A body is moving down a long inclined plane of angle of inclination θ. The coefficient of friction between the body and the plane varies as μ = 0.5 x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by

The acceleration of the body down the plane is gsin⁡θ−μgcos⁡θ=g(sin⁡θ−μcos⁡θ)=g(sin⁡θ-0.5xcos⁡θ). Therefore, the body will first accelerate up to x < 2 tan θ. The velocity will be maximum at x = 2 tan θ, because for x > 2 tan θ, the body starts decelerating. Hence, the correct choice is (a).