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The Parametric aplet can be used to visually display vector motion in one and two dimensions.
Example 1
A particle P is moving in a straight line. Its velocity
v
(in ms
-1
) at any time
t
(in seconds,
t>0
) is given
3
( )
=
2
t
−
5
t
2
+
2
t
−
3
. Illustrate its motion during the first 2.5 seconds.
by
v t
Enter the motion equation from (v) as X(T) and enter
Y(T)=T. The only purpose of this second equation is to
move the particle up the y axis as it traces out its path,
thereby making it easier to view.
Changing to the
NUM
view lets me scroll through the first three seconds
of movement, allowing me to choose a good scale for the x axis.
I’m interested in the first 2½ seconds only, so I’ll also restrict TRng to 0
to 2.5. Using Y(T)=T for this TRng means the y values will also range
from 0 to 2.5. Maximizing visibility of this range of values is the reason
for setting YRng to be –0.5 to 3 in
PLOT SETUP
. The range for the x
axis is chosen from the values shown in the
NUM
view . The value of
TStep is carefully chosen so that when the motion plots, the speed is slow
enough to show its progress.
The graph makes it plain that it doubles back twice in the first two
seconds. The really nice part about this method though is that the motion
can be
seen
on the screen. As the particle slows down near the turning
points it does so on the screen. As it accelerates in the final section you
can see this on the screen too. Obviously this can’t be seen on this page,
and I recommend you try this for yourself.
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