Question

The position co-ordinates of a particle moving in a 3-D coordinate system is given by
x = a cos $\omega$ t
y = a sin $\omega$ t
and z = a$\omega$t
The speed of the particle is :

• A. $a\omega$
• B. $\sqrt{3}a\omega$
• C. $\sqrt{2}a\omega$
• D. $2a\omega$

Answer 1

Answer: (C)

$\sqrt{2}a\omega$

$v_x=-a\omega sin\omega t\Rightarrow v_y=a\omega cos\omega t$
$v_z=a\omega$ $\Rightarrow v=\sqrt{v_x^2+v_y^2+v_z^2}$
$v=\sqrt{2}a\omega$