a smal mass slides dwn an inclined plane of inclination @.th coef of friction varies as k=k1x.whr x is th distance through wch block slides down.then the distance covered by mass before it stops is??

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net force on the mass = mgsin@ - friction force

                           ma = mgsin@ - kmgcos@

                             a = g(sin@-kcos@)      or

                                =g(sin@-k₁xcos@)       .........1

                     a = dv/dt

                    adx = dv(dx/dt)

                    adx = vdv          .................2

from 1 & 2

            g(sin@-k₁xcos@)dx = vdv

           g(sin@x - k₁cos@(x²/2)) = 0          

               x = 2tan@/k₁