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).