Question

state Newton's second law of motion and derive it's mathematical formula
i)as compared to mud floor we hurt more if we fall on a cemented floor

Answer 1

NEWTONS SECOND LAW : it states that the rate of change of momentum is directly proportional to external force applied on it..
Derivation:
Consider a body of mass ‘m’ moving with velocity v.

The linear momentum of a body is given by:

p = mv

Now According to Newton’s 2nd Law of Motion:

Force is directly proportional to rate of change of momnetum, that is

F α dp/dt

F  = k dp/dt

F = k d(mv)/dt

F = k md(v)/dt

F = k ma

where k= praporanlity constant
therfore F=ma .
Hence proved..

Answer for the q1,
It pains more when we fall on a cemented floor rather than sand bed, it is due to the particles of sand. ... Therefore the opposite force applied by sand bed is less than the cemented floor. Thats why cemented floor hurt more on falling rather then sand bed.

Answer 2

newtons 2nd law says that force is directly perpotional to rate of change in momentum
f=ma
derivation:
suppose there is a body a mass m and it is on rest with velosity u and travel some distance velosity v
f perpotional mv-mu
______
t
f =km(m-u)
__
t
f=kma(equation of motion)
f=ma(k=1)