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

(i) t^1/2 (ii) t (iii) t^3/2 (iv) t²

The correct answer is (iii).

Explanation:

Power, P = F v = k (constant)

Considering the dimensions,

[P] = [F][v]

⇒ [P] = [MLT^-2][LT^-1]

⇒ [P] = [ML²T^-3]

So, [ML²T^-3] = k

⇒ [L²T^-3] = k

⇒ [L²/T³] = k

⇒ [L²] = k[T³]

⇒ [L²] ∝ [T³]

⇒ [L] ∝ [T^3/2]

Hence, l ∝ t^3/2