A body starts from origin and moves along $x$-axis such that at any instant velocity is $v_{t} = 4t^{3} - 2t$ where $t$ is in second and $v_{t}$ in $ms^{- 1}$. The acceleration of the particle when it is 2m from the origin is

Question

Dr. Abubacker · Accepted Answer

(b) $v_{t} = 4t^{3} - 2t$
$\Rightarrow \ \frac{dx_{t}}{dt} = 4t^{3} - 2t$
$\Rightarrow \int_{}^{}{dx_{t} = \int_{}^{}\begin{array}{r}
4t^{3}dt - \int_{}^{}{2tdt} \
\ 
\end{array}}$
$\Rightarrow \ x_{t} = t^{4} - t^{2}$
Since, $x_{t} = 2$m
$t = \sqrt{2}$s (rejecting negative time)
Now acceleration,
$a_{t} = \frac{dv_{t}}{dt} = 12t^{2} - 2 = 12(2) - 2 = 22ms^{- 2}$

Q. A body starts from origin and moves along $x$-axis such that at any instant velocity is $v_{t} = 4t^{3} - 2t$ where $t$ is in second and $v_{t}$ in $ms^{- 1}$. The acceleration of the particle when it is 2m from the origin is

Explanation

Reviewed by Dr. Abubacker

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