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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 by
3 2
() 2 5 2 3vt t t t
−+−.
Illustrate its motion during the first 2.5 seconds.
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, but I recommend you try this for yourself.
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