Question

Define the force state newton second law of motion ans derive

Answer 1

According to the Newton's 2ndLaw of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of force. It means that the linear momentum will change faster when a bigger force is applied.

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

Experimentally k =1

F = k ma

Which is the required equation of force.

Answer 2

Hey Chika ❤

Here's ur answer-

$\underline{second \: law \: of \: motion}$

It states that the rate of change of momentum of a body is directly proportional to the applied force, and the best place in the direction in which the force acts.
$force \: = \: mass \times acceleration \\ or \\ f \: = \: m \times a$
________________________

✴ Consider a body of mass 'm' having an initial velocity 'u'.
✴The initial momentum of the body will be 'mu'
-----------------
✴ Suppose a force 'F' acts on this body for time 't' and causes final velocity to become 'v'.
✴The final momentum of this body will be 'mv'.

Now, Change in momentum of this body is (mv-mu) and the time taken for this change is 't' .

So, according to Newton's second law of motion:-
(in the attachment 1)

But [(v-u)/t ] represents change in velocity with time which is known as acceleration 'a'.
So we write 'a' instead [(v-u)/t ] in the attachment 1. and we get,
(check in the attachment 2)

Thus, the force acting on a body is directly proportional to the product of mass and acceleration.

Which gives:-
$f = m \times a$
The Newton's second law of motion gives us a relationship between Force and acceleration.

Hope it helps ✔