Question

The displacement of the particle is given by $x=2t^3-6t$ in $\text{m}$. The acceleration of the particle at $2\text{sec}$ is

• A. $36m/s^2$
• B. $24m/s^2$
• C. $12m/s^2$
• D. $20m/s^2$

Answer 1

The correct option is B $24m/s^2$

As we know that the acceleration of the particle is given by
$a=\frac{dv}{dt}$ and also, $v=\frac{dx}{dt}$
Given, $x=2t^3-6t$
So, $v=\frac{dx}{dt}=\frac{d(2t^3-6t)}{dt}$
$\Rightarrow v=6t^2-6$
also, $a=\frac{dv}{dt}=\frac{d(6t^2-6)}{dt}=12t$
Thus, the acceleration of the particle is $12\times 2=24m/s^2$