3310.sagews

var('t')
s=vector([e^t,t^2-1,t+4])
v=diff(s,t)
print"problem 1a:", v
a=diff(v,t)
print"problem 1b:",a
b=parametric_plot3d(s,(t,-10,10),thickness=5)
c=parametric_plot3d(v,(t,-10,10),thickness=5,color='yellow')
d=parametric_plot3d(a,(t,-10,10),thickness=5,color='red')
f=v(t=2)
print"problem 1e:",f
b+c+d

problem 1a: (e^t, 2*t, 1) problem 1b: (e^t, 2, 0) problem 1e: (e^2, 4, 1)

var('t')
a=vector([t+1,3,3*t])
v=integral(a,t)
p=integral(v,t)
vel=vector([1/2*t^2 + t-2, 3*t+3, 3/2*t^2])
pos=vector([1/6*t^3 + 1/2*t^2, 3/2*t^2+3, 1/2*t^3]) 
print "problem 2a:",vel
print "problem 2b:",pos
y=pos(t=2)
print "problem 2c:",y
z=vel(t=2)
print "problem 2d:",z
b=vector([abs(1/2*t^2 + t-2),abs(3*t+3),abs( 3/2*t^2)])
c=sqrt(2^2+9^2+6^2)
print "problem 2f:",c

problem 2a: (1/2*t^2 + t - 2, 3*t + 3, 3/2*t^2) problem 2b: (1/6*t^3 + 1/2*t^2, 3/2*t^2 + 3, 1/2*t^3) problem 2c: (10/3, 9, 4) problem 2d: (2, 9, 6) problem 2f: 11