A constant power delivering machine has towed a box,
Question:

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 :-

  1. $t^{2 / 3}$

  2. $\mathrm{t}^{3 / 2}$

  3. $t$

  4. $\mathrm{t}^{1 / 2}$


Correct Option: , 2

Solution:

$\mathrm{P}=\mathrm{C}$

$\mathrm{FV}=\mathrm{C}$

$\mathrm{M} \frac{\mathrm{dV}}{\mathrm{dt}} \mathrm{V}=\mathrm{C}$

$\frac{V^{2}}{2} \propto t$

$V \propto t^{1 / 2}$

$\frac{\mathrm{dx}}{\mathrm{dt}} \propto \mathrm{t}^{1 / 2}$

$x$ of $\left\lfloor^{3 / 2}\right.$

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