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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 gsinθμgcosθ=g(sinθμcosθ)=g(sinθ-0.5xcosθ).

 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).

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