Question

The equation of motion of a particle started at $t=0$ is given by $x=10\text{sin}(20t+\frac{\pi }{3})$, where $x$ is in $\text{cm}$ and $t$ is in seconds. Find the time when the particle first comes to rest.

• A. $\frac{\pi }{60}\text{s}$
• B. $\frac{\pi }{120}\text{s}$
• C. $\frac{\pi }{30}\text{s}$
• D. $\frac{5\pi }{3}\text{s}$

Answer 1

The correct option is B $\frac{\pi }{120}\text{s}$

Given, $x=10\text{sin}(20t+\frac{\pi }{3})$
Differentiating on both sides with 't' we get
$v=\frac{dx}{dt}=200\text{cos}(20t+\frac{\pi }{3})$
$v=0$ for the first time when,
$20t+\frac{\pi }{3}=\frac{\pi }{2}$
$\therefore t=\frac{\pi }{120}\text{s}$