Question

Starting from origin, a body moves along $x$ -axis. Its velocity at any time is given by $v=4t^3-2tm/s$
Acceleration of the particle when it is $2m$ away from the origin is

• A. $28m{s}^{-2}$
• B. $12m{s}^{-2}$
• C. $22m{s}^{-2}$
• D. $14m{s}^{-2}$

Answer 1

Answer: (C)

The velocity at any time
$v=4t^2-2t$

$v=\frac{dx}{dt}=4t^2-2t$
$\Rightarrow x=\frac{4t^4}{4}-\frac{2t^2}{2}$
$\Rightarrow t^4-t^2=2$
$\Rightarrow t^4-t^2-2=0[\because x=2]$
$\Rightarrow t^2=\frac{1\pm \sqrt{1+8}}{2}=\frac{1\pm 3}{2}$
$t=\sqrt{2}s$
Now, $a=\frac{dv}{dt}=12t^2-2$
At $t=2s$, accelaration of the particle
$a{|}_{ort=\sqrt{2}}^{x=2}=12\times 2-2$
$=22m/s^2$