Question

A body starts from orgin and moves along x-axis such that its velocity is $v=(4t^3-2t)$ m/s. Acceleration of particle when it is 2 m from origin is.

• A. $10m/s^2$
• B. $20m/s^2$
• C. $11m/s^2$
• D. $22m/s^2$

Answer 1

The correct option is D $22m/s^2$

$a=\frac{dv}{dt}=12t^2-2$ ...(1)
$v=\frac{dx}{dt}=(4t^3-2t)\Rightarrow {\int }_0^{2}dx={\int }_0^t(4t^3-2t)dt$
$2=t^4-t^2\Rightarrow t^4-t^2-2=0\Rightarrow t^2=2$
$\therefore a=12t^2-2=12\times 2-2=22m/s^2$