Question

derive f=ma and expain newton second law

Answer 1

Newton's 2nd law of motion : 
The law states that the rate of change of momentum of a body is proportonal to the Force 
producing it and takes place in the direction in which the force acts. 
Momentum of a body = P = mass* velocity = mV (Vector quantity) ; V = Velocity
Let m = mass of the body 
Initial velocity = u ; initial momentum = mu (Vector) 
Final velocity = v ; final velocity = mv (vector) 
Time interval = t 
Change in velocity = m(v - u) (vector) 
Rate of change of momementum = m(v - u) / t = m{(v- u)/t} = ma (vector) ; a = acceleration (vector) 

Answer 2

second law of newton : the rate of change of momentum of a body is directly proportional to the net force acting on it and it take place in the direction of net force

according to newton's second law
appiled force= f
mass=m 
intial velocity =u 
final velocity= v
time= t
intial momentum (p) =mu 
final momentum (p) =mv
change in momentum (delta P) =mv-mu
rate of change in momentum = (delta p/t) 
=mv-mu/t
m(v-u)/t
=ma(∴a=v-u/t)
=according to 2nd law 
f alfa ma 
=f=kma
where k= proportional constant 
k=1 
f=1×ma
=f=ma