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Home » A body is moving unidirectionally under the influence of a source of constant power. Its dis placement in time t is proportional to(i) (ii) (iii) (iv)
A body is moving unidirectionally under the influence of a source of constant power. Its dis placement in time t is proportional to
(i) t^{\frac{1}{2}}
(ii) t^{\frac{3}{2}}
(iii) t^{2}
(iv) t
CBSE | Class 11 | NCERT | Physics | Work, Energy, and Power
A body is moving unidirectionally under the influence of a source of constant power. Its dis placement in time t is proportional to
(i) t^{\frac{1}{2}}
(ii) t^{\frac{3}{2}}
(iii) t^{2}
(iv) t

Power is given by,

P=F V

=\operatorname{mav}=\operatorname{mv} \frac{d v}{d t}

vdv =\frac{k}{m} \mathrm{dt}

On integration, we get,

10

\frac{v^{2}}{2}=\frac{k}{m} d t

\mathrm{v}=\sqrt{\frac{2 k t}{m}}

\mathrm{v}=\frac{d x}{d t}=\sqrt{\frac{2 k}{m}} t^{\frac{1}{2}}

\mathrm{dx}=k^{\prime} \quad t^{\frac{1}{2}} \mathrm{dt}

where k^{\prime}=\sqrt{\frac{2 k}{3}}

\mathrm{x}=\frac{2}{3} k^{\prime} \quad t^{\frac{2}{3}}

As a result, from the above equation we can write x \propto t^{\frac{3}{2}}

i

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