Question

A particle is executing the motion $ x=a\,\cos (\omega t-\theta ). $ The velocity of the particle is:

• A. $ a\omega \cos \theta $
• B. $ a\omega $
• C. $ a\omega \sin \theta $
• D. none of these

Answer 1

Answer: (B)

Given equation is $x=a \cos (\omega t-\theta)$
So, velocity $\left|\frac{d x}{d t}\right|=a \omega \sin (\omega t-\theta)$
At $(\omega t-\theta)=90^{\circ}$,
the velocity will be maximum,
therefore the maximum velocity is
$v=\alpha\, \omega$