Given, angle of inclination, θ=30∘. Coefficient of friction µ=
2
3
x, (where x is distance) and final speed, v=0
From given diagram, Net force, ma=mgsinθ−µmgcosθ a=g(sinθ−µcosθ) where, a is acceleration. ∴a=10(sin30∘−
2
3
xcos30∘) a=10(
1
2
−
2
3
x⋅
√3
2
) =10(
1
2
−
1
√3
x) We know that, a=v
dv
dx
⇒vdv=adx . . . (i) where, v is velocity and dv,dx are elemental velocity and displacement, respectively. Now, on integrating Eq. (i) both sides, we get
