A Body Is Moving Unidirectionally Under The Influence Of A Source Of Constant Power. Its Displacement In Time T Is Proportional To

P = C, where C is constant.

\( P = F * v = m * a * v \) \( a = \frac{dv}{dt} \) \( C = m * \frac{dv}{dt} * v \)

Therefore, \( C * dt = m * v * dv \)

Now taking Integrating both sides,

\( \int C * dt = \int m * v * dv \)

Therefore, \( C * t = m * \frac{v^{2}}{2} \) \( \Rightarrow v = \frac{ds}{dt} = (\frac{2 * C * t}{3})^\frac{1}{2} \) \( Let, {C}’ = (\frac{2 * C}{3})^\frac{1}{2} \)

where C’ is constant.

Therefore, \( ds = {C}’ * t^\frac{1}{2} * dt \)

Now taking Integrating both sides,

\( \int ds = \int {C}’ * t^\frac{1}{2} * dt \) \( \Rightarrow s = {C}’ * \frac{2}{3} * t^\frac{3}{2} \) \( \Rightarrow S \propto t^\frac{3}{2} \)

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