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(B) Power $P$ is constant, so $P = F \cdot V = 	ext{constant}$.Since $F = m \cdot a = m \frac{dV}{dt}$, we have $m \frac{dV}{dt} \cdot V = 	ext{cons

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$t^{3/2}$

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(B) Power $P$ is constant, so $P = F \cdot V = 	ext{constant}$.Since $F = m \cdot a = m \frac{dV}{dt}$, we have $m \frac{dV}{dt} \cdot V = 	ext{constant}$.This implies $V \frac{dV}{dt} \propto 1$, which integrates to $\frac{V^2}{2} \propto t$, or $V^2 \propto t$.Therefore, $V \propto t^{1/2}$.Since $V = \frac{dx}{dt}$, we have $\frac{dx}{dt} \propto t^{1/2}$.Integrating both sides with respect to time $t$, we get $x \propto \int t^{1/2} dt$.Thus, $x \propto t^{3/2}$.

$A$ constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time $t$ is proportional to

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