HP 10413 Datasheet download pdf (Page 104)

104

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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HP 10413 Datasheet Page 104