Calculate the velocity and acceleration vectors, and speed for r(t)=⟨cos(6t),sin(t),sin(6t)⟩ when t=5π/6 .

Answer 1

r(t)=⟨cos(6t),sin(t),sin(6t)⟩
v = r' = <-6sin(6t),cos(t),6cos(6t)>
a = r" = <-36cos(6t),-sin(t),-36sin(6t)>
Now just plug in t=5π/6 (6t=5π)
and recall that speed is |v|

Answer 2

10 miles per hour south