3309.sagews

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(Speed)
a = parametric_plot3d(v,(t,0,3))
veloVector+accelVector+posVec+a

sqrt(e^4 + 17)

var('t')
aVector = vector([t+1,3,3*t])
vVector = integral(aVector,t)
givenVelocity = vector([-2,3,0])
velocityConstants = givenVelocity-vVector(0)
vVector = vVector+velocityConstants
pVector = integral(vVector,t)
givenPosition = vector([0,3,0])
positionConstants = givenPosition - pVector(0)
pVector = pVector + positionConstants
print("2a)")
print(pVector)
print("2b)")
print(vVector)
print("2c)")
print(pVector(2))
print("2d)")
print(vVector(2))
print("2f)")
normal=norm(vVector)
print("2e)")
a = parametric_plot3d(pVector,(t,0,5))
normal(2)
a

2a) (1/6*t^3 + 1/2*t^2 - 2*t, 3/2*t^2 + 3*t + 3, 1/2*t^3) 2b) (1/2*t^2 + t - 2, 3*t + 3, 3/2*t^2) 2c) (-2/3, 15, 4) 2d) (2, 9, 6) 2f) 2e)

var('t')
vVector = vector([cos(2*t),e^t, sin(t)])
origPos = vector([0,1,3])
pVector = integral(vVector,t)
pConstants = origPos-pVector(0)
pVector = pVector+pConstants
print("3a)")
print(pVector(5))
print("3b)")
print(norm(pVector(5)-pVector(0)))
print("3c)")
print(norm((vVector(5)-vVector(0))/5))
aVector = diff(vVector,t)
print("3d)")
print(aVector)

3a) (1/2*sin(10), e^5, -cos(5) + 4) 3b) sqrt((cos(5) - 1)^2 + (e^5 - 1)^2 + 1/4*sin(10)^2) 3c) sqrt(1/25*(cos(10) - 1)^2 + 1/25*(e^5 - 1)^2 + 1/25*sin(5)^2) 3d) (-2*sin(2*t), e^t, cos(t))