...
Definitions
...
of
...
Position
...
and Velocity 
If we start knowing the position vs. time x ( t )
...
,
...
then
...
the
...
velocity,
...
v ( t )
...
,
...
is
...
the
...
derivative
...
of
...
its
...
position,
...
and
...
the
...
derivative
...
in
...
turn
...
of
...
this
...
velocity
...
is
...
the
...
particle's
...
acceleration,
...
a ( t )
...
.
...
The
...
force
...
is
...
the
...
particle's
...
mass
...
times
...
a ( t ).
| Latex |
|---|
{*}. {latex}\begin{large}\[ v = \frac{dx}{dt} \]\end{large} |
| Latex |
|---|
\begin{large}\[ a = \frac{dv}{dt} = \frac{d^{2}x}{dt^{2}}\]\end{large}{latex} |
In
...
fact,
...
as
...
you
...
can
...
see,
...
the
...
velocity
...
and
...
acceleration
...
are
...
defined
...
as
...
derivatives
...
of
...
the
...
position,
...
a
...
fact
...
acknowledged
...
by
...
the
...
phrase
...
"the
...
calculus
...
of
...
motion".
...
Newton
...
had
...
to
...
invent
...
calculus
...
of
...
one
...
variable
...
to
...
deal
...
with
...
motion
...
!
...