Computer Algebra Recipes

3.1. FIRST-ORDER MODELS 117
Evil Knievel's velocity is plotted over the time interval t = 0 to 10 time units,
labels being added to the graph.
> plot(Vel,t=0..10,labels=["t","Vel"],tickmarks=[3,3]);
0.3
Vel
0.2
0.1
0
2 4 6 8 10
t
Figure 3.3: Evil Knievel's velocity pro¯le.
The resulting picture is shown in Figure 3.3, the velocity curve increasing from
zero to a maximum and then decreasing to zero again as t !1.
The distance traveled in the time interval t = 0 to 10 is equal to the area
under the velocity curve between these limits, this area obtained by performing
the integration R 10
Vel dt. However, if the integer 10 is used, the integral will
0
not be evaluated. A °oating-point answer could be obtained by apply the evalf
command. An alternative way used here in Professor Nerd's answer key is to
enter the upper limit as 10.0, which forces a °oating-point evaluation of the
integral. It does not imply any increase in accuracy.
> distance:=int(Vel,t=0..10.0); #note floating point number
distance := 0:9943356328
So, Evil Knievel travels just under 1 Erehwonian spatial unit in the time interval.
PROBLEMS:
Problem 3-5: Direct solution
Solve Professor Nerd's problem directly with the dsolve command and check
that the answer is identical to that derived in the text recipe.
Problem 3-6: Di®erent drive force
The drive force in the text recipe is replaced with Fdrive =sin(t) t2 e ¡t . Determine
the velocity as a function of time and plot the result over the interval
t = 0 to 10. What is Evil Knievel's maximum velocity and at what time does
this occur? What is his maximum displacement from the origin in this interval
and at what time does this occur?