The acceleration of the disc along the plane is determined by the projection of the force of gravity on this plane F_x=mg\\sin{\\alpha} and the friction force fr=kmg\\cos{\\alpha} . In our case k=\ an{\\alpha} and therefore fr=F_x=mg\\sin{\\alpha} Let us find the projection of the acceleration on the direction of the tangent to the trajectory and on the x-axis mw_t=F_x\\cos{\\varphi}-fr=mg\\sin{\\alpha}(\\cos{\\varphi}-1) mw_x=F_x-fr\\cos{\\varphi}=mg\\sin{\\alpha}(1-\\cos{\\varphi}) It is seen from this that w_t=-w_x , which means that the velocity v and its projection v_x differ only by a constant value C which does not change with time, i.e. v=v_x+C ,Where v_x=v\\cos{\\varphi} . The constant C is found from the initial condition v=v_0 , whence C=v_0 since \\displaystyle\\varphi=frac{\\pi}{2} initially. Finally we obtain \\displaystyle v=\\frac{v_0}{1+\\cos{\\varphi}} In the course of time \\varphi\\rightarrow0 and \\displaystyle v\\rightarrow\\frac{v_0}{2} . (Motion then is unaccelerated.)