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A block of mass $2 \mathrm{~kg}$ is initially at rest on a horizontal frictionless surface. A horizontal force $\overrightarrow{\mathbf{F}}=\left(9-x^2\right) \hat{\mathbf{i}}$ newtons acts on it, when the block is at $x=0$. The maximum kinetic energy of the block between $x=0$ and $x=3 \mathrm{~m}$ in joule is
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$18$
$\begin{aligned} & \mathrm{KE}=\int F d x \\ & \qquad \begin{aligned} \mathrm{KE} & =\int_{x=0}^{x=3}\left(9-x^2\right) d x \\ & =9 \int_{x=0}^{x=3} d x-\int_{x=0}^{x=3} x^2 d x \\ & =9[x]_0^3-\left[\frac{x^3}{3}\right]_0^3=27-9=18 \mathrm{~J} .\end{aligned}\end{aligned}$
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