What does the ration of the net force to the total mass of on object represent?

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Isaac Newton developed his Second Law of Motion by examining the change in an object's momentum over time when a net force is applied.  What he presented was:

 

F = (Pf - Pi)/t  where Pf and Pi are the final and initial momentum respectively.

P = mv and in Newton's initial analysis he kept the mass constant producing

F = (mVf - mVi)/t = m(Vf - Vi)/t

By definition, (Vf - Vi)/t is acceleration, so

F = ma.  Solving this for a gives

a = F/m

Therefore, the ratio of the net force on an object and its mass is the resulting acceleration of the object.

 

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