Question

Calculate the velocity and acceleration vectors, and speed for
r(t)=⟨cos(4t),cos(t),sin(t)⟩
when t=7π/4.

Answer 1

$v(t)=r'(t)=<-4\sin4t,-\sin t, \cos t >$

$a(t)=v'(t)=r''(t)=<-16\cos 4t,-\cos t,-\sin t>$

Substituting the values we get

$v(t)=<-4.\sin7\pi,-\sin7\pi/4,\cos7\pi/4>=<0,\frac{1}{\sqrt2},\frac{1}{\sqrt2}>$

$a(t)=<-16.\cos7\pi,-\cos7\pi/4,-\sin7\pi/4>=<16,-\frac1{\sqrt2},\frac1{\sqrt2}>$