A body of mass 2 kg, is driven by an engine delivering a constant power $1 \mathrm{~J} / \mathrm{s}$. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) ____.

JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Work, Power & Energy

A body of mass 2 kg, is driven by an engine delivering a constant power

1 J / s

. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) ____.

Answer: 18

Solution

At constant power

P = F v = m v \frac{d v}{d t}

, so

m v d v = P d t

. Integrating from rest,

\frac{m v ^{2}}{2} = P t

, hence

v = \frac{2 P t}{m}

. Writing

v = \frac{d x}{d t}

and integrating again,

x = \frac{2 P}{m} \cdot \frac{2}{3} t^{3/2}

. With

P = 1

m = 2

kg and

t = 9

x = 1 \times \frac{2}{3} \times 27 = 18

JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Numerical answer

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