Sure, here's the translation to English:

We are considering a particle that follows the path described by the parametrization: x(t)=5cos(t)cos(t),x(t)=5cos(t)cos(t), y(t)=5sin(t)cos(t),y(t)=5sin(t)cos(t), z(t)=8sin(2t),z(t)=8sin(2t), where t>0t>0 is the time. What is the first positive time such that the velocity and acceleration vectors are perpendicular to each other? The answer should be an exact real number.

Comment: If the length of the velocity vector is not constant, this time will correspond to the first critical point of v(t)v(t). This is, of course, not coincidental, and it holds generally.