# Sliding Down An Inclined Plane

A small mass slides down an inclined plane of inclination $$\theta = 60^\circ$$ with respect to the horizontal. The acceleration of the block varies as $$a = k x^{2}$$, where $$x$$ is the distance through which the mass slides down and $$k$$ is a constant. The coefficient of friction is 1 when the block covers a distance of $$\sqrt{10}$$. Find the value of $$k$$.

Details and Assumptions:
Take $$g=10 \text{ m/s}^2$$.
Every quantity is in SI unit.

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