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

(i) $$t^{\dfrac{1}{2}}$$

(ii) $$t^{\dfrac{3}{2}}$$

(iii) t2

(iv) t

Asked by Abhisek | 1 year ago |  72

##### Solution :-

We know that the power is given by:

P = Fv

= mav = mv$$\dfrac{dv}{dt}$$

= k (constant)

vdv = $$\dfrac{k}{m}$$dt

On integration:

$$\dfrac{v^2}{2}​ = \dfrac{k}{m}dt$$

$$v = \sqrt{\dfrac{2kt}{m}}$$

To get the displacement:

v =$$\dfrac{dx}{dt}= \sqrt{\dfrac{2k}{m}}​ t^{\dfrac{1}{2}}​$$

dx = $$k′ t^{\dfrac{1}{2}} dt$$

where $$k′ = \sqrt{\dfrac{2k}{3}}$$

x = $$\dfrac{2}{3}k′ t^{\dfrac{2}{3}}​$$

Hence, from the above equation it is shown that $$x ∝ t^{\dfrac{3}{2}}$$

Answered by Pragya Singh | 1 year ago

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