The equation of motion of a particle started at t = 0, is given by $y=5\sin \left(40t+\frac{\pi }{6}\right)cm$.  The least time after which acceleration becomes maximum is

The least time at which acceleration is maximum can be obtained using the  relation  $a=-{\omega }^{2}y$ 
. $$\begin{gathered} acceleration is maximum when given \sin e function is maximum \\ {a}_{max}=-{\omega }^2{\left(y\right)}_{max} \Rightarrow \sin \left(40t+\frac{\pi }{6}\right)=maximum=\sin \frac{\pi }{2} \\ \left(40t+\frac{\pi }{6}\right)=\frac{\pi }{2} \\ \Rightarrow t=\frac{\pi }{120}second= least time after which acceleration becomes maximum \end{gathered}$$ .