Q: A body of mass 2 kg is driven by an engine delivering a constant Power of 1 J/s . The body starts from rest and moves in a straight line . After 9 sec , the body has moved a distance (in m) …..

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$\displaystyle P \times t = W = \Delta K$

$\displaystyle P \times t = \frac{1}{2} m v^2$

$\displaystyle 1 \times t = \frac{1}{2} (2) v^2$

$\displaystyle t = v^2 $

$\displaystyle v = \sqrt{t} $

$\displaystyle \frac{ds}{dt} = \sqrt{t} $

$\displaystyle \int_{0}^{s}ds = \int_{0}^{9} \sqrt{t} dt $

$\displaystyle s = [\frac{t^{3/2}}{3/2}]_{0}^{9}$

$\displaystyle s = \frac{2}{3} \times 27 = 18 m$