A particle $$\(P\)$$ of mass $$\(0.4 \mathrm{~kg}\)$$ is on a rough horizontal floor. The coefficient of friction between $$\(P\)$$ and the floor is $$\(\mu\)$$. A force of magnitude $$\(3 \mathrm{~N}\)$$ is applied to $$\(P\)$$ upwards at an angle $$\(\alpha\)$$ above the horizontal, where $$\(\tan \alpha=\frac{3}{4}\)$$. The particle is initially at rest and accelerates at $$\(2 \mathrm{~m} \mathrm{~s}^{-2}\)$$. Find the time it takes for $$\(P\)$$ to travel a distance of $$\(1.44 \mathrm{~m}\)$$ from its starting point. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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