Question

A particle is moving along x-axis whose instantaneous speed is $v^2=108-9x^2$. The acceleration of particle is

• A. $-9x{\text{m/s}}^2$
• B. $-18x{\text{m/s}}^2$
• C. $\frac{-9x}{2}{\text{m/s}}^2$
• D. None of these

Answer 1

The correct option is A $-9x{\text{m/s}}^2$

We know,
$a=\frac{dv}{dt}$
We can also write it as, $a=\frac{dv}{dx}.\frac{dx}{dt}$
$\Rightarrow a=v.\frac{dv}{dx}........\left(1\right)$

We have,
$v^2=108-9x^2$, differentiating this function with $x$, we get

$2v\frac{dv}{dx}=-18x$, using equation $\left(1\right)$.
$\Rightarrow a=-9xm/s^2$