Acceleration as a function of distance to Velocity?

[Berdi]

Homework Statement

A block of mass m lies on a rough surface, inclined at an angle $$\theta$$ to the horizontal. It is attached to a spring of force constant k; the other end of the spring is fixed to point on the table below the block. The coefficient of static friction between the block and the surface of the table is $$\mu$$ _s and the coefficient of kinetic friction is $$\mu$$_k< $$\mu$$_s
(the friction between the spring and the table is negligible).

There are a lots of parts to this question, but I'll post the relevant parts for the time being:

($$l$$ is $$mg/k$$)

i)Find the initial acceleration of the block;
ii)Show that the acceleration is zero when the spring is compressed by $$l(sin\theta +\mu_{k}cos\theta)$$
iii) Find the speed v₀ at this point

Is where I get stuck.

Homework Equations

I have found the inital acceleration to be given by $$a = k\Delta x/m -gsin\theta - \mu_{k}gcos\theta$$

where $$\Delta x$$ is the compression of the spring.

And I believe this to be correct as part ii) works out.

The Attempt at a Solution

I understand that the velocity would be the integral of the acceleration, but I'm confused due to the acceleration equation I have doesn't seem to involve time, so I'm not sure how to begin integrating it.

 

[Doc Al]

Rather than try to integrate the acceleration equation, use energy conservation.

 

[Berdi]

Okay, I'll give that a try. Thanks!