How newton's first law can be derived from Newton's second law?

Answer 1

From's Newton's second law of motion:

F=ma

or, F=m(v-u)/t

or, F=(mv - mu)/t

or,Ft=mv - mu

where F=force, m=mass, v=Initial Velocity, v=Final Velocity, t=time

The above equation could be called Newton's first law of motion when u=v and F=0. So it could be concluded that a body of mass m would continue in a state of uniform motion(i.e it would move with Initial Velocity u) over a time t seconds

such that no external force acts on it(as F=0). When the body is at rest(i.e when u=v=0) then also it would remain at rest over a time t.
By second law of motion, F is directly proportional to m, the mass and acceleration "a".

F = k .m .a

where k is the constant of proportionality.

a = F / k .m.

when a = 0,

F = 0 as m cannot be infinite.

hence, if a body is at rest or in uniform motion, a = 0. thus the body remains in its state of rest or uniform motion.

which is the first law.

Answer 2

Newton's 1st Law: If F = 0 then object is at rest or in a uniform rectilinear motion.

Newton's 2nd Law: F = ma.

Starting from Newton's second Law: F = ma, if F = 0 then a = 0 then v = constant. then the object is either at rest (v = 0 = constant) or in a uniform rectilinear motion (v=constant).

This is what is widespread, but wait...

Newton is not stupid! If his First Law could be derived from his second law, so why he stated it as separate law?!

There is a common misconception about Newton's first law. The correct statement of Newton's first law is:

"In the absence of forces, it is possible to specify a frame of reference where the object is either at rest, or in a uniform rectilinear motion. This frame of reference is called inertial frame of reference".

Notice that! Newton's first law central point is to define inertial frame of reference, and guarantee that such frame exists.

Absolutely, There is no way to derive this from newton's second law.

Hope you best times.

You may contact me at: vina.vinarue.rue@gmail.com

Newton's 1st Law is derived from the 2nd Law F=ma, by setting F to zero, 0=ma,

thus a=o/m or no force, no acceleration.

Answer 3

Newtons 2nd law is F=ma.

as a= dv/dt

thus F=m dv/dt

F=d/dt(mv)

as you know p=mv

thus F=d/dt(p)=dp/dt

F= dp/dt

thus newton's 2nd law can be stated as "the rate of change of momentum (dp/dt)of a body is equal to the resultant force on the body and is in the same direction as the resultant force.

if F=0 then dp/dt=0

and if m=0 then a=0

which implies that if force is equal to zero than rate of change of momentum is equal to zero.if it concern to constant mass,then acceleration is equal to zero which is newton 1st law which states that"any body constitute it states of rest or uniform motion in straight line unless a resultant force acts on it to cause it to accelerate".

Answer 4

If you think about the first law(law of inertia), it says that an object at rest wants to stay at rest and an object in motion wants to stay in motion.

Ex: if a skinny guy gets pushed a big guy compared to a big guy pushing a small guy one would think that the big guy would be more likely to stay in one spot while the skinny guy woul be more likely to move.

So basicly, the bigger the mass and the more the acceleration, the more force that will come from it, and vice versa.

Which is basically the second law. The relatinonship between force and its two vectors(determining factors), force and acceleration

Newtons first law is that a force is required to move an object. His second Law defines the magnitude of that force relative to the object to be moved.

Answer 5

By newton s second law, F=ma;

now suppose that net force acting on the body is zero , so that F=0;

so, 0=ma;

so either m=0 or a=0.As mass m can never be zero. so acceleration a=0;

i.e if F=0, then a=0. This is Newton s first law of motion , if net force acting on a body is zero, it continues in its state of rest or uniform motion (which means that its acceleration is zero)

Answer 6

2nd law f=ma, force on a mass creates an acceleration of the mass and conversely no force on the mass indicates no acceleration of the mass or constant velocity. Constant velocity includes the constant zero velocity or rest or no motion.

Thus the 2nd law f=ma ia also a=f/m =0/m = 0, the 1st law, no force no change in motion.

Answer 7

Set force to zero.

Newton's first law states that an object in motion will stay in motion and an object at rest will stay at rest unless acted upon by another force. Newton's second law says that Force = mass times acceleration (F=ma). If we set F equal to 0, and mass is greater than 0, then acceleration must be 0, telling us from the second law that an object will not accelerate if no force is applied. An object must accelerate to start moving from rest, or to change it's speed while moving.

Answer 8

Force = mass x acceleration; acceleration = force / mass. If force is zero, then obviously, acceleration will also be zero.