#### dock

newton the 1st states:

when no force acts upon one object its speed is constant.

this means that at that time (F1,V1)=(0,const).now if this speed drops down to zero the force will rize to some nonzero value and then (F2,V2)=(const,0).the force-speed domain is two-dimensional tush it's a plane.in that plane according to newton 1st there are two events (F1,V1) and (F2,V2) which represent two points on the same plane.two points only define striath line only and the line's equation is:

(F-F1)/(F2-F1)=(V-V1)/(V2-V1)

this equation is the math form of the newton 1st(honestly).if you implement the values of the events above you'll get:

F/[da]F=-(V-V1)V1_________________if x/V=x1/V1=t then

F/[da]F=-(x-x1)/x1________________x1=x2+[da]x and x2=0 => x1=[da]x =>

(F/[da]F)+(x/[da]x)=1_____________F=F1+[da]F and x=x1+[da]x =>

(F1/[da]F)+(x1/[da]x)=-1

F1[da]x+x1[da]F+[da]F[da]x=0______adding F1x1 lefth and right

Fx=(F1+[da]F)(x1+[da]x)=F1x1=const

Fx=Energy=const

CONCLUSION:

NEWTON 1st IS SAME AS CONSERVATION OF ENERGY IN THAT CLOSED SYSTEM.

(dis)agree?

P.S.:i wonder why [da] doesn't draw delta!!