JEE Main 2026 — Apr 2, Shift 2 — Physics solution

JEE Main2026Apr 2, Shift 2Physics

The equation of motion of a particle is given by $x = a sin (50 t + π /3)$ 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_____.

A
$\frac{π}{300}$ s, $\frac{π}{75}$ s
B
$\frac{π}{75}$ s, $\frac{π}{300}$ s
C
$\frac{π}{300}$ s, $\frac{π}{25}$ s
D
$\frac{π}{50}$ s, $\frac{π}{100}$ s

Solution

Velocity vanishes when the phase reaches $π /2$ (extreme position). Setting $50 t_{1} + π /3 = π /2$ gives $50 t_{1} = π /6$ , so $t_{1} = \frac{π}{300}$ s.

Acceleration is zero at the mean position, where phase equals $π$ . Setting $50 t_{2} + π /3 = π$ gives $50 t_{2} = 2 π /3$ , so $t_{2} = \frac{2 π}{150} = \frac{π}{75}$ s.

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