Question

The magnitude of the acceleration of a particle which moves along the curve x=2 sin ¡3t,y=2 cos ¡3t and z=8t at any time t>0 is

Answer 1

$a=\sqrt{(\ddot{x})^2+(\ddot{y})^2+(\ddot{z})^2}\\ \ddot{z} = 0\\ \dot{x}=6a\cos(3at)\\ \ddot{x} = -18a^2\sin(3at)\\ \dot{y}=-6a\sin(3at)\\ \ddot{y}=-18a^2\cos(3at)\\ a=\sqrt{18^2 \sin^2(3at)+18^2\cos^2(3at)}=18\sqrt{2}$