Q 11-13-043JEE MainJEE Main 2026 (2 Apr, Shift 2)Easy
The equation of motion of a particle is given by $x=a\sin(50t+\pi/3)$ cm. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$. The $t_1$ and $t_2$ respectively are ______.
Answer: (A) $\dfrac{\pi}{300}$ s, $\dfrac{\pi}{75}$ s
The particle is at rest at an extreme position, where the phase is $\pi/2$:
$50t_1+\dfrac\pi3=\dfrac\pi2\Rightarrow t_1=\dfrac{\pi/6}{50}=\dfrac{\pi}{300}$ s
Acceleration is zero at the mean position, where the phase is next $\pi$:
$50t_2+\dfrac\pi3=\pi\Rightarrow t_2=\dfrac{2\pi/3}{50}=\dfrac{\pi}{75}$ s
Solution by Sreeraj P, M.Sc Physics