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 s, the body has moved a distance (in m)

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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 s, the body has moved a distance (in m)

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answer is 18.

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Detailed Solution

Work=change in KE

$P o w e r T i m e = ∆ K E$

$p t = \frac{1}{2} m v^{2}$

$p = 1 J / st = 9 sm = 2 kg$

$1 \times 9 = \frac{1}{2} \times 2 \times v^{2}$

$V = 3 m / s$

$P = F \times V = m a v$

$P = m \cdot \frac{d v}{d t} v$

$P = m (\frac{d v}{d t}) v = m \frac{d v}{d s} \frac{d s}{d t} v$

$2 v^{2} d v = d s$

$\int_{0}^{3} 2 v^{2} d v = \int_{0}^{s} d s$

$\frac{2}{3} {(V^{2})}_{0}^{3} = s$

$s = 18 m$

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