Question

first law of motion and it derivation

Answer 1

hey

Newton's first law states that a body stays at rest if it is at rest and moves with a constant velocity unit if a net force is applied on it. Newton's second law states that the net force applied on the body is equal to the rate of change in its momentum.

F = ma

or F = m(v-u) / t

or Ft = mv - mu

That is, when F = 0, v = u for whatever time, t is taken. This means that the object will continue moving with uniform velocity, u throughout the time, t. If u is zero than v will also be zero, i.e., object will remain at rest.

Answer 2

According to the Newton's 2nd Law 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. ... So we can state the first law: A body will remain at rest or constant velocity unless a force in acted upon it.

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.

NEWTON'S FIRST LAW

The body moves (accelerates) when a force is applied to it that is 

F = ma --> a = F / m 

When there is no force acting on the body (F = 0), then the body won't move or would remain in motion with constant velocity (won't accelerate in both cases: a = 0), why? Because 

a = F / m and F =0 --> a = 0 

So we can state the first law: A body will remain at rest or constant velocity unless a force in acted upon it.