Question

The displacement of the particle (in $m$) is given by

$y=2t+t^2-2t^3$

What is the velocity (in $m/s$) of the particle at the instant when its acceleration is zero?

• A. $\frac{13}{6}$
• B. $\frac{6}{13}$
• C. $\frac{5}{2}$
• D. $\frac{2}{5}$

Answer 1

The correct option is A $\frac{13}{6}$

$y=2t+t^2-2t^3$
$\mathrm{Velocity,\; v}=\frac{dy}{dt}=2+2t-6t^2$
$\mathrm{Acceleration,\; a}=\frac{dv}{dt}=2-12t$
Now acceleration is zero
$2-12t=0t=\frac{1}{6}s$
Putting this value in velocity equation
$v=2+\frac{2}{6}-6{\left(\frac{1}{6}\right)}^{2}v=2+\frac{1}{3}-\frac{1}{6}=\frac{13}{6}m/s$