A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to (i) t^{\frac{1}{2}}t21 (ii) t^{\frac{3}{2}}t23 (iii) t2 (iv) t
Correct option is C) P=C, where C is constant. P=F×v=m×a×v a=dtdv ∴C=m×dtdv×v ∴C×dt=m×v×dv Integrating both sides, ∫C×dt=∫m×v×dv ∴C×t=m×2v2 ∴v=dtds=(m2×C×t)21 Let, C′=(m2×C)21, where C' is constant. ∴ds=C′×t21×dt Integrating both sides, ∫ds=∫C′×t21×dt s=C′×32×t23 s ∝ t3/2
