Have dv/dx need to find dx/dt ? (have velocity w/ respect displace - find Accel?)

Hi all,

I'm trying to figure out this problem related to motion of a spring. I know the solution but I don't know how to make it work.

Thanks in advance (Nod)

I'm given velocity (v) = $\displaystyle \sqrt{25-x^2}$ where 'x' is displacement

Normally velocity is a function of time, so this one has really thrown me.

I want to find a formula for Acceleration $\displaystyle \frac{dv}{dt}$ which would normally be quite easy, but the above formula is Velocity as a function of x.

I've done a bit of related rates & differentiating w/ respect other variables, but I can't figure that out for this one....

If Acceleration = $\displaystyle \frac{dv}{dt}$ = $\displaystyle \frac{dv}{dx}$ x $\displaystyle \frac{dx}{dt}$

and I know $\displaystyle \frac{dv}{dx}$ (by differentiating the provided equation: ---> $\displaystyle \frac{dv}{dx} = \frac{-x}{\sqrt{25-x^2}}$

then how do I find $\displaystyle \frac{dx}{dt}$ please?

(btw, using trial and error on my graphics calculator, I think the Acceleration in this case is actually inverse to the displacement).