A particle starts moving at t = 0 with its position given by the...

Given the position of the particle as x = 5 \sin \left(20t + \dfrac{\pi}{3}\right).<br><br>The velocity of the particle is the rate of change of position with respect to time:<br><br>v = \dfrac{dx}{dt} = \dfrac{d}{dt} \left[5 \sin \left($20t +$\dfrac{\pi}{3}\right) \right]

$v = 100 \cos \left(20t + \dfrac{\pi}{3}\right)$

The particle comes to rest when its velocity becomes zero. Thus, $v = 0$.

100 \$\cos \left(20t + \dfrac{\pi}{3}\right) =0$<br><br>$\\cos \left(20t + \dfrac{\pi}{3}\right) =0$<br><br>For the first time the particle comes to rest, the phase angle must be equal to$\dfrac{\pi}{2}.$<br><br>$20t + \dfrac{\pi}{3} = \dfrac{\pi}{2}$<br><br>$20t = \dfrac{\pi}{2} - \dfrac{\pi}{3}$<br><br>$20t = \dfrac{\pi}{6}$<br><br>$t = \dfrac{\pi}{120} \text{ s}$