The equation of a particle executing simple harmonic motion is given by $x =\sin \pi\left( t +\frac{1}{3}\right) m$. At $t =1 \,s$, the speed of particle will be .......... $cm s ^{-1}$ (Given : $\pi=3.14$ )
JEE MAIN 2022, Medium
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$x =\sin \pi\left( t +\frac{1}{3}\right)$
$x =\sin \left(\pi t +\frac{\pi}{3}\right)$
$V =\frac{ dx }{ dt }=\cos \left(\pi t +\frac{\pi}{3}\right) \pi$
$=-\pi \times \frac{1}{2}=157 \,cm / s$
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