Question

The velocity of a particle moving on the $x$-axis is given by $v=x^{2}+x$, where $v$ is in $m / s$ and $x$ is in $m$. Find its acceleration (in $m / s ^{2}$ ) when passing through the point $x=2 \,m$.

Answer 1

$v=x^{2}+x $
$\Rightarrow \frac{d v}{d t}=2 x \frac{d x}{d t}+\frac{d x}{d t}$
$\Rightarrow a=(2 x+1) v$
$=(2 x+1)\left(x^{2}+x\right)$
$\therefore $ When $x=2 m$,
$ a=(2 \times 2+1)\left(2^{2}+2\right)$
$=5 \times 6=30\, m / s ^{2}$