Question

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

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

Answer 1

The correct option is B $-18xm{s}^{-2}$

$v^2=108-9x^2$

$2v\frac{dv}{dx}=-18x$

As we know $a=\frac{dv}{dx}\frac{dx}{dx}=\frac{dv}{dx}\frac{dx}{dt}=v\frac{dv}{dx}$

So, $a=-18xm/s^2$.