The power supplied by a force acting on a particle moving in a straight line is constant. The velocity of the particle varies with the displacement x as

Step-by-step solution

P ⁡ = F v ⁡ = ma v ⁡ = m ⁡ d ⁡ 2 x ⁡ d ⁡ t ⁡ 2 d ⁡ x ⁡ d ⁡ t ⁡ Since, power is constant d ⁡ 2 x ⁡ d ⁡ t ⁡ 2 d ⁡ x ⁡ d ⁡ t ⁡ = k ⁡ or d ⁡ d ⁡ t ⁡ d ⁡ x ⁡ d ⁡ t ⁡ 2 = k ⁡ d ⁡ x ⁡ d ⁡ t ⁡ 2 = k ⁡ 1 t ⁡ d ⁡ x ⁡ d ⁡ t ⁡ = k ⁡ 1 t ⁡ d ⁡ x ⁡ d ⁡ t ⁡ = k ⁡ 2 t ⁡ 1 / 2 ∵ k ⁡ 1 1 / 2 = k ⁡ 2 x ⁡ = k ⁡ 3 t ⁡ 3 / 2 ∵ k ⁡ 3 = 2 3 k ⁡ 2 Hence d ⁡ x ⁡ d ⁡ t ⁡ ∝ t ⁡ 1 / 2 ∝ x ⁡ 1 / 3