After \(t\) seconds, the acceleration of a particle, which starts from rest and moves in a straight line is \(\left(8-\frac{\mathrm{t}}{5}\right) \mathrm{cm} / \mathrm{s}^2\), then velocity of the particle at the instant, when the acceleration is zero, is

Acceleration \(=\left(8-\frac{\mathrm{t}}{5}\right) \mathrm{cm} / \mathrm{s}^2\)
\(\Rightarrow \frac{\mathrm{dv}}{\mathrm{dt}}=8-\frac{\mathrm{t}}{5}\)
Integrating on both sides, we get
\(v=8 t-\frac{t^2}{10}+c...(i)\)
At \(t=0, v=0\)
\(\begin{array}{ll}
\therefore & 0=8(0)-0+c \Rightarrow c=0 \\
\therefore & v=8 t-\frac{t^2}{10}...ii[From(i)]
\end{array}\)
Acceleration \(=0\)
\(\begin{aligned}
& \Rightarrow \frac{\mathrm{dv}}{\mathrm{dt}}=0 \\
& \Rightarrow 8-\frac{\mathrm{t}}{5}=0 \\
& \Rightarrow \mathrm{t}=40
\end{aligned}\)
Substituting \(\mathrm{t}=40\) in (ii), we get
Velocity \((v)=8(40)-\frac{(40)^2}{10}=160 \mathrm{~cm} / \mathrm{s}\)