, represented as N.

I hope helps you