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(B) Power $P$ is defined as the rate of doing work, given by $P = F \cdot v$.Since $F = m \cdot a = m \frac{dv}{dt}$, we have $P = m \frac{dv}{dt} \cd

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$v \propto t^{\frac{1}{2}}$

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(B) Power $P$ is defined as the rate of doing work, given by $P = F \cdot v$.Since $F = m \cdot a = m \frac{dv}{dt}$, we have $P = m \frac{dv}{dt} \cdot v$.Rearranging the terms, we get $P \cdot dt = m \cdot v \cdot dv$.Integrating both sides, $\int_{0}^{t} P \cdot dt = \int_{0}^{v} m \cdot v \cdot dv$.Since $P$ and $m$ are constant, $P \cdot t = m \cdot \frac{v^2}{2}$.Solving for $v$, we get $v^2 = \frac{2Pt}{m}$, which implies $v = \sqrt{\frac{2P}{m}} \cdot t^{\frac{1}{2}}$.Therefore, $v \propto t^{\frac{1}{2}}$.

An object is moving in a straight line under the influence of a source of constant power. If $v$ and $t$ are velocity and time respectively, then

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