Question

The equation of motion of a particle started at $t=0$ is given by $x=5\sin (20t+\frac{\pi }{3})$, where $x$ is in cm and $t$ in sec. When does the particle first have maximum speed?

Answer 1

$X=5\sin (20t+\frac{\pi }{3})$
$v=\frac{dx}{dt}=100\cos (20t+\frac{\pi }{3})$
$a=\frac{dv}{dt}=-2000\sin (20t+\frac{\pi }{3})$
v=0 for the first time when,
$20t+\frac{\pi }{3}=\frac{\pi }{2}$
$\therefore$ $t=\frac{\pi }{120}$ s