A constant power delivering machine has towed a box, which was initially at rest,
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. $\mathrm{t}$

4. $t^{1 / 2}$

Correct Option: , 2

Solution:

(2)

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

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

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

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

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

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

$\mathrm{x} \propto \mathrm{t}^{3 / 2}$