var('t')
v = vector([e^t,t^2-1, t+4])
Velocity = diff(v,t)
Acceleration = diff(Velocity,t)
mag = norm(Velocity)
Speed = mag(2)
a=parametric_plot3d(Velocity,(t,-10,10))
veloVector = line([(0,0,0),v(t=2)],color='red',thickness=7)
accelVector = line([v(t=2),Velocity(t=2)],color='green',thickness=7)
posVec = line([v(t=2),Acceleration(t=2)],color='blue',thickness=7)
print("1a)")
print(Velocity)
print("1b)")
print(Acceleration)
print("1e)")
print(Speed)
a = parametric_plot3d(v,(t,0,3))
veloVector+accelVector+posVec+a
__main__:1: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
1a)
(e^t, 2*t, 1)
1b)
(e^t, 2, 0)
1e)
sqrt(e^4 + 17)
