Sliding Down An Inclined Plane

A small mass slides down an inclined plane of inclination θ=60\theta = 60^\circ with respect to the horizontal. The acceleration of the block varies as a=kx2a = k x^{2}, where xx is the distance through which the mass slides down and kk is a constant. The coefficient of friction is 1 when the block covers a distance of 10\sqrt{10}. Find the value of kk.

Details and Assumptions:
Take g=10 m/s2g=10 \text{ m/s}^2.
Every quantity is in SI unit.

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