x(t)=asin(ωt):y(t)=acos(ωt);z(t)=bt i have to find the velocity, the acceleration and then their absolute values

Question

x(t)=asin(ωt):y(t)=acos(ωt);z(t)=bt i have to find the velocity, the acceleration and then their absolute values. I did not understand how I can calculate the absolute value.

Answer 1

By definition of velocity: $$\nu = (a\omega\cos(\omega t), -a\omega\sin(\omega t), b) \Longrightarrow |\nu| = \sqrt{a^2\omega^2+b^2}$$ By definition of acceleration: $$\alpha = (-a\omega^2\sin(\omega t), -a\omega^2\cos(\omega t), 0) \Longrightarrow |\alpha| = |a|\omega^2$$