Chapter 16: Some Important Examples and a Formulation in Physics

Introduction

Newton's Laws state that the motion of an object with mass
$m$
and coordinate
$x$
can be described by the equation
$\stackrel{\u27f6}{F}=m\stackrel{\u27f6}{a}$
, where
$\stackrel{\uf577}{a}$
, the acceleration of the object is the second derivative of its position
$x$
with respect to the variable time,
$t$
and
$\stackrel{\u27f6}{F}$
is the force experienced by the object.
Single objects move in three dimensional space, in which force, position and acceleration are vectors. There are some simple essentially one dimensional examples that are so fundamental as to be of general importance. We consider two of these.
We also consider an important alternate formulation of
$\stackrel{\u27f6}{F}=m\stackrel{\u27f6}{a}$
.