Question

A body is moving unidirectional under the influence of a source of constant power. Its displacement in time t is proportional to??

Answer 1

As power, P = force × velocity

P = [MLT-2] [LT-1] = [ML2T-3]

As, P = [ML2T-3]

= constant

∴ L2T-3 = constant

or, L2/T3 = constant

∴ L2 ∝ T3

or, L ∝ T3/2

Answer 2

Answer:

ANSWER

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′×t2