## الجمعة، 31 أكتوبر، 2014

### Position, Velocity and Speed

The motion of a  particle  is  completely known if  the  particle’s  position  in  space  is
known at all times.  A  particle’s  position is  the  location  of the  particle  with respect  to a
chosen reference point that we can consider to be the origin of a coordinate system.
Consider a  car  moving back and  forth  along  the  x axis  as in Figure 2.1a. When  we
begin  collecting  position  data, the  car  is  30m to the  right  of a  road sign, which  we will
use  to identify  the  reference  position  x = 0. (Let us assume that  all data in this  example  are  known to two  significant  figures. To  convey this  information,  we should report
the  initial  position  as 3.0 * 10 m. We  have written this  value  in the  simpler  form  30m
to make the  discussion  easier  to follow .)  We  will  use  the  particle  model by identifying
some  point  on the  car,  perhaps the  front  door handle,  as a  particle  representing  the
entire car.
We  start our  clock  and  once ever y  10s  note the  car’ s  position  relative  to the  sign at
x=0. As you  can  see  from  Table  2.1,  the  car  moves  to  the  right  (which  we have
defined  as the  positive  direction)  during the  first  10s  of motion, from  position  to
position .  After ,  the  position  values  begin  to decrease, suggesting  that  the  car  is
backing  up from  position  through  position  .  In fact, at ,  30s  after we start mea-suring, the  car  is  alongside  the  road sign (see Figure 2.1a)  that  we are  using  to mark
our  origin  of coordinates.  It  continues  moving to the  left  and  is  more than 50m to the
left  of the  sign when we stop recording  information  after our  sixth data point.  A  graph-ical  representation  of this  information  is  presented  in Figure 2.1b. Such a  plot  is  called
a  position–time graph.
Given  the  data in Table 2.1,  we can  easily  determine  the  change  in position  of the
car  for  various time intervals. The displacement of a  particle  is  defined  as its  change
in position  in some  time interval.  As it  moves  from  an initial  position  xi to a  final  posi-tion
Xf ,  the  displacement of the  particle  is  given  by We  use  the  Greek  letter
delta ()  to denote the  change in a  quantity.  Therefore,  we write the  displacement, or
change in position, of the  particle as